# Physics 13 Using Rollers

Remember a simple machine doesn’t change the amount of work you do. You will still move an object the same distance. What a simple machine does is make that work take less effort. Are rollers a simple machine? What are rollers anyway?

These are not the kind girls use to curl their hair.

Question: How do rollers work?

Materials:

Book

String (scissors to cut it)

Rubber band

Six or seven round pencils

Procedure:

Wrap the string one and a half times around the book

I used a smaller book. The book could be twice as thick and this project will still work.

Cut off the piece of string

Tie a loop in one end of the string

The loop can be an inch or a little more long. If it is less than half an inch, it will be harder to attach it to the rubber band.

Put the other end of the string through the rubber band and the loop

The end of the string goes through the rubber band first and then the string loop.

Pull the string tight

The string loop must be pulled tightly to the rubber band so it will not slip pulling the book later.

Tie the string around the book

The string should be tied around the middle of the book so it will pull evenly across the table.

Use the rubber band to pull the book across the table

Set the book back at the beginning

The pencils should be fairly evenly placed so the book can move from one to the next without falling off.

Space out the pencils so three will be under the book and the others in front of it

Set the book on the last three pencils

Use the rubber band to pull the book across the pencils

Observations:

Describe how the rubber band behaves as you pull the book on the table

Pulling the book across the table creates friction for the entire surface. Friction makes the book harder to pull.

Describe how it feels pulling the book on the table

Describe how the rubber band behaves as you pull the book across the pencils

Describe how it feels pulling the book across the pencils

Conclusions:

Assuming you pulled the book the same distance both times, did you do the same amount of work? Why do you think so?

Was it easier to pull the book on the table or on the pencils?

The pencils roll as the book is pulled over them making the name rollers apt.

What did the pencils do under the book as it went over the top of them?

Why would the pencils be called rollers?

Can you think of another name for a roller? What is it?

What I Found Out:

My book had a slick book cover on it so it pulled across the table easily. The rubber band stretches out at first then sprang back once the book started moving. The book dragged a little on the table.

The rubber band barely stretched before the book started pulling over the pencils. It moved very fast over the pencils. The book didn’t drag at all.

The pencils do roll but some roll better than others. They are not attached to the book so they bunch up losing their spacing.

Since work is the distance times the mass, I did the same amount of work. The mass of the book and the distance did not change with and without the pencils.

What did change is how easy it was to pull the book over the pencils. The pencils turned and rolled under the book.

The pencils could be called rollers because that is what they did: rolled. Something else that rolls is a wheel.

# Physics 12 Double Levers

Scissors are so useful. They are one of several common double levers.

Take a look at a pair of scissors. Each blade moves like a lever: one end goes down pushing the other end up.

Where is the fulcrum on a pair of scissors? Remember the lever turns on the fulcrum which remains in place. On double levers the fulcrum is where the two levers cross each other and are fastened together.

I forgot to take a picture of my scissors. You know what they look like, don’t you? These are double levers. Do you see where the fulcrum is?

Get a piece of cardboard and a pair of scissors. Where should you put the cardboard to cut it the easiest? Close to the fulcrum or far away?

Let’s review how a fulcrum increases force. Get a 200 page book and 2 pencils. Prop the book on the end of one pencil. Put the second pencil crosswise under the first pencil to act as a fulcrum. Try lifting the book with the second pencil away from the book and near the book. Which placement makes lifting the book the easiest?

Should the cardboard be near the fulcrum of the scissors or farther away? Double check by trying to snip the cardboard from both positions.

Pliers are a useful tool around the house. They can be used for gripping things or turning tight small lids. Do you see the two levers?

Another of the common double levers is a pair of pliers. Perhaps you have one to look at. Where is the fulcrum? Why are the handles for your hand to grip longer than the gripping ends of the levers?

Tin snips are used to cut sheet metal, flat plates of metal. The length of the handles can vary. As the handles get longer, will the snips part get more powerful?

On the farm I have another of the double levers. It’s called tin snips. These are used to cut sheets of metal such as metal roofing. If you don’t know anyone with a pair of these, you can look at the picture. Find the fulcrum. Like the pliers, one end of the levers is longer than the other.

Perhaps you can find some other double levers around your house. How do you recognize them?

What I Found Out:

The book lifted the easiest when the fulcrum pencil was close to the book. In the same way, putting the cardboard close to the fulcrum made cutting it much easier.

On both the pliers and the tin snips like with the scissors the fulcrum is where the two levers cross and has the bolt connecting the two.

Double levers are easy to recognize because they have two long pieces crossing each other and joined where they cross. That join is the fulcrum. Others I found included pruners for trimming plants, loppers for cutting brush and bolt cutters for cutting thick wires up to 1/2 inch thick.

# Physics 11 Mass a Coin With Levers

Last Project we found out we could balance a heavy object with a light one by moving a lever over the fulcrum. Can we do this to mass a coin?

Question: Can a lever be used to mass a coin?

Materials:

Piece of thin cardboard 3 cm x 28 cm

Dime

Balance

Metric ruler

Table

Procedure:

Mark a line 2 cm from one edge of the cardboard piece

Label the line R

The real purpose of the R line is to mark one end of the lever to tell the ends apart. It marks a good place to set the coin.

Place the cardboard piece on the edge of the table

Slide the piece over the edge of the table until it balances on the edge

As the cardboard lever moves out over the edge of the table, the end begins to rise. Take care it does not rise too far or the lever will slip to the floor.

Mark this point and draw a line across it

Label the line E

Measure the distance from line R to line E to the nearest mm

Mass the cardboard piece

Remember that a lever balances when the mass is equal on each side of the fulcrum.

Set the cardboard piece on the edge of the table

Set the dime centered on the line labeled R

Slide the cardboard piece over the edge until it balances on the edge

Mark this point and draw a line across it

Label this line 1

Measure the distance from the R side of the cardboard to line 1 in to the nearest mm

Mass the dime

Observations:

Mass of:

Cardboard:

Dime:

Distance:

R to E line:

Line 1:

Analysis:

Divide the line R distance by the line 1 distance for a mechanical advantage for the dime

Line 1 is where the lever balances with a dime on the R line. Go a millimeter too far and the dime slides down flipping the lever onto the floor.

Multiply this mechanical advantage by the mass of the cardboard to get a mass for the dime

Conclusions:

How important is balancing the cardboard to mass a coin?

How important is it to measure accurately?

Where is the fulcrum for your lever in this Project?

A lever has two arms. What were the two arms for the lever in this Project?

Do you think a lever is a good way to mass a coin? why do you think this?

What I Found Out:

Balancing a piece of cardboard on the edge of a table is harder than it sounds. I slid the cardboard piece out until it seemed balanced. When I moved toward my camera, it slid onto the floor. I started over again.

Since the distances are being measured to the millimeter and one of these is small, It’s important to get as close to the final balancing point as possible. Any breeze makes this impossible.

I used a regular ruler with centimeters and millimeters on one side and inches on the other. It helps that the 0 line for the centimeters is not on the edge of the ruler. This makes it easier to get an accurate starting place. If the 0 line was the edge of the ruler, I would have started on the 1 cm line and deducted the 1 from the reading. one reading did come out between two millimeter lines. I used the closest line for the distance.

It takes care to keep the lever perpendicular to the table edge. You have to tap it lightly in the center, not on a corner to move it slightly until it balances.

I again had the lever slide to the floor with the dime on it. When I balanced the lever, the line R distance was 9.5 cm and the line 1 distance was 18.5 cm. The mechanical advantage was 0.51. Multiplying this by 3.5 g gave a coin mass of 1.9 g for the dime. My dime had a mass of 2.3 g on the scale. The two masses were close.

The edge of the table was the fulcrum. The R line marked one arm of the lever. The E line marked the other arm of the lever.

I don’t think this is a very good way to mass a coin. Finding the true balancing point is difficult. A regular ruler is not very accurate for measuring. There are too many places where errors can creep in.

# Physics 10 Exploring Levers

The Greek Archimedes once said that given a fulcrum and a lever, he could move the world. Levers are another simple machine. What is it and how does it work?

Question: How do levers work?

Materials:

Wood slat 40 cm long by 5 cm wide

Triangular or 1” wood block [I found the 1” block works best.]

Several weights, 2 the same, 1 heavier, 1 lighter

Scale

Ruler

Pencil

Procedure:

Place the block on a table

The slat is not exactly level. This shows as my measurement of each end gave two slightly different values.

Place the wood slat on the block moving it back and forth until it balances

Note: The slat is your lever

Mark the balancing point

Measure from the end of the slat to the line from both ends

Mass your weights unless they are from a weight set so you know the masses

Keeping the balancing point over the fulcrum, place a mass at one end of the slat

Placing a mass on one end causes that end to drop to the table while the other end rises.

Observe what the lever does

Place the identical weights, one at each end

Adjust the slat until it is again in balance

Take one weight off

Place the light weight on the other end of the slat

A teeter totter on a playground behaves this way when a heavier person sits down on one end. How can this person make it balance so both people have fun?

Move the slat back and forth until it balances

Measure the distance from the balance point over the fulcrum to each weight

Remove the weights

Return the slat to the original balancing line

Place the heaviest weight on one end of the slat and a lighter weight on the other end

Predict how you will need to move the slat to balance the two masses

Move the slat until the two are in balance

Observations:

Mass of weights

Distances:

From ends to balancing line

From masses to balancing line

Same mass weights

Mass and light mass

Mass and heavy mass

Describe what happens:

When you balance the slat

When one mass is put on one end of the slat

When the two identical weights are on the slat

When the light weight is put on one end

When the light weight is balanced

When the heavy weight is put on the slat

Prediction of where the slat will balance

When the heavy weight is balanced

Analysis:

Multiply the mass times the distance for the two identical masses

Multiply the mass and distance for the mass and the light mass

If you consider the formula of Fd = Fd it explains why a heavy mass is at a short distance to balance with a light mass.

Multiply the mass and distance for the mass and the heavy mass

Conclusions:

Compare the lengths when the salt is balanced.

If you could mass each end of the slat, how do you think these would compare?

Draw the lever, fulcrum and one mass

Put arrows to show where the forces are acting on the lever system

The mass exerts mass downward on one end of the lever. That puts an equal upward force under the other end. The force vectors are equal and opposite so the center, on the fulcrum, has no net force acting on it.

Why does the slat balance at the same place when two equal masses are balanced?

How does the mass x distance results compare for the two identical masses?

How do these results compare for the light weight and the heavy weight?

A rule for levers is that the force times the distance for one arm or side equals the force times the distance for the other arm or side. Do you think this is correct? Why do you think this?

How can this be used to move a heavy object?

What I Found Out:

I tried using a triangular fulcrum. The slat would balance on the edge but it was very difficult to do this. It worked much better to use the 1” board piece as a fulcrum. I did have to watch that the slat was level as it would balance a little before it was really level.

I was in a hurry. I hope you take your time. My lever is not quite balanced between the 20 g and 50 g masses. You can tell because the slat is not level.

When I balanced the slat on its own, the ends measured 37.0 cm and 38.7 cm. This was nearly equal. The two ends would have the same mass as the slat would be divided in half.

The mass pushes down on the lever so it sinks to the table top. That means a force is pushing up the other end.

When I put masses of equal mass on the ends of the slat, the force pushing on each end was the same, the total mass of each end remained the same so it would balance at the same place as it did without the masses.

The balancing point puts equal mass on each side of the fulcrum. since the masses are equal, the rest of the set up is equal.

My two equal masses gave 740 g-cm and 772 g-cm. When I looked at the pictures of this, the slat wasn’t completely level so the two were probably even closer in size.

When I balanced the lighter mass, the slat moved the heavier mass closer to the fulcrum. The distances were 30.0 cm for the 50 g mass and 43.0 cm for the lighter20 g one. This gave the Fd values as 150 g-cm and 91.2 g-cm. The distances for the 500 g mass was 13.0 cm and 62.6 cm for the 50 g mass. The Fd values were 6500 g-cm and 3030 g-cm.

The Fd values for my experiment weren’t very close. This is the rule a lever normally follows so I need to look over my Procedure and Observations more closely.

The idea of a simple machine is to do the same amount of work using less effort. A lever would do this if the distance to the heavy object was short and the distance to where the force is applied is long. A long distance times a small effort will equal and larger effort over a short distance.

# Physics 9 Simple Machine Called Wedge

Perhaps you have learned to sew on a button. Take a close look at the sewing needle. One end is a point. The needle gets thicker the farther up the needle you go. This is one kind of wedge.

A yarn needle for sewing with yarn is large so it’s easy to see the pointed end and how the needle thickens going away from that end.

Find a door stop, one of the brown rubber kind that is pushed under a door to keep it open. Look at it from the side. It has a point and gets thicker farther from the point. this is another kind of wedge.

Maybe you know someone who carves wood. Ask to see a flat chisel. Look at it closely top and from the side. It starts at a broad point and gets thicker as you go away from the point. A chisel is a wedge.

Look at a wood chisel. Is it a wedge?

Question: How does a wedge work?

Materials:

Sewing needle

Piece of cloth

Procedure:

Look at the piece of cloth observing the thread pattern

Hold the piece of cloth

Push the needle through the cloth

Observe what the cloth does

Observations:

Describe and draw part of the piece of cloth

Describe how the cloth threads change as you push the needle through

From the side it’s easy to see a wood chisel has a point at the end the slopes up from there.

Special Section on Wedges:

Look at the pictures of a splitting maul. Does it look like the other wedges? Why do you think so?

A splitting maul has a typical wedge shape. The end comes to a broad point. The maul gets thicker going away from the point. Unlike the chisel this wedge goes out in two directions. The needle goes out evenly all around. All have a point.

Splitting mauls are used to split firewood. Usually the maul is swung down so the head hits the piece of wood. This is repeated as the crack in the wood widens until the piece splits into two pieces.

For this I used the maul as though it did not have a handle to show how the maul splits the wood. First I tapped the maul until it stood up in a piece of wood.

Even tapping the splitting maul enough so it will stand up creates a crack in the piece of wood.

Then I hit the top of the maul with a sledge hammer. This applies force to the top of the maul. Where does this force go?

The maul goes down into the piece of wood so some of the force pushes the maul downward.

The crack in the wood gets wider. Does some of the force go sideways? Why do you think so?

As the splitting maul goes further into the wood, the split gets wider. This crack follows the grain in the wood going to the center of the piece then splitting into two paths.

Conclusions:

When you push on a needle, you are applying force. Where does that force go?

How is a wedge like an inclined plane?

How is a wedge different from an inclined plane?

What I Found Out:

My piece of cloth had threads running up and down and other threads going across. The threads went over and under each other. They were tight so the threads did not shift.

When I pushed the needle through the cloth, the point went through between the threads and pushed them apart. After the needle went through the cloth, the threads tried to go back into place but left a small hole where the needle had been.

The splitting maul has a broad point and gets thicker going away from the point. It is a wedge.

The force goes into the maul. Part of the force goes down and pushes the maul further into the wood.

Part of the force pushes the wood apart. There must be force pushing the wood apart. The only place any force is being applied is on the top of the maul. Some of it pushed the wood apart.

An inclined plane has a broad point at one end and gets thicker going away from that point.

An inclined plane sits still. Objects are pushed or pulled up the ramp.

Force is applied to a wedge. That force pushed the wedge forward and pushes outwards to push things apart.

# Physics 8 Exploring How Screws work

What do a pencil sharpener, a screw, a scissor jack and an inclined plane have in common? Find yourself several different kinds of screws and take a look.

Common screws have one of two heads. The top one is a straight slot and takes a regular screwdriver. The bottom one has a cross slot and takes a Philips screwdriver.

Note: The raised metal going around a screw is called a thread. The top is called the head. Some screws have slots on their heads and take straight screwdrivers. Some have crossing slots and require a Philip’s screwdriver.

Question: How do screws work?

Material:

Several different screws, same diameter but different threads

Screwdrivers for the screws

Block of wood with drilled holes the size of the screws in it

Ruler

Procedure:

Examine one of the screws closely to see how the threads are arranged

Hold a screw between your finger and thumb turning it with the other hand

The screw turns into the wood a tiny bit then the head cuts into my fingers as I try to turn it a little more and can’t make it budge.

Put the end of the screw in a hole in the board and try to turn the screw several turns using your fingers then use a screwdriver.

Take that screw out of the hole

Find two screws with different threads, one with threads far apart and one with threads close together

Start these two screws in the board until they stand up by themselves

The head is shaped like a wood screw’s head so this screw is used for wood. Fine threads are often used for fine work such as furniture.

Measure the height of the two screws

Turn each screw two complete revolutions

This was the longest screw as well as the one with the finest threads. If you measure from one thread down two, this should be the same as the amount turning the screw twice will put it into the wood. For this screw that was 0.2 cm.

Measure the height of the two screws

Observations:

How are the threads arranged on the screw?

How does it feel to turn a screw with your fingers?

How does it feel to turn a screw into the wood?

How it feels to turn a screw with a screwdriver

This is a wood screw with definite threads not too far apart but not real close together either. The top will fit into the wood so it won’t catch on anything rubbed over the wood later.

Height of the screws:

beginning

ending

At first glance this screw went in the farthest but it was the shortest so it really only went in 0.4 cm in two full turns.

beginning

ending

Conclusions:

If you could unwrap the threads on a screw, what simple machine would they become? Why do you think so?

Why do we use a screwdriver to put in a screw?

Compare how fast a screw with wide threads goes in to one with narrow threads.

Looking at the three screws it is easy to see the right one has fine threads and the left on has coarse threads. The middle one is in between the other two.

What I Found Out

When I held a screw and turned it, it crawled up between my fingers. It felt like my fingers were sliding up the threads.

Of course I can’t really take the threads off. But if I could, the thread would become a slanted line and be like an inclined plane from the bottom to the top of the screw. I think that because the thread is a continuous line going up the shaft.

This is a deck screw. It has widely spaced threads to make it easy to put it into coarse wood. The top is angled to fit into the wood smoothly so the deck surface will be smooth.

Trying to put a screw into a hole in the wood using fingers does not work. The very tip will go in but then the fingers can’t turn it anymore. A screwdriver gives more power to my hand and makes the threads go into the wood.

After two full turns the coarsely threaded screw was only 1.5 cm high. It went in 0.6 cm.

My screw with fine threads started at 2.6 cm and ended at 2.3 cm so it went in .3 cm. The medium threads started at 1.7 cm and ended at 1.3 cm going in .4 cm. The coarse threads started at 2.1 cm and ended at 1.5 cm going in .6 cm.

The reason for using a simple or complex machine to do work is to use less effort or force to do the same amount of work. How much force a machine will save is its mechanical advantage.

Question: What is the mechanical advantage of an inclined plane?

Materials:

2 boards, one twice as long as the other

stack of thick books, at least four 5 cm or more thick

spring scales

Procedure:

Set up the stack of four books

Measure the height of two, three and four book stacks

Lift your block using the spring scale to the top of the stack

The blocks are being lifted to the top of the book pile. No matter how the blocks get there, this is the work being done. Lifting a heavy weight is easier using a ramp. Mechanical advantage determines how well the ramp works.

Record the force needed

Measure the length of the two boards

Set up one board as an inclined plane to the top of the stack of four books

Pull the block up the ramp recording the force needed

Pulling a weight up a ramp takes less effort than lifting the weight straight up. How efficient is the ramp?

Remove one book from the stack

Pull the block up the ramp recording the force needed

Remove another book from the stack

Pull the block up the ramp recording the force needed

Replace the ramp with the other board

Pull the block up this ramp recording the force needed

Add a book to the pile

Pull the block up the ramp recording the force needed

Add the last book to the pile

Pull the block up the ramp recording the force needed

Analysis:

Calculate the work done lifting the block up the height of two, three and four books using the formula W = Fd.

The short ramp is much steeper and takes more effort. It is also shorter. Is it more efficient? Is its mechanical advantage greater?

Calculate the mechanical advantage of the inclined planes using the formula M.A. = R/E where R is the force needed to lift the block up the pile of books and E is the effort or force needed to pull the block up the ramp.

Another way to calculate the M.A. of an inclined plane is to divide the length of the plane by the height it goes to. Use these measurements to calculate the M.A. of your ramps.

Conclusions:

The scale reading when you lifted the block up is the mass of the block, the force needed to lift it and the resistance for calculating mechanical advantage. How can it be all three?

How do the M.A. you calculated using R/E and using L/H compare? Should they be the same? If yours are not, why not?

The shorter the height and/or the longer the ramp, the less effort is needed to get the blocks up onto the books. Do these increase mechanical advantage of the ramp?

Does a short or a long inclined plane have more mechanical advantage?

Does the height of the ramp end matter for the mechanical advantage?

The total amount of work done by each ramp for each pile of books was the same. What was not the same?

The work done is the same so, why use a ramp? How do you get the most mechanical advantage out of a ramp?

What I Found Out:

My scale read 200 g lifting the block up the pile of books.  Two books were 14.5 cm high making the work done 2900 g-cm. Three books were 21.5 cm tall making the work done 4300 g-cm. The tallest pile of four books was 29 cm high making the work done 5800 g-cm.

The mass of the block is the pull of gravity on it. Lifting the block requires enough force to counter gravity, equal to the mass. Since gravity is pulling on the block, it is resisting being moved by the mass amount making the force needed to lift the block equal to the resistance from gravity which is the mass of the block.

The two boards I used were 74 cm and 105 cm long.

My long board was 1.5 cm thick so I added that to the height of the stacks. The short board was .5 cm thick.

For the short ramp the force needed was 100 g [2 books], 130 g [3 books] and 150 g [4 books]. For the long ramp the force needed was 80 g [2 books], 110 g  [3 books] and 130 g [4 books].

Using the first formula the mechanical advantage for the long ramp was 2.5 [2 books], 1.8 [3 books] and 1.5 [4 books]. For the short ramp the mechanical advantage was 2 [2 books], 1.5 [3 books] and 1.3 [4 books].

Using the second formula the mechanical advantage for the long ramp was 6.6 [2 books], 4.6 [3 books] and 3.4 [4 books]. For the short ramp the values were 4.9 [2 books], 3.7 [3 books] and 2.5 [4 books].

My calculated mechanical advantages by the different formulas were very different. I had expected them to be similar. Perhaps my measurements were not as accurate as they should have been.

The special formula for calculating mechanical advantage for an inclined plane is the second one so I would prefer using those values. Another reason I would favor those is that my spring scales are not easy to read and inaccurate whereas my meter stick and rulers are easy to read and much more accurate.

Both ways indicate the longer ramp has a greater mechanical advantage. This value went down as the height the ramp went to became greater.

In all cases, the height of the book pile was the same for the 2, 3 and 4 books. The amount of work done was the same. What really changed was the distance the blocks had to be moved to get to the top of the book piles.

# Physics 6 Meet the Inclined Plane

You are going to visit a friend and run up to the porch. How are you going to get onto the porch? You can jump up or you can walk up the steps.

Jumping up may be more fun. Walking up takes less effort. Those stairs are one kind of inclined plane.

Hailyann Workman’s help was greatly appreciated on this project. She seemed to think this was fun to do.

Question: How does an inclined plane work?

Materials:

3 Boards or pieces of stiff cardboard 10 cm wide and 0.5 m, 1 m and 1.5 m long

3 Bricks or 3 books about 5 cm thick

Spring scales

Meter stick

Block with loop

Procedure:

Set up the pile of books

Measure the height of the pile of books

Stand the block next to the pile of books

Use a spring scale to lift the block onto the books recording the force in grams

Remove the block

Measure the length of the boards

A short ramp is steep. Since work is force times distance, the longer distance makes the amount of work much higher.

Lean the short board on the pile of books to form an inclined plane or ramp

Set the block just on the edge of the board

Use the spring scale to pull the block up onto the books recording the force needed

Repeat this for each of the other boards

Observations:

Height of book pile:

Length of short board:

Length of medium board:

Length of long board:

Force needed:

To lift the block

Short board

Medium board

Long board

Analysis:

Calculate the work needed to get the blocks onto the books by multiplying the force on the scale times the height of the books. This is W = Fd or Work = Force times distance.

Using a simple machine is supposed to reduce the force needed to get the same amount of work done. Now that we know how much total work is needed, we can calculate the force needed for each of the inclined planes by rearranging the formula so W/d = F or work divided by distance equals force.

Calculate the force needed for each inclined plane.

Go back to the Procedure to complete the Project

Conclusions:

Compare the force you measured for each inclined plane with the force you calculated.

Compare the force needed for each ramp with the force needed for the others and to the force needed to lift the blocks.

A longer ramp has less of a slope making it easier to pull the blocks up.

What happens to the distance you must pull the block to use less force?

Would it be better to lift or use a ramp for a lightweight object? Why do you think so?

Would it be better to lift or use a ramp for a heavyweight object? Why do you think so?

What is the advantage of using a ramp?

What I Found Out:

This week I found Hailyann Workman to help me do this project. She is five and in kindergarten. She thought pulling the blocks up a ramp fun to do.

My stack of books was 15 cm tall. The scale registered 200 g lifting the blocks up. The work done was 3000 g-cm.

The short ramp was 44.5 cm long. The scale showed 150 g needed to pull the blocks up the ramp. I calculated 67.4 g-cm.

Next the blocks went up a 74 cm ramp using 100 g of force. I calculated needing 40.5 g-cm.

Remember finding out about friction last week? My long ramp was rough making lots of friction. Covering the ramp with paper made it smooth.

The long ramp was 109 cm and rough. It was hard to pull the blocks up so I taped paper onto the ramp to make it smooth. The blocks pulled up easily with 70 g of force needed. My calculated amount was 27.5 g-cm.

My measured forces were much higher than my calculated forces. Perhaps I misread the scale. My block was smooth but not slick. My ramps were not slick so there was friction.

The needed force did decrease as the ramp got longer. The medium ramp took half the force of lifting the blocks.

The distance increases as the force needed decreases.

A lightweight object can be lifted up to move it the shortest distance. A heavyweight object should be moved up a ramp. This takes more distance but requires less force and is easier on you than lifting something heavy.

A ramp is a way to decrease the force needed to move an object even though it increases the distance needed to move it.

# Physics 5 Exploring Friction

Rub your hands past each other once. What do you feel?

My hands feel rough against each other. I can feel friction between them.

Now rub your hands back and forth a dozen times or so. What happens?

My hands warm up. I use this when my hands get cold in the winter.

Friction makes the heat. It does other things too.

Question: How does friction work?

Materials:

Smooth block of wood like a couple of inches of a 2 x 4

2 Pieces of Sandpaper

Tape

Smooth board about 0.5 m long

Meter stick

Procedure:

Rub the block of wood on your hand

Describe how it feels

Rub the piece of sandpaper on your hand

Describe how it feels

Push the block of wood down the smooth board

Describe how it feels

Set the block of wood on one end of the board

Lift that end of the board until the block slides down the board

It didn’t take long for the block to slide down the varnished board. The two smooth surfaces had little friction between them.

Measure how high you lifted the board

Tape the sandpaper rough side out on the block

The sandpaper on the block felt very rough especially compared to the smooth sanded block surface.

Push the block on the board

Describe how it feels

Set the block on one end of the board

Lift that end of the board until the block slides down the board

Measure how high you lifted the board

Tape a piece of sandpaper on the long board

I had a long piece of sandpaper used on a belt sander so it covered the length of the board.

Push the block on the long board

Describe how it feels

How high do you think you will have to lift the board this time?

Set the block on one end of the board

Lift the end of the board until the block slides down the board

Measure how high you lifted the board

Observations:

Describe how the block feels against your hand

Describe how the sandpaper feels against your hand

Describe pushing the block on the board

Describe pushing the block with sandpaper on it down the board

Describe pushing the block with sandpaper down the board with sandpaper

How high do you think you will lift the board the last time?

Measurements:

Plain block on plain board

Block with sandpaper on plain board

Block with sandpaper on board with sandpaper

Even the varnished board was rough enough for the sandpaper to hold to and keep the block from sliding down.

Conclusions:

Does the block or the sandpaper have more friction? Why do you think so?

Which of the three times you lifted the board was there the most friction? Why do you think this?

What did increasing the friction between the block and board do?

How could you decrease the friction between the block and board?

How could you increase the friction between the block and board?

Car tires use friction to keep and move the car on the road. What creates this friction?

Why is it important to not have smooth tires?

Why is driving on ice so dangerous?

The block seemed stuck to the board as I raised the board higher and higher. Shortly after taking this picture, the block tumbled down the board.

What I Found Out:

My block was a piece of a two by four so it was sanded smooth and felt smooth against my hand. The board was varnished on one side and that side felt slick. Rubbing them against my hand made my hand a little warm.

I put the block on the varnished side of the board and lifted the end. The end was 17.3 cm high when the block slid down.

The sandpaper was rough on my hand and made my hand hot rubbing it. I put the block on the varnished side of the board and started lifting that end. It was 30.5 cm high before the block slid down.

When the block with sandpaper on it was set on the board with sandpaper on it, I had to lift the end up 35.5 cm and the block tumbled off instead of sliding.

The block had a lot less friction than the sandpaper because it felt smooth and only warmed my hand up rubbing it. The sandpaper scraped my hand and made it feel hot.

Friction makes it harder for an object to move so the third time with sandpaper on both the block and the board had the most friction. I had to raise the board really high to get the block to move and then it fell off.

The smooth block and board had  the least friction so any way to make them smoother would decrease the friction even more. Using rougher sandpaper on both the block and board would increase the friction.

A car tire has treads. Roads are usually rough. Rougher kinds of tread and rougher roads would increase the friction. Smooth tires would have a lot less friction letting the tires slide on the road.

Ice is really smooth and slick. It would reduce the friction a lot so the tires would slide.

# Physics 4 Exploring Work in Physics

Picture yourself helping to push a car. You shove. You turn around and push with your back. The car doesn’t move. Did you do any work?

According to your muscles you did a lot. According to the physics definition you did none.

In physics work is defined as moving something over a distance. Since the car did not move, you did no work. In physics this is written as: W = FD or work equals force times distance.

Question: How much work do you do?

Materials:

Spring scales [My set of 3 has a sensitive scale, a medium scale and a harder scale.]

Several blocks of different masses

Note: Another solution is to have stackable blocks.

Ruler

Procedure:

Each block will need a small loop to hook the spring scale to. An easy way to make such a loop for lighter blocks is to take a length of masking tape, attach one end to the block, crimp a length of the tape and attach the other end beside or over the other end on the block.

The masking tape loop will only work for pulling light objects. It does a good job for that and is easy to make.

Place a block on a smooth table top

Set the ruler so you can see how far you will move the block

Hook a spring scale to the block

It is important to pull steadily on the spring scale but reading the force can be difficult. Be sure to read it when the blocks are moving along.

Pull the block steadily for 30 cm

Observe the amount of force on the scale in grams

Note: If the scale barely moves, try a scale with a more sensitive scale on it.

Repeat this for each block or additional block

Observations:

Record the distance and force for each block

My wood scrap blocks were mostly flat pieces making them easy to stack for pulling.

Analysis:

Multiply the grams times the distance in centimeters for each block to get the work done for each block.

Conclusions:

Which block has the most mass? Why do you think so? [You can check this by massing the blocks.]

Do you do more work moving a block with less mass or more mass?

Each block added to the stack increased the amount of force needed to pull the stack.

If you pulled a block 15 cm, would you do more or less work? Why do you think this?

What I Found Out:

I used some scrap wood pieces for blocks so they came in various sizes and shapes. The biggest one was the one I chose to put the loop on. the others were piled on top of it one by one to increase the mass pulled by the spring scale.

The first block took 6 g to pull it the 30 cm. This made the work done 180 g-cm.

Two blocks took 40 g to pull the same distance. Now the work done was 1200 g-cm.

Three blocks took 49 g to pull. Now the work done was 1470 g-cm.

Four blocks took 52 g of effort making the work done 1560 g-cm.

Five blocks took 75 g of force making the work done 2250 g-cm.

Six blocks took 85 g of force making the work done 2550 g-cm.

Seven blocks took 90 g of force making the work done 2700 g-cm.

The last block was added to the stack. The pile was pulled for the 30 cm so work was done.

The more blocks on the pile, the more force it took to pull the pile across the table. That makes me think a heavier block will take more force than a lighter one.

Looking at the increases in effort, the first block took 6 g but the second took an additional 34 g so the second block must have more mass than the first one.

The third block increased the force 9 g and the fourth a mere 3 g. These are lighter than the second block.

The fifth block increased the force needed 23 g. The sixth added 10 g and the last one 5 g. The second block was the biggest block with the fifth block next.

Pulling the first block 30 cm required work of 180 g-cm. If I had pulled the block only 15 cm, it would be 6 g times 15 cm or 90 g-cm. It takes less work to move half the distance.

# Physics 3 Using Vectors To Show Forces

You are asked to join a game of tug of war by one friend. Each of you grabs an end of the rope and starts pulling. Neither of you can pull the other one.

Another friend comes over and grabs the rope with your friend. What happens?

At first the forces you and your friend exert on the rope are the same and opposite. The result is no force.

Let’s show this using vectors.

A vector is an arrow pointing in the direction the force is going. In tug of war the forces go away from each other as both sides are pulling on the rope.

When the third person starts pulling, one force stays the same. The other force doubles. Can vectors show this?

There is one vector arrow for each tug of war participant. Each arrow points the way that person is pulling. Two of the arrows are equal and opposite cancelling each other out. That leaves one arrow to show what happens in the game.

When you put the vectors together, they show what happened in your game of tug of war.

What Is a Vector?

As you can see, a vector is an arrow. The arrow shaft shows the amount of the force. You can do this with labels or drawing to scale.

The head of the arrow shows the direction the force is acting in.

Let’s Draw some Vectors

Materials:

Paper or Graph paper

Pencil

Ruler

Drawing the Vectors:

Draw your block from Project 1

From the bottom center of the block draw a line 2 cm long straight down

Every object on Earth has this vector arrow pointing down. If that force didn’t exist, everything would float into space.

Put the head of the arrow on the end going down

What does this arrow show? What force is holding the block on the table?

You made the block move by pushing on it. Draw a line to the side of the block. How long should the line be?

Using vector arrows for forces makes it easy to see how strong a force is, which direction it is going and how it is acting on an object.

The block moved. Think back to the game of tug of war. As long as the two forces were the same, the forces cancelled each other out.

If the force line showing you pushing the block is shorter than the gravity arrow, will the block move?

Your push vector must be longer than your gravity vector. Let’s make it 3 cm long. Now put the head of the arrow on.

Where does this go? Which way did the force push? It pushed against the block so the head of the arrow points at the block.

Can you draw the pulling force on the block using vectors? Try it. My drawing will be down below.

Using Vectors for Changing Forces

Put your block out on the table. This time push on the block from two adjacent sides at the same time.

Gravity always pulls on objects on Earth. This time we are interested in two forces pushing on two adjacent sides of the block at the same time. Which way will the block move? Can vectors be used to tell us?

Which way did the block go?

Draw your block on the graph paper again. This time have two pushing forces on adjacent sides on the block.

Now, copy one of the vectors from the tip of the opposite corner. Make sure it points in the same direction and is the same length.

The vector arrows are the same ones as before only moved. they point the same way and are the same length. Moving the vectors lets you draw a resultant vector showing the actual path the block took when acted on by two forces.

Next copy the other vector with the end starting at the point of the other vector. Make sure it points in the same direction and is the same length.

If you draw a final vector from the point of the block to the point of the last vector, you have the direction the block moved when you pushed on it with two forces.

The vector arrow for gravity still points down. The other vector arrow now points away from the block as you were pulling on it.

Why Use Vectors?

You can see the forces acting on your block, right? You can see some of them but not others.

Using vectors makes what is happening easier to see. As we go on to look at work and simple machines, we will often use vectors to better understand what the forces are doing.

# Physics 2 Putting Forces Together

Do you like to fly paper airplanes? The beginner model doesn’t fly very well. A modified one zips along.

What do paper airplanes have to do with physics and forces? They can show us how putting forces together changes the strength of the forces.

Introducing my helper for this physics project Tyler Green.

Question: How does putting forces together change them?

Materials:

Paper airplane

Fan

Tape

Large room

Procedure:

Set up the fan at one end of the large room

Stand by the fan, not turned on, and fly your paper airplane

Paper airplanes have several forces working on them. Air pushes them up and back. Your hand pushes them forward. Gravity pulls them down. Tyler isn’t thinking about this as he practices flying his airplane.

Put a piece of tape where it lands

Repeat this two more times

Turn on the fan

Fly your paper airplane several times over the fan so the moving air catches it

Mark where the airplane lands each time

Walk out from the fan to about where your paper airplane would land with the fan off

Fly your paper airplane toward the fan and into the stream of air several times

Mark where it lands each time

Observations:

Describe where the paper airplane lands

Without the fan

With the fan

Against the fan

Describe how the paper airplane flies

Without the fan

With the fan

Against the fan

Conclusions

What forces are acting on your paper airplane when it flies without the fan?

Does the air from the fan provide a force?

Who says physics is boring? Not Tyler. His paper airplane really took off when the fan’s air current helped push it aloft and across the room.

What happens when this force acts against your paper airplane?

How does putting forces together change the force acting on an object?

What I Found Out:

It is hard to fly a paper airplane and take pictures of it flying at the same time. I asked Tyler Reed for help. He was a bit young for the physics but very enthusiastic about flying the airplanes.

A paper airplane launched into the air has several forces acting on it. One is the push you give it to make it go called thrust. Another is gravity pulling it down to the ground. Another is the air which helps hold it up but pushes against it slowing it down.

Tyler had a lot of thrust so the paper airplanes, two styles, flew very well without the fan. They zipped along moving up a little then going lower until they hit the floor at the laundromat where I do the physics projects as there is so much more room than at home.

With the fan turned on the paper airplanes flew higher and farther before. This depended on Tyler throwing the planes near the fan so the fan’s air could push on them.

Tyler threw the paper airplane at the fan. If you look carefully you can see the airplane off to the right side and slightly below the fan pushed there by the air current.

Then Tyler threw the paper airplanes at the fan. The air was still being pushed out from the fan. Now the air stream was pushing against the airplanes. They tended to go up over the air current, turn aside out of the current or dive bomb into the floor.

Putting forces together changes how an object moves. When the forces act in the same direction, they add up to a bigger force so the object moves farther. When the forces act against each other, they make the object go slowly, stop or turn aside from the force.

# Physics 28 Building Arches

Lots of bridges have arches under them. The Romans used arches under their aqueducts for thousands of miles carrying water to their cities. What’s so special about arches?
Question: How does an arch work?
Materials:
Paper
Tape
Procedure:
Make two small diameter paper tubes

The two tubes should be a small diameter and about the same diameter.

Overlap the ends 2 cm and tape them together [You will need to flatten the ends.]

The two tubes only need 2 or 3 cm overlap but must be flattened for the overlapping part.

Bend this long tube into an arch but don’t fold it

The tape must extend over the paper joint on both sides.

Place one end of the arch against a book or other heavy thing
Hold the other end lightly to make it an arch
Press down on the center of the arch letting the end move if it wants to
Hold the end of the arch firmly in place
Press down on the center of the arch
If you can, suspend a cup from the center of the arch and fill it with weights
Observations:
Describe what happens to the end of the arch when you put pressure on the top:

Force applied to the top of an arch flows down each leg into the ground or other base under the arch.

Describe what happens when you hold the ends firmly and put pressure on the arch:
Conclusions:
Where does the pressure go when you press on the arch?
How does this make the arch a good way to build a bridge?
What must a builder do to use an arch safely?

When weight or force is applied to an arch, the base of the arch tends to spread. This tendency must be countered when the arch is used in construction.

If two arches are side by side, what happens to the forces acting on the bottom of one arch?

What I Found Out:
My arch tried to fold at the sides of the flattened part a little making the top look a little flat. When I pressed on the center of the arch the first time, the free end moved out letting the arch flatten.
The pressure I put on the arch went down both legs of the arch. The one leg was trapped against the box and wall so the force pushing that leg out was stopped by force from the wall. The free end had no force acting against it so the end moved outward.

Arches are more rounded than this paper version but this one shows how arches move forces so they can support a lot of weight.

When I held the second leg firmly in place, I supplied the force against the outward force. The arch held firmly.
I could not suspend weight from my arch but think the cup would hold a lot of weight. The force from the weight would go down the legs into the table and the wall and my hand.
Since an arch moves the force from weight off the bridge, the bridge can carry a lot of weight. Since the arch has an opening in the middle under it, other traffic or water can move freely below the bridge.
The problem with using an arch is the outward force acting on the legs. There has to be something strong pushing back to keep the arch in place.
Two arches side by side will do this for each other. The outward force from one leg pushes against the leg from the next arch which is pushing back as weight force moves onto it.

# Physics 27 Making Walls Stronger

Changing the shape of a sheet of paper made it much stronger. But people don’t live or walk on tubes or folds. People live in buildings with walls.

The sheet of paper got stronger when forces were moved from the center to the edges of the paper. Can walls do the same thing?

Question: How can walls be made stronger?

Materials:

Paper

Tape

Ruler

Scissors

Procedure:

The physics project will use nine tubes of about the same diameter.

Make 9 small diameter long tubes of paper

The four tubes for the square must be shorter than the two used for the diagonal pieces. The distance diagonally across the square is farther than across a side.

Trim 6 cm off the ends of four tubes

I put each left tube on top of the right tube so the square would be close to a square not a rectangle. You can do the opposite as long as you do the same for each corner.

Tape the four trimmed tubes into a square

A strip of tape across each corner on both sides held the tubes in place. The tape wrapped around the tube at each end about half way.

Hold the square in one hand or with the bottom on a table

The tape crossing each corner holds the square together. Is the tape strong enough to hold the square together?

Push the side

Pushing on one side of the square makes the side slope. All the pushing force goes across the top tube to push on the top far corner making it buckle.

Tape a tube diagonally across the square

The diagonal tube is taped into place. Notice the tape itself stiffens the corners.

Hold the square in one hand or with the edge on a table

Putting a diagonal inside the square wall cut it into two triangles. Pushing on one side with another side of the triangle on the table is like pushing on the triangle. The side does not move.

Push gently on one side then the other side of the square

Tape a tube diagonally across the square in the other direction

Both diagonals must be flattened a little in the center so the two diagonals will lie flat.

Hold the square as before

Push gently on one side then the other side of the square

Laying the tubes out for the triangle shows that each corner has less angle than those of the square.

Tape three tubes into a triangle

The tubes meet at an angle so I flattened the tips a little and taped over the top of the joint.

Hold the base of the triangle in one hand or on the table

Push on one side then the other side of the triangle

Observations:

Describe how the square feels to hold

Describe what happens when you push on the sides

Describe how the square with one diagonal feels

Pushing on the side of the square with one diagonal going up makes the square twist. The pushing force tries to push on the far corner but the diagonal tries to take the force back to the table not letting the corner move.

Describe what happens when you push on the sides

Describe how the square with two diagonal feels

Describe what happens when you push on the sides

Describe what the triangle feels like when you hold it

Describe what happens when you push on the sides of the triangle

Conclusions:

Is a plain square very stable? Why do you think so?

Why did you have to trim the four tubes for the square?

What has the square become when you add a diagonal?

The triangle side does not push over. The force goes down the other side and into the table.

Compare how the square with a diagonal and the triangle act when pushed on.

Compare how the square with two diagonals and the plain square feel when you hold them.

Compare how the force of a push on the plain square compares to the force of a push on the square with one or two diagonals.

Why do you think the diagonals make a wall stronger?

Can you think of another way to make a square wall stronger with out using diagonals?

Try your idea out and see if it works. Compare your method to the diagonal method.

What I Found Out:

The plain square was very flimsy. It was easy to push the side over turning the square into a rhombus. This is not very stable.

The longer tube fit into the square. If the sides had not been trimmed, the longer tube would not have been long enough to reach across the diagonal.

Once the diagonal is in place the square becomes two joined triangles. It feels much stiffer than the plain square did. The sides do not push. The square does twist when I push on the side.

The sides of the triangle did not move when I pushed on them. The triangle felt rigid.

The square became two triangles with the diagonal in place so the sides did not want to move. But pushing on the top triangle made the side twist because it was not flat on the table.

Pushing on the side of the square with two diagonals in it has the forces being split so some goes across the top, some from the top to the bottom down the diagonal even some into the second diagonal. The square will not push.

With two diagonals in it, the square is stiff. It feels rigid, not at all flimsy like the plain square. The sides do not move when pushed. It does not twist.

When I pushed on the side of the plain square, all the force went across the top tube to push on the other side tube. It moved.

When I pushed on the side of the square when the diagonals were in place, some force still went across the top. But some of the force went down the diagonal to the base of the square.

Diagonals make the square stronger by redirecting the force, breaking it up. That way less force pushes on the top of the side tube and it doesn’t move easily.

The square gets stronger if the corners do not move. Diagonals move the forces around. If the corners are reinforced somehow, it would take a lot more force to move them.

One way would be to put small diagonals across each corner. Another way would be to put a solid piece over the entire square to hole the tubes in place.

# Physics 26 How Strong Is a Paper Bridge?

We met force as a push or a pull. When we balanced forces, we found we could set two forces against each other. The new force was found by adding those forces up.

When an engineer builds a building or a bridge, forces are very important or the structure will fall down. How can an engineer move forces around to keep a structure standing?

Question: How strong is a sheet of paper bridge?

Materials:

Several sheets of paper

Tape

Plastic yoghurt cup or plastic cup of similar or slightly larger size

Marbles or other small weights – enough to fill the cup, over 3 pounds worth

String

Scissors

Scale

2 Chairs

Small blanket or several bath towels

Procedure:

Put the two chairs back to back with a gap between them two thirds as big as the paper is long

Place the two chairs back to back so they are parallel. The towels are to catch the marbles or rocks when they fall.

Place the blanket or folded towels on the floor between the chairs

Place a sheet of paper across the gap

A sheet of paper suspended over the gap between the chairs sags down in the center.

Carefully set the cup on the sheet of paper

If the paper stays put, add a marble

The sheet of paper seemed to fall even before the cup was set on it.

Continue adding marbles until the bridge falls down

Mass the cup and any marbles in it [You may have to pick these up.]

The sheet of paper couldn’t hold even the 11.7 g cup.

Take the sheet of paper and fold it lengthwise so the fold is 1.5 cm

Now make a second fold the other way 1.5 cm

The folds are made lengthwise to span the gap. If the folds went across the paper, would they change how the sheet of paper acted? Probably not.

Repeat this until the paper is accordion folded [This is called concertina.]

Put the folded piece of paper across the gap between the chairs

The concertina bridge is straight across the gap between the chairs. The cup sits up on the folds.

Carefully set the cup on the sheet of paper

If the paper stays put, add marbles until it falls down

Mass the cup and marbles

Put four small holes [big enough for the string.] equal distances apart around the rim of the cup

If the four strings are the same length, the cup should be close to level when suspended. This lets the weights distribute evenly and not tip out.

Cut 4 pieces of string about 45 cm long

Tie knots in one end of the strings

Put the untied ends through the holes, one piece in each hole

Tie the ends together [You might want to tape it together too so the knot doesn’t untie.]

Take another piece of paper and roll it up lengthwise so the roll is 10 cm in diameter

Note: The diameters don’t have to be exact. You need a large, medium and small tube.

The tube sizes can vary but one is large, one small and one in the middle. A couple of short pieces of tape keep the tubes from unrolling.

Tape the roll so it won’t unroll

Roll another sheet of paper into a 7 cm diameter tube

Roll another sheet of paper into a tube with a 1 cm diameter

Put the 4 cm roll through the string loop of the cup and suspend the cup between the chairs

The cup is suspended below the middle of the bridge. An interesting comparison could be done putting the cup at different places along the tube. Each attempt would use a new tube of the same size.

Add marbles one by one until the bridge fails

Using a wide top cup made it easy to add the rocks. Another advantage was having my hand inside the strings so I caught the cup as it fell before the rocks were scattered over the towels.

Mass the cup and marbles

The large tube bridge held 478.3 g, an increase of 75.4 g over the concertina bridge.

Repeat this with the 2 cm and 1 cm tubes

Observations:

Describe how the sheet of paper looks suspended between the chairs

Mass of cup and marbles the sheet of paper held up

Describe how the concertina or folded paper looks suspended between the chairs

A single additional rock caused the folds to flatten under the cup. The concertina bridge did hold several more rocks before crashing down to the floor.

Describe what happens to the concertina as you add marbles to the cup

Mass of cup and marbles the concertina held up

Describe how the 10 cm tube acts before and as you add marbles to the cup

Mass of cup and marbles the tube holds up

Describe how the 7 cm tube acts before and as you add marbles to the cup

Mass of cup and marbles the tube holds up

The medium tube bridge held up 699.7 g which was 221.4 g more than the large tube.

Describe how the 4 cm tube acts before and as you add marbles to the cup

Mass of cup and marbles the tube holds up

Conclusions:

Compare how the plain sheet of paper and the concertina looked suspended.

Where was all the force from the cup focused on the sheet of paper?

Where was all the force from the cup focused on the concertina bridge?

Note: Think about how the tops and bottoms of the folds act.

How is the force from the cup focused with the tubes?

Adding rocks to the cup below the large tube bridge caused the tube to flatten.

What happens to the tube bridges to make them fail?

What do you think would happen if you could make an even smaller diameter tube?

How do you think the forces would focus if the tube were a solid cylinder?

Why is a hollow tube stronger than a solid cylinder?

What I Found Out

I didn’t have enough marbles so I went out to the creek and gathered pieces of gravel about the size of marbles.

The sheet of paper barely stayed up suspended between the chairs. It bowed down in the middle. The 11.7 g cup never really sat on it before the paper fell to the floor.

After the sheet of paper was folded into the concertina, it went straight across between the chairs. It did not sag. The cup sat on it as though it was on a table.

The only difference between the sheet of paper and concertina bridges were the folds yet the weight capacity increased a lot.

I started adding rocks. Finally the folds buckled under the weight. A few more rocks and the concertina fell. It held up 402.9 g of cup and rocks.

All the force of the cup was in the middle of the sheet of paper and it couldn’t hold it up. The folds of the concertina bridge let the force push and pull between the top and bottom of the folds. The folds carried a lot of the force away from them to the chairs. This let the concertina carry weight until the folds finally broke. Then the force was more in the center and it fell down.

The tube bridges acted much the same but the small tube took longer to change. They were straight across the gap. As the rocks were added, the tubes began to flatten. As the tube bridges failed, the tubes crushed.

The force of the weight is spread around the tube bridge and passed on to the chairs. As the tube collapses, more of the force is concentrated on the middle where the strings are. When the tube fails, all the force has moved to where the strings are crushing the tube and making it bend.

I did have some more rocks but couldn’t get them to stay on the pile. The tube had started to flatten so the small tube bridge was approaching its weight capacity.

The smallest tube had not failed when the cup was filled to overflowing with rocks. Perhaps I could have added some small lead wheel weights at the beginning so the tube would fail.

An even smaller diameter tube should hold more weight as long as the center is hollow. This lets the force of the weight move away from where the strings are hanging and go into the chairs. The forces on a solid tube would stay mostly where the strings are hanging putting the weight on the bar there until the bar would break.

# Physics 25 Stable or Unstable

In some states like Montana with lots of high winds, there are signs warning van drivers to stay off the roads when the winds are blowing hard.

Race cars are built low to the ground to go around corners at high rates of speed. Other vehicles going around a corner too fast will tip over.

An object balances at its center of gravity. So, if the center of gravity is over the object’s base, it should be stable and just stand there, right?

Question: Why do objects fall over?

Materials:

Roll of quarters [40 quarters]

Pieces of 1 x 2 of various lengths, at least six pieces [I used 2”, 4”, 6”, 8”, 10” and 12”]

Procedure:

Stack the quarters in a straight stack

The tall straight stack wasn’t quite straight but close. The blue dot shows where the center of gravity is.

Push the stack in the middle until it falls over

When the tall straight stack of quarters fell, only the top half from where the pressure was applied fell. The rest of the stack remained standing.

Stack the quarters so each quarter is slightly [the width of the edge ridge] over from the one below it

The blue dot shows the center of gravity is half way up the stack of quarters and over the edge of the bottom quarter. The stack is stable because it stands but is unstable as a slight push will cause it to fall.

Push the stack from the side it is leaning toward

Restack the quarters as before

Push the stack from the side

Restack the quarters as before

Push from the side it is leaning away from

Pushing on the leaning stack of quarters shifts the center of gravity quickly so it will fall over.

Stack half the quarters in a straight stack

Push over the stack

The blue dot is in the center of the stack of quarters. Pushing the stack is making the center shift.

Restack the quarters and lean the stack

Push this stack over

Stack the wood pieces so the longest piece is on the bottom and each piece is centered

The blue dot showing where the center of gravity is is low and centered over the base.

Push the tower from about half way up the side until it falls over

Stack the wood pieces in the same order but with all the pieces evened up on one side

The blue dot shows where the center of gravity is in the center of the stack. It is low and over the base.

Push the tower from about half way up until it falls over

Stack the wood pieces so the shortest piece is on the bottom centering each piece

Push the stack from about half way up until it falls over

Observations:

Draw each kind of stack and put a dot where the center of gravity is

Describe how the stack of quarters acts as you push it over:

It took a lot of pressure to shove the quarters over off the tall straight stack of quarters.

Straight tall stack:

Leaning tall stack:

Against the lean:

Sideways to the lean:

With the lean:

Straight short stack:

The short leaning stack quickly overbalanced when pushed with the lean. Unlike the straight stack, most of the quarters tipped over not just the top of the stack.

Leaning short stack:

Describe how the wood stack acts as you push it over:

Centered, longest on bottom:

Longest on bottom, flat side

The center of gravity shifted easily when all the blocks were lined up on one edge so the stack tipped over.

Centered, shortest on bottom:

Conclusions:

Where is the center of gravity for each of the stacks, quarters and wood, you built?

Note: Remember how the spoon balanced so your centers of gravity work for the height, width and depth of each stack.

A stable object will stand by itself. Are your stacks of quarters stable?

Pushing against the lean on the leaning stack of quarters first moved the quarters over the base of the stack then over to where they would fall.

An unstable object may stand by itself but is easy to push over. Are any of your stacks of quarters unstable?

What happens to the center of gravity as you push a stack over?

Does the size of the base of the stack of wood affect how stable the stack is? Why do you think this?

How does the center of gravity change as you push over the stacks of wood?

Is it easier to push over a stack with a high center of gravity or a low center of gravity?

Is it easier to push over a stack with the center of gravity square over the base of the stack or when the center of gravity is off center?

How does the center of gravity determine how stable or unstable an object is?

Can an object be both stable and unstable? Why do you think this?

Why is a car more stable going around sharp curves than a van?

What I Found Out:

It was difficult to stack the 40 quarters into a straight stack. Once they were stacked, they didn’t want to fall over. The stack didn’t fall over until I pushed half the stack sideways half way off the stack. This stack was stable. The center of gravity was in the center half way up the stack.

The short stack of quarters was much easier to stack. It was even harder to push over. I had to push the top half more than half way off the stack before it fell over. The center of gravity was in the middle half way up the stack making the stack very stable.

The tall leaning stack of quarters acted differently pushed from the different directions. Pushed from the leaning side the quarters first moved to make a straight stack then fell over the same way as the straight stack. Pushed from the side the quarters acted the same way.

Pushing the stack in the direction in which it was leaning was easy. Almost the entire stack fell over quickly.

The center of gravity was not in the center of the stack. It was moved toward the lean but still half way up. The leaning stack stood up by itself so it was stable to start with but it was unstable too as it would fall over easily.

The center of gravity moved in the direction I pushed the quarters. The stacks fell over when the center of gravity got too far over from the center of the stack.

The regular wood pyramid was very difficult to tip over. The pieces had to be pushed all the way off the ones below before falling. This was a very stable arrangement.

The pyramid stack of wood was very difficult to push over. I had to shove all the pieces off the bottom piece to make them fall.

Even when the edges were in a straight line the boards did not want to fall over until I shoved the boards farther over. It was easier with this stack than with the other stack.

The stack with the big pieces on top was easy to push over. Pushing the top piece an inch made the stack tip over.

The stack of wood with the biggest pieces on the bottom had low centers of gravity. They were very stable. The other stack had a high center of gravity and was unstable.

When pushed, the inverted wood pyramid easily tipped over with the pieces sliding down to the table.

The size of the base did seem important as the pieces had to be pushed off of it before falling. I think I should try different stacking arrangements to see if the base is that important.

Stability seems to depend on the center of gravity as well as the size of the base of an object. Objects with higher centers of gravity are not as stable as those with low centers of gravity. Small bases make it easier to shift the center of gravity and make an object fall over.

Cars have wide bases and low centers of gravity making them very stable. Vans can have wide bases but their centers of gravity are much higher and putting luggage or air conditioning units can make the centers go even higher. Like the two wood pyramids, the van is stable unless going around a corner too fast when the center of gravity shifts making it fall over.

# Physics 24 Center of Gravity

Have you ever picked up a long board? How is it different to pick it up in the middle from picking up one end?
Have you ever watched a waitress balance a tray on one hand?
How do you balance an object on a small point?
Question: How does an object balance?
Materials:
Cardboard from a box
Marker
Scissors
Scale
Spoon
Procedure:

The best way I’ve found for cutting out a rectangle rather than a trapezoid is to measure out across twice, once toward the top and once toward the bottom so the line is straight across the piece of cardboard.

Cut out a square 15 cm on a side, a circle 15 cm diameter, a 15 cm x 20 cm rectangle [These can be a little bigger or smaller.]

The rectangle is cut out by cutting down the line. The entire piece of cardboard was a rectangle and could have been used that way.

Mass the shapes

Massing the rectangle.

Balance each geometric shape on your fingertip marking the place your finger is

The rectangle is longer than its width. This makes finding the balancing point harder as both the length and width must be balanced.

Record where the point is in your Observations

Finding the balancing point for the rectangle took some moving around and a couple of tries to mark it accurately. I marked the first one and tried balancing from that point and found the point was a little further over.

Mark a line straight across each geometric shape going through the marked point
Cut each shape in two on the line
Mass each piece

The mass of the split cardboard rectangle is roughly half the total mass.

Balance the spoon on your finger marking the balancing point
Observations:
Balancing points of the geometric shapes

The mass of the entire cardboard square is 14.32 g.

Masses of the geometric shapes
Masses of the two pieces of each shape:
Balancing point of the spoon
Conclusions:
Is the balancing point always in the measured middle of the object? Why do you think so?
Compare the mass of the object on either side of the balancing point of the cardboard shapes.

The mass of half the cardboard square is 7.16 g , exactly half of the total mass.

Does mass determine the balancing point of an object?
If you could cut the spoon at the balancing point, how do you think the masses of the two pieces would compare?
Another name for this balancing point is the center of gravity. Why is this a good name for the balancing point?

Finding the center of a square without measuring first can take some shifting around but the square finally balances on the tip of my finger.

What I Found Out:
My rectangle was 15 cm x 20 cm. The square was 14 cm x 14 cm. The diameter of the circle was 10 cm.

The mass of the entire cardboard circle is 6.41 g.

The rectangle would sort of balance when my finger was close to the center of the rectangle. It balanced the best, the flattest when my finger was in the center. The same was true for the square and the circle.

Dividing a circle in half even with a center point isn’t easy but still the half is about half the total mass.

The spoon was different. The balancing point was closer to the spoon bowl than to the end of the handle. The balancing point is not always in the middle of a shape.
When I cut the cardboard shapes into two pieces, the two pieces had similar masses. The square halves were the same. The others were tenths of a gram different.

It’s easier to see the circle balances at a point in the center. This is the circle’s center of gravity.

The balancing point seems to be where the mass is the same all around it. If I cut the spoon at the balancing point, I would expect the masses of the two pieces to be very close to the same.
Gravity creates weight. As the balancing point is at the place in an object where the mass and the weight will be the same on all sides, it is at the center of the gravitational pull on the object, the center of gravity.

# Physics 23 Balancing Force and Mass

Find yourself a half gallon juice or milk plastic jug and fill it two thirds with water. You can use a gallon jug but only half fill it. Set it on a table or stool so it is about waist high.

First stand next to the jug. Grab it and lift it up a foot or so.

Next stand at arm’s length away. Grab the jug and lift it up a foot or so.

What happened to the jug? Did anything change about the jug? What did change?

Question: How can you balance force and mass?

Materials:

Several different masses like a set of masses

Unknown mass like a wood block

Scale

Slat board 30 cm to 40 cm long

Wedge 5 cm tall

Metric ruler

Procedure:

Mass all your different masses unless they are a marked set

Set the wedge on a table top pointing up

Balance the slat on the wedge

I used a piece of scrap wood for a slat so it was not smooth. that made it harder to balance on the wedge. Having more of a flat area on the tip of the wedge would make balancing the slat easier too.

Note: This is easier if the wedge tip is a little flattened. Work slowly moving the slat back and forth a speck at a time finally until the slat seems to balance. It will probably never balance levelly on the wedge. Get as close to the balance point as you can.

Mark the place on the slat where it balances, the mass center point

Set a lighter mass on one end of the slat

Placing a mass on one end of the slat or lever makes that end sink to the table.

Take a heavier mass and move it around on the other length of the slat until it balances

Note: Again the slat will probably not balance levelly on the wedge. Move the heavier mass until you find the point closest to balancing.

A 50 g mass must be closer to the wedge or fulcrum to balance with a 20 g mass on the other end.

Measure the distances from the center point of the slat to each mass

Do this again with another set of masses

Mark the slat halfway from the balancing point to one end of the slat

Place the slat on the wedge so the new place is on the tip of the wedge

Place a heavy mass on the short end of the slat

Take a lighter mass and move it up and down the other end of the slat until the two masses balance

Measure the distances from the mark on the slat to each of the masses

Do this again using other masses

Place the unknown mass block on one end of the slat

Use a mass to balance the slat

Measure the distances

Mass the unknown block

The wood block had a mass of 55.29 g on the scale.

Observations:

Masses of the masses:

Distances to the masses (mark down which mass is where each time):

Distances for the unknown mass:

Mass used to balance the unknown block:

Mass of unknown block:

Analysis:

Multiply the distance times the mass for each pair of masses to get the force each mass exerts

Getting the two masses to balance takes careful nudging of one mass until the slat or lever slowly shifts from one side to the other.

You are using the formula Md = Md where M is mass and d is distance. Use this formula to find the mass of the unknown block.

Conclusions:

Compare the forces exerted for each pair of masses.

Compare your calculated mass for the unknown block to its actual mass.

How could you get the calculated mass and actual mass to be the same?

Why did the effort needed to lift the jug of water change?

If you are playing on a teeter totter with a small child who weighs much less than you do, where would you sit so the child could move up and down instead of being stuck in the air?

A 10 g mass must be twice as far from the wedge as the 20 g mass to balance.

The slat could be considered to be a lever. The wedge is the fulcrum. If you wanted to move a very heavy rock with a lever, where would you place the fulcrum to use the least effort? Why?

What I Found Out

My slat was not smooth. Its thickness varied so the balancing point was not quite in the middle of the slat. My wedge did not have a flattened tip so the slat never really stayed level. I moved the slat then the masses until the slat tipped slowly from one end up to the other end up.

I tried to time my pictures for when the slat was slowly shifting. That is how I got the slat to look so balanced in some of them. I had to get the masses very close to balancing so the slat moved slowly for the picture.

When I used the 50 g and 20 g masses, the distance for the 20 g mass was 21.3 cm and the 50 g distance was 7.7 cm. The forces were 426 g-cm and 385 g-cm.

When I used the 10 g and 20 g masses, the distance for the 10 g was 21.1 cm and the 20 g distance was 11.5 cm. This gave forces of 211 g-cm and 230 g-cm.

Balancing the 10 g and 5 g masses, I had distances of 9.3 cm and 19.8 cm. this gave forces of 93 g-cm and 99 g-cm.

Because my slat was so short, I had to use the 50 g mass to balance the wood block. Could I use a smaller mass if I moved the wedge or fulcrum closer to the block end of the slat? Probably.

I used the 50 g mass to balance the wood block. The mass had a distance of 21.4 cm. The block had a distance of 17 cm. This gave me a calculated mass of 63 g. The mass on the scale was 55.29 g.

It took a lot of time to keep moving the mass a speck at a time to get the balance really close. I got impatient and tried to hurry so I wasn’t as accurate as I should have been.

Having a better wedge with a flat spot so the slat would balance better would help too.

I forgot my metric ruler and used the meter stick. This was long and clumsy making it hard to read the distances accurately.

The jug of water did not change. What did change was the distance from the jug to my shoulder. The force exerted downward by the jug was the distance from me to the jug times the mass of the jug. Increasing the distance increased the force and made the jug seem heavier even though it wasn’t.

Playing on a teeter totter is only fun if both people can go up and down. The heavier person can slide forward so the beam balances better.

A lighter force farther from the wedge or fulcrum can exert more force on the other mass. So I would want the fulcrum close to the rock. that way I can push down a little to push hard on the rock.

# Physics 22 Force and Mass

Newton’s Second Law of Motion is Force = Mass x Acceleration. He says the three are related. According to this Law, increasing the acceleration and leaving the mass the same should increase the force. Does it? How are force and mass related?

Question: How are acceleration, force and mass related?

Materials:

Spring scale

2 Small plastic cups (like those from apple sauce or fruit servings)

String

Stopwatch

Tape

Meter stick

Procedure:

Mark off a 1 m + 10 cm course on a smooth table (if the table is rough, use smooth cardboard or a smooth board)

Put two small holes directly opposite from each other in each plastic cup near the rim

Cut a length of string two times as wide as the cup

Put the ends through the holes in the cup and knot them to form a handle

Put the masses in the cups

Zero the spring scale

A regular scale is much more accurate for finding the mass of an object.

Use the scale to mass Cup 1 and Cup 2

Remove the mass from Cup 1

Pull one end of the string out of the hole it is in

Knot the string and pull it through the other hole until the knot holds the end

Put a loop in the loose end of the string

Put the cup 10 cm before the starting line

Put the mass in the cup

Hook the spring scale to the loop

Practice pulling the cup down the course using a constant force on the spring scale

Pulling a mass with a spring scale shows the force used. It is hard to read the force accurately especially when pulling the force quickly.

Time how long it takes to pull the cup down the meter course

Record the force needed

Try pulling the cup faster recording the time and force

Remove the mass from Cup 2

Change the string the same way for Cup 2 but attach it to Cup 1

Put the second mass in Cup 2

Time how long it takes to pull the two cups down the course

Record the force needed

Pull the cups faster recording the times and force needed

Observations:

Masses

Hanging a mass on a spring scale reads more force than pulling the same mass across a table. The mass is the same but the acceleration of gravity is much greater so the force is greater.

Cup 1:

Cup 2:

Times:

One mass:

Force needed:

Both masses:

Force needed:

Conclusions:

Should you start pulling the cup before the starting line? Why?

Compare the force needed for one mass and for two masses.

How are force and mass related?

Does the force needed seem to change if you pull the cup fast or slowly?.

Why do you think this is the case?

Did you expect to need more force to make the cups go faster? Why?

How could you use greater force to move the cups?

Newton’s Second Law of Motion says increasing the acceleration should increase the force. Did the force increase? Is a spring scale a really accurate way to measure this acceleration force?

Doubling the mass being pulled does double the force needed.

What I Found Out:

I used four smaller lead wheel weights used for balancing tires for masses. One cup of weights was a little heavier than the other one. I tried using smaller masses but found it too hard to read the forces on the scale. The ones I used were 68 g and 48 g.

As was the case in the last Project, it took more force to start the cup moving than it did to keep it moving. Starting to pull before the starting line let me measure the steady force only.

When I pulled Cup 1 the first time, I did it slowly in 5.15 sec and had a force of .1 N. I expected to use more force when I pulled the cup faster.

When I pulled Cup 1 in 3.34 sec, it still took .1 N. I tried it at several different speeds. As long as the cup moved steadily, the force remained the same.

When I tied Cup 2 to Cup 1, the force needed to pull the two increased to .2 N. Again this didn’t change if I pulled fast or slowly.

Force and mass are related as increased mass increases the amount of force needed to move the mass. Once the pulling force gets the mass moving, that is all the force needed to keep it moving regardless of how fast or slow the force is applied.

I think I could increase the force used to move the cups if I pushed on them. Possibly I could use a collision to apply the forces like with the projectiles but that would not be sustained over a distance.

The spring scale didn’t stay steady very well. It is difficult to read accurately. Trying to read the scale and time pulling the cup was difficult. I don’t think the force increased but it may have. Having a much heavier mass might have made the force easier to see too.

# Physics 21 Balancing Forces

Many Projects ago we defined a force as a push or a pull. We found forces could add to or subtract from each other. This Project we will try balancing forces so an object does not move when pulled by three forces at the same time in different directions.

Question: How do forces balance?

Materials:

Metal or other rigid ring

3 Spring scales [You can use three identical rubber bands but will not be able to measure the forces instead measure the rubber bands]

Protractor

Procedure:

This Project works well with friends to help. If you are working alone like I do, you will need tape to fasten the scales in place.

A simple spring scale has a pull strip to zero the scale and two scales. One is in grams for obtaining mass. The other is in Newtons, a unit of force.

Secure one scale to the table

Attach the secured scale and another scale to the ring

Pull on the second scale until it reads the same force as the first scale and  stops moving around the ring balancing forces

Record the measurements on the two scales

Note: I have three spring scales that measure forces in three levels of magnitude. If this is how your scales are, check your measurements carefully as each scale will look different.

Secure the second scale to the table

Attach the third scale to the ring

Pull on the third scale until it has the same force reading as the other two scales again balancing forces

Pull the third scale a little more and record the forces shown on the three scales

Secure the scale to the table

Use the protractor to measure the angles between the scales

Observations:

Record the force you use on your scales (or length of rubber bands):

Draw out where the two scales are on the ring

Draw out where the three scales are on the ring

Measurement of angles between the three scales

Record what happens to the three scales when you pull harder on one

Conclusions:

Do you think you could move one of the two scales pulling on the ring so they were not opposite and still balance the forces? Why do you think this?

Even if the second scale is next to the first one when hooked to the ring, it will shift to opposite the scale balancing forces with equal and opposite vectors.

If you used vectors to show the forces of the two scales, would they be the same length? Would they point the same direction?

What happened when you started pulling with the third scale?

What happened when you pulled harder on one scale?

What do you think would happen if you pulled on the ring with a fourth scale? Try it and find out.

What I Found Out:

All three of my scales used a gram and a Newton scale. All three would register .5 Newtons so I decided to use this amount of force.

I attached one scale to the table, put the ring on the hook and put the hook of another scale on the ring. As soon as I started pulling with the second scale, the hook slid until the two scales were exactly opposite of each other. The scales had to be opposite each other for the forces to balance each other so I couldn’t move one scale.

If I drew vectors to show the forces, the arrows would be the same length because both scales pulled with the same force. The arrows would point in opposite directions.

Adding a third scale causes the ring to shift. Having the same force with each scale balances the forces. Putting a ruler from the end of one scale to the next will create an equilateral triangle.

The second scale was attached to the table. I put the third scale’s hook on the ring and started to pull it. The hook slid around the ring until the three scales were the same distance apart around the ring.

Whatever force I pulled with on the third scale, the other two scales showed the same force.

# Degrees of Friction

In the last Project we found that rough surfaces cause more friction between objects. There are several degrees of friction to explore. Force is often measured in Newtons which is mass in kg times distance in m divided by time in seconds squared.

You might have noticed I am not doing a lot of math but knowing what the units are can be important when you do.

Question: How does friction vary?

Materials:

Spring scale

Note: If you do not have a sensitive spring scale, you can use a thick rubber band. You will not be able to measure the friction but you can see what it does. Get a thick rubber band so the loop is about 5 cm long. Use a paperclip to make a hook on one end.

Wood block

Screw eye

Sandpaper

Smooth board

Procedure:

Put the screw eye in one end of the wood block

Attach the spring scale to the eye

Lift the block and get the measurement force in Newtons

Gravity is the force pulling the block down creating weight in grams or force in Newtons.

Place the block of wood on one end of the board

Watch the measurements on the scale as you very slowly pull on the block

Check the measurement on the scale as you pull the block down the board

There is friction even between the plain board and the plain block. It takes more force to start the block moving than to keep it moving across the board.

Repeat this two or three times observing what the scale does as you apply force on the block

Prop up the end of the board 10 cm and repeat your measurements

Move the prop to the other end of the board 10 cm and repeat your measurements

Remove the prop

Can you draw the force vectors for this? The hand is pulling upward. The sandpaper is pulling back. Gravity is pulling downward which splits for both down straight and down the ramp.

Tape sandpaper on the bottom of the block

Watch the measurements as you very slowly pull on the block then pull it down the board

Prop up the end of the board 10 cm and repeat your measurements

Move the prop to the other end of the board and repeat your measurements

Remove the prop

Tape sandpaper on the board

Watch the measurements as you very slowly pull on the block then pull it down the board

Prop up the end of the board 10 cm and repeat your measurements

Move the prop to the other end of the board and repeat your measurements

Note:

If you use the rubber band, watch how it stretches as you slowly pull on the block then pull the block along the board. Describe what the rubber band does.

Observations:

Force to lift the block

Greatest force before the block moves

Going down the ramp gravity helps pull the block down so less force is needed to move the block and keep it moving.

Plain block, plain board

No prop

Top prop

Bottom prop

Sandpaper block, plain board

No prop

Top prop

Bottom prop

Sandpaper block and board

No prop

Top prop

Bottom prop

Force to pull the block

Plain block, plain board

No prop

Top prop

Bottom prop

Sandpaper block, plain board No prop

Top prop

Bottom prop

Sandpaper block and board

No prop

Top prop

Bottom prop

Conclusions:

Did you need the same amount of force to start the block moving as you needed to keep it moving?

Why do you think this is the case?

Was the amount of force needed to pull the block the same as the force to lift the block?

Why do you think this is the case?

Sandpaper on both the block and the board causes more friction between them so it takes more force to move the block. Going up the ramp, gravity pulls the block down so even more force is needed.

Did you use the same force to pull the block down the board, along the board and up the board?

Why do think this is the case?

Tires use friction to keep a car on the road and moving down the road. How does ice on the road change things?

Does a car engine work harder to make a car go up a hill or down a hill? why do you think so?

What I Found Out:

I forgot my screw eye. I took a long piece of tape and made a loop with it. This worked fine as the block had a small mass.

My wood block had a mass of 49 g on the spring scale. This was the same as .49 Newtons.

The smooth block didn’t move until the scale read .14 N. It was really hard to get a good reading as the scale went up then suddenly dropped as the block moved. It only took .09 N to pull the block across the board. There were two degrees of friction: one to start the block moving and one to keep it moving.

Sandpaper is rough. Putting sandpaper on the block means more force is needed to move the block.

When I propped up one end of the board 10 cm and placed the block at the top, the block almost moved by itself. Only .06 N started the block moving and the scale dropped to less than 0 N to keep it moving down the ramp.

Pulling the block up the ramp was much different. This took .22 N to start the block moving and .18 N to keep it moving.

Putting sandpaper on the block made it much harder to move the block. On the level it took .48 N to move and .4 N to keep moving. Going down the ramp was easier with only .3 N to move the block and .1 N to keep it moving. Going up the ramp took. 56 N to move the block and .3 N to keep it moving.

Having sandpaper on both the block and the board was even more difficult. Now it took .52 N to start the block moving on the flat board and .48 N to keep it moving. Sliding down the board took .32 N to start the block moving and .18 N to keep it moving. Going up the ramp took .7 N to start the block moving and .36 N to keep it moving.

Pulling the plain block up the board takes more force than when the board was flat or the block was going down the ramp. It takes more force to start the block moving than to keep it moving. Different forces cause different degrees of friction.

Every time it took more force to start the block moving than it did to keep it moving. It was as though the block and board resisted the motion as long as possible then suddenly couldn’t hold still any longer. The block shot forward, jerked and then moved steadily.

I think friction held the block in place. Once enough force was applied, this friction was overcome. Then less friction was working on the block as it moved. The block also had momentum because it was moving and that helped overcome the friction.

When I held the block up, gravity pulled it down .49 N. Gravity always pulls down. When the block is resting on the flat board, gravity keeps it on the board so only the force to overcome gravity is needed to move the block. The sandpaper added enough friction so the force needed was as much as gravity or more with both pieces covered with sandpaper.

When the block was going down the ramp, gravity helped pull the block down. this is why it took less force to pull the block down a ramp than on a flat surface. Pulling the block up the ramp added gravity to the friction so more force was needed.

Ice is very smooth and slippery. Road pavement is rough. There is less friction on a smooth surface like ice so a car can slide instead of staying on the road.

It takes more force to go up a hill than down a hill because gravity pulls the car down the hill. The engine will work harder to go up the hill.

Friction changes for many reasons. It is a force that resists movement of an object. This project show many degrees of friction. Take a look for where these show up.

# Physics 19 How Friction Works

Up until now we have ignored the effects of friction on our balls and cars. The effect on them was so small, it did not affect our results.

Friction does have a big effect on our lives everyday. It keeps a car on the road and lets it stop. It creates static electricity.

Question: How does friction work?

Materials:

Block of wood [a piece of a 2×4 is great]

Sandpaper or rough cloth

Tape

Long smooth board [about 0.5 m long]

Meter stick

Procedure:

Rub the piece of wood on your hand

Describe how it feels

Rub the piece of wood back and forth on your hand really fast several times

Describe how it feels

Set the piece of wood on one end of the long board

The block should be set with the same side down and with the same side on the downside each time as a control of variables.

Lift that end of the board up slowly until the piece of wood slides down

Measure how high you lifted the end of the board

Describe how the block of wood acts

Since I taped the sandpaper on only one way, I had to place the block the same way on the board each time or the results changed.

Tape the sandpaper on the block of wood [only tape from the edges]

Place the block of wood on the end of the long board

Lift that end of the board up slowly until the block of wood slides down

The board had to be lifted twice as far before the block with sandpaper on it would slide down the board.

Measure how high you lifted the board

Describe how the block of wood acts

Tape sandpaper on the long board

The sandpaper had to be taped on the sides and the ends to lie flat on the board.

Place the block of wood on the end of the long board

Lift that end of the board up until the block of wood slides down

Measure how high you lifted the board

Describe how the block of wood acts

Take the sandpaper off the block of wood

Place the block of wood on the end of the long board

Lift that end of the board up slowly until the block slides down

Measure how high you lifted the board

Observations:

Describe how the block of wood feels on your hand

Describe how your hand feels when you rub it with the block of wood

The block with sandpaper on a board with sandpaper did not want to slide down. I had to lift the board up a lot. One time the block tumbled down instead of sliding.

Measurements:

Plain board:

Sandpaper on block:

Sandpaper on block and board:

Sandpaper on board:

Describe how the block of wood acts:

On the plain board:

With sandpaper on it:

With sandpaper on it and the board:

With sandpaper on the board:

Conclusions:

What creates the heat when you rub the board on your hand?

Why do you think the block with sandpaper on it didn’t slide down as soon as the block without the sandpaper did?

What is one way to increase friction between two objects?

A smooth block on a smooth board showed the least friction.

What I Found Out:

My piece of wood was varnished on one side so it felt very smooth. When I rubbed it back and forth on my hand, my hand felt a little warm.

The block slid down the board when it was 17.3 cm off the table.

After putting sandpaper on the block, I had to raise the board up 30.5 cm before the block slid down. The sandpaper was rough and held on to the board keeping the block in place longer.

When the block with sandpaper was wet on the board covered with sandpaper, I had to lift the board up 35.5 cm, almost vertical before the block slid down. The first time the block didn’t slide off, it tumbled off.

It didn’t matter whether the sandpaper was on the block or on the board, I lifted the board the same amount.

When only the board had sandpaper on it, I lifted it 30.5 cm to make the block slide down. This was the same as when the sandpaper was on the block and not on the board.

When both the block and the board were smooth, the friction was much less than when one or both had sandpaper on them. Roughness increases friction between two objects.

# Physics 18 Momentum

We met Newton’s First Law of Motion some time ago when we ran the little cars down a ramp with pennies on their roofs. The car stopped. The penny didn’t. Inertia was the reason but the penny also had momentum. Where did that momentum come from?

Recently we dropped a ball while walking. Even though we didn’t try to push the ball, it still moved forward as it fell. The ball had momentum. Where did it come from?

When a moving object hits another motionless object, some of the momentum must transfer to the other object. Think about what happens when a bowling ball hits the pins. Think about catching a ball and how your hand feels especially the difference between a fast ball and a slow ball.

Question: How do mass and velocity affect momentum?

Materials:

Ramps [1 with marked meter]

2 identical balls [Ball 1 and Ball S]]

1 smaller, lighter ball [Ball L]

1 heavier ball [Ball H]

Stopwatch

Meter stick

Scale

Procedure:

Mass the balls

Ball 1 has a mass of 18 g. It’s momentum will change with its velocity.

Set up the ramps so one ends at the edge of a table [like in Project 17]

Mark 2 starting lines so one is twice the height of the other

The sloped ramp accelerates the ball. The flat ramp sets up the collision.

Use the stopwatch to find the velocity of Ball 1 released from each of the starting lines

Remember to do several times for each

Timing is important for determining velocity of Ball 1.

Set Ball L at the end of the ramp

Release Ball 1 at the lower starting line

Mark where Ball L lands [You may want to use a long box with towels in it to catch the balls.]

Observe what Ball 1 does after the collision

Measure the distance

Repeat this several times

Put Ball L back at the end of the ramp

Release Ball 1 at the higher starting line

Mark where Ball L lands

Observe what Ball 1 does after the collision

Measure the distance

Repeat this several times

Repeat this using Ball S and then Ball H

Observations:

Mass of balls

Ball 1

Ball L

Ball S

Ball H

Velocity (m/s):

Low starting line

High starting line

Distances:

Ball L

Low starting line:

High starting line

Ball S

Low starting line

High starting line

Ball H

Low starting line

High starting line

What Ball 1 does after the collision

Ball L

Low starting line:

High starting line

Ball S

Low starting line

High starting line

Ball H

Low starting line

High starting line

Analysis:

Calculate the average time for the low and the high starting line to get the velocities

Momentum is the mass (in grams) of an object times its velocity (m/s). Any moving object has momentum because it is moving.

Ball 1 accelerates down the ramp. Increased velocity turns into momentum transferred to the ball at the end of the ramp when the two collide.

Calculate the momentum of Ball 1 for each starting line.

Make a graph of the distances for the balls [ball vs. distance]. Do the three low starting line distances in a group and the three high starting line distances in a group.

Conclusions:

Which starting line provides the most velocity to Ball 1? Why?

Which starting line provides the most momentum to Ball 1?

Which starting line transfers the most momentum to the other ball? Why do you think so?

Which ball, L, S or H, had the most momentum? Why do you think so?

How does mass affect momentum?

How does velocity affect momentum?

If you are riding in a car going 60 MPH [2.5 m/s], what is your momentum? [1 pound is about 2.2 kg]

If you divide the momentum by 2.2, you get your relative mass if the car suddenly stops as in a crash and you continue on like the pennies did. Why are seat belts useful in a car crash?

What I Found Out:

I set up my ramps a little longer than for Project 17 so I would have a little more time to do the timing for the velocity. This helped a lot since I work alone.

My ball masses were 18 g for Balls 1 and S, 2.08 g for Ball L and 53.78 g for Ball H.

From my low starting line my velocity was 1 m/.68 s. This gave me a momentum of 26.4 g-m/s. The high starting line had an average velocity of 1 m/.47s giving a momentum of 36.1 g-m/s.

Gravity pulls the ball down the ramp. The more time and height. The more gravity pulls making the ball go faster. Since the mass remains the same from either line, the velocity affects the momentum. The greater the velocity, the greater the momentum.

The lightest ball was one ninth the mass of Ball 1. When hit by Ball 1, it almost flew out of the ramp.

When Ball 1 hit Ball L from the low line, Ball 1 bounced out of the ramp and Ball L went an average of 68.5 cm. When Ball 1 started at the high line, both balls went off the ramp but Ball L went an average of 106 cm and Ball 1 mostly fell straight down.

When Ball 1 hit Ball S from the low line, it bounced back inside the ramp. Ball S went an average of 17.8 cm. From the high line Ball 1 bounced back less and Ball S went an average of 29.9 cm.

When Ball 1 hit Ball H from either line, it stopped. Ball H went an average of 10 cm from the low line and 22.4 cm from the high line.

The higher starting line gave Ball 1 more momentum so it could give more to the other balls. This showed as the average distances for the high line were greater for all the balls than the average distances for the low line.

Ball L went the farthest both times so it got the most momentum from Ball 1. I think this was because the ball had the least mass so more force was used to create velocity than to make the ball move. The greater the velocity, the greater the momentum.

Once a ball is moving, if all the balls moved at the same velocity, the heaviest ball would have the most momentum.

If I were in a car moving 60 MPH, I would have a momentum of 605 kg-km/s. this would give me a relative mass of 275 pounds. A seat belt keeps me from hitting the front of the car that hard.

# Physics 17 Projectile Challenge

Do you like a challenge?

We are going to set up a slanted ramp leading to a level ramp ending at the edge of a table. When we release the ball at the top of the first ramp, it will accelerate as it comes down into the second ramp which will launch it out in an arc from the edge of the table until it hits the floor.

Where will the ball land on the floor? That’s the challenge. Can you calculate where the ball will land?

Question: Where will the ball land?

Materials:

Two ramps [one must be over a meter long]

Meter stick

Stopwatch

Pan 10 to 15 cm across

Ball

Procedure:

Mark out 1 m on the long ramp

Knowing the velocity of the ball is critical in your calculations. Using a 1 meter section is long enough so timing can be done but not so long the ball will slow down much due to friction.

Set up the long ramp level on the table top so it ends at the edge of the table

Set up the second ramp on a slant so the bottom end leads into the long ramp

The ramps are set up and appear straight. I found the ball itself would cause the ramps to shift a little. I didn’t tape the central part in place and should have.

Make sure both ramps are secured in place

Put a barrier at the edge end of the long ramp to stop the ball [a cloth will work]

Why stop the ball? So you won’t know where to put the bucket without calculating the distance using your measurements.

Mark a starting line near the top of the slanted ramp

Release the ball at the starting mark

Time how fast the ball goes over the marked meter in the long ramp

Repeat this at least three times or until each time is close to the others

Take the barrier out of the long ramp

Measure the distance from the edge of the long ramp to the floor in meters

Calculate the distance the ball will go before hitting the floor [See analysis]

Place your pan with a cloth or sand in it to keep the ball from bouncing where you think the ball will land [Make sure it is straight out from the ramp.]

Note: Be sure you measure from straight down from the edge of the ramp. Why?

Release your ball at the starting mark

If your ball does not land in your pan, try the challenge again

Observations:

Velocity times:

Timing a ball for one meter is difficult. It covers the meter in about half a second.

Distance to the floor:

Analysis:

You have two formulas to work with: d = vt and d = at2.

Remember a is due to gravity and is known to be 9.8 m/s2.

Look back at Physics Project 16 to see which formula tells you how the ball moves, forward or downward. Which values do you know?

Give it a try on your own.

If you have trouble:

When you measure the time it takes for your ball to travel one meter on the long ramp, you have the v for the first equation. The d will be how far the ball goes when it leaves the ramp which you don’t know yet. The time is how long the ball will be in the air when it leaves the second ramp which you also do not know yet.

The height from the edge of the ramp to the floor is the d in the second equation. You also know the a. Use a calculator to solve for t as you must find the square root.

Now you know the t for the first equation and can calculate the d.

Notice the jag in the ramp. I had to correct this then place my bucket to catch the ball.

Conclusions:

What I Found Out:

I will admit I do these Projects in a hurry and am often a bit careless in my measurements. That is a recipe for disaster in this challenge.

First problem: The ramps must line up in a straight line or the ball will wobble from side to side or even jump out of the ramp.

Second problem: Both releasing the ball and working the stopwatch. It helps a lot to work with a friend.

Third problem: Measuring the height at which the ball is released accurately if this is not the very top of the ramp. My first measurement was off by almost 2 cm. Also note this measurement is not to the top edge of the ramp but the place the ball is set.

Will the ball land in the bucket? It took several measurement corrections and calculations, but it finally did.

In case you haven’t figured it out by now, my ball missed my bucket for several tries. I redid my height measurement first. This helped. Then I retimed the ball and found I was off by over half a second.

My ball did finally land in the bucket.