# 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.