# 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:

If your ball missed your bowl, try to figure out why.

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.

# Physics 15 Projectile Motion

There’s straight line motion. Our balls and cars have shown us a little about it.

There’s pendulum motion. Nuts on strings showed us about this.

There’s circular motion. We used a nut on a string to find out a little about it.

One last type of motion is projectile motion.

What happens if you throw a ball straight up?

If you don’t dodge, it will come straight down and hit you. Why?

If you throw a ball across a room, it curves down to the floor. Why?

Question: How does projectile motion work?

Materials:

Ball

Stopwatch

Paper

Pencil

Procedure:

Toss the ball up from your hand

The ball leaves the hand, goes up then comes back down into the hand.

Observe how the ball goes up and down

Catch it when it returns to your hand

If you have a friend to help, have your friend gently toss the ball across a space

Observe how the ball moves

Throwing a ball or other projectile gives it an arch shaped path.

Play catch outside with your friend

Start with gentle tosses and gradually throw the ball harder

Observe how the motion of the ball changes as you throw it harder

Start the stopwatch and throw your ball straight up as hard as you can [It helps to have a friend help with this.]

Stop the stopwatch when the ball hits the ground

Repeat this only if you did not get the stopwatch stopped on time

Observations:

Draw your ball going up and down one time

Describe how your ball goes up and down

Draw your ball going across a space

Describe the motion of your ball

Describe how the motion of your ball changes as the throws get harder

Time for your ball to go up and down:

Conclusions:

What makes your ball go up?

Newton’s First Law of Motion says an object in motion will continue that motion unless acted on by another force. What force keeps your ball from going up forever?

Why do you think the projectile motion of your ball changes as you change how you throw it?

Throwing a ball is more like the projectile motion people think of because the ball goes over a distance. At the beginning most of the force pushes the ball up, some goes sideways and gravity pulls down. At the top of the arch there is no more force pushing the ball up but it still has force pushing it sideways and gravity pulls it down. When the ball lands, only gravity is still pulling on the ball.

Draw your ball going across a space. Show your ball at the beginning, middle and end of the toss.

Add vectors to show how the forces are acting on your ball at each point to change how it moves.

How does projectile motion work?

Why can’t you use an average time for throwing your ball straight up?

Analysis:

How high did you throw your ball?

Your ball spent half its time going up and half its time coming down. Divide your time in half.

What provided the force to make the ball go up?

When the ball first leaves the hand, most of the force is pushing the ball upward with gravity pulling against it. At the top of the loop, gravity and upward force cancel each other out and the ball stops. Then gravity pulls harder than the upward force so the ball falls back down into your hand. This is projectile motion.

What provided the force to make the ball come down?

Remember the formula from the last Project was a = d/t2

This time we know the acceleration is 9.8 m/s2 and the time and want to know the distance. We can rearrange the formula to be d = at2

Calculate how high you threw the ball.

What I Found Out

First I found out this Project is much easier with two people and I am only one so pictures were not possible. So I did drawings on my computer.

Tossing a ball up and down in one hand isn’t hard. The ball went up out of my hand then stopped and fell back down into my hand.

Playing catch can be fun. When the ball is tossed easily, it arches up then down into the other person’s hands. As the ball is tossed harder, the arch flattens out until it is almost a straight line.

Throwing or tossing a ball uses force from my hand. Gravity is always pulling down on the ball.

Throwing a ball harder means it is going faster so gravity doesn’t slow it down as fast flattening the curve the ball makes.

The ball must go fast enough to overcome gravity. The harder I throw the ball, the faster it goes and the longer before gravity slows it down enough to make it fall.

In projectile motion the ball starts off with lots of force pushing it upwards. Gravity pulls a little of that force at a time slowing the ball down. At the top of the arch gravity is equal to the force making the ball go forward. Then gravity is greater making the ball fall down.

When a ball goes straight up, gravity pulls down until the ball stops and starts to fall down. Even if I try very hard, I won’t throw the ball with the same force every time so I must time each throw separately.

When I tossed my ball up, it took 1.94 sec to hit the ground. Half the time is .97 sec. Squaring the time gives .88 s2. Multiplying that by 9.8 m/s2 tells me I threw the ball 8.6 m or about 28 feet up.

# Physics 12 Harmonic Motion

In physics motion happens when something changes its position. We’ve watched toy cars and balls race down ramps for straight line motion. Nuts swung back and forth for pendulum motion. A nut went in a circle for circular motion. How else can something move?

Pick up a ball point pen and press the end. The knob pushes in then out again. It moved but why does it move that way?

If you take the pen apart, you find a tiny spring inside. You can compress or push the spring down then release it and it goes back to its original length.

Springs are very useful items. They show harmonic motion. They can be used to build a spring scale.

Question: What is harmonic motion?

Materials:

Spring as from inside a pen

A length of wire

Procedure:

Hold most of the Slinky in your hand allowing part of it to dangle down

Move your hand up and down then keep it still

Hold the small spring between your thumb and finger

A spring does show harmonic motion but only when force is directly applied to the coils to compress or pull apart the coils then easing off to allow the coils to return to their original position.

Press the spring down then let it loosen several times [Don’t let go of it, keep it between your thumb and finger.]

Pull the spring out a little longer and let it go back several times

Wrap the wire around something round like a marker or a pencil keeping the coils close together

The wire coils must be tight around the pencil and close together to create a spring.

Attempt to compress and release these coils

Attempt to pull and release these coils

Observations:

Describe how the Slinky moves

The coils of the Slinky go down and up in harmonic motion. All springs show some amount of this motion but this toy shows it very well.

Describe compressing and releasing the spring [amount of force needed etc.]

Describe stretching and releasing the spring

Describe how your coiled wire behaves

Conclusions:

Is speed constant in harmonic motion? Why do you think this?

Does the spring seek to maintain a certain length and shape? Why do you think so?

What do you think would happen if you compressed the spring then let it go?

Compressing an unsupported spring shows a problem engineers face building columns, the spring buckles to the side. If the compression continues, the spring sill shoot off to the side.

What do you think would happen if you pulled the spring out to twice its length?

How does a spring keep its ability to produce harmonic motion?

Does a tightly coiled wire behave differently from a straight wire?

Does the shape of a spring affect how it behaves?

What I Found Out:

The end of my Slinky went down then up over and over. Eventually it stopped but it took a long time.

When I looked at the pictures of the Slinky in motion, I could see the coils stretching out from top to bottom. They didn’t stretch out very far. Then the coils pulled back together as the Slinky pulled back up.

Watching the end of the Slinky, the wire loops zoomed down then stopped, zoomed back up and stopped. The speed was not constant as the loops slowed to a stop, sped up then stopped to start over again.

Once the Slinky stopped moving, gravity pulled the coils out a little. Otherwise the Slinky tried to keep its coils close together.

The small spring compressed down until the coils touched each other and returned to its original length. Pulling the spring stretched out the coils. When the spring was released it returned to its original length.

If I pulled the spring until it was twice its length, the coils straightened a little. The spring returned a little but not to its original length.

Coiling a wire seems to make the wire try to behave like a spring.

A spring seems to need to keep its coils in a certain position. The harmonic motion is produced when the coils are pushed or pulled out of position.

A straight wire stayed bent when I pushed it over. It didn’t straighten out again until I straightened it out.

My wire was hard to wrap around a fat pencil. When I pushed the coils together, it got harder as the coils got closer together. After releasing the coils, they moved out a little way then stopped. These coils acted a little like a spring. They would compress and return to place, pull a little and return to place.

The wire I used had been heated and cooled. From a Chemistry Project, wire that is heated and cooled behaves differently from wire that hasn’t been heated and cooled. It is stiffer and more brittle.

That makes me think, if I had new wire and wrapped it around a pencil, it would act more like a spring.

# Physics 10 Pendulum Motion

Both Galileo and Isaac Newton came up with the laws of motion. Yet we call them Newton’s Laws of Motion. Why?

Time.

Newton could measure time and Galileo could not. Why didn’t Galileo go out and buy a watch? Because there were no watches or clocks in the early 1500’s.

One way Galileo tried to measure time was with his pulse. A pulse is how fast a heart beats. Can you take your pulse?

There are two ways you can take your own pulse. One is in your neck Press your first two fingers against your neck on the side near the top of your trachea or windpipe.

Be sure to use your fingers not your thumb to take your pulse. Your thumb has an artery in it and you will feel this too making your pulse count confused.

The second place is in your wrist. Feel on the inside of your wrist below your hand. There is a hard ridge of bone then a softer area. Several tendons like hard ropes run up your wrist. Press your fingers in beside these below your thumb. You can feel your pulse beat.

Both of these take a little practice. I find it easiest to find the one in my neck. It’s easier to find the wrist pulse in someone else’s wrist.

Galileo would use his pulse to time balls running down a ramp. Stop and think about the last Project. Would Galileo use a steep ramp or one much flatter?

Once you can take your own pulse, watch a clock with a second hand and count the beats for 15 seconds. Get up and run in place or jump up and down 15 times. Now count your pulse again.

Is using your pulse to time some event very accurate?

Galileo decided to try to make a more accurate clock. He used a kind of motion to build a pendulum clock.

For this Project, the pole must be level, the eyes hanging down and far enough from a wall so the nuts will not hit it.

Question: How does a pendulum work?

Materials:

String

Meter long board with small metal eyes or staples in it

A screw eye looks like a screw with a metal loop for a head.

Heavy and light metal nuts, one of each

Stop watch

Ruler

Procedure:

Put two small eyes or staples 20 cm apart near the center of the board

Be sure the eyes or staples have their holes parallel to the board

The two eyes need to be far enough apart for the two pendulums to swing without tangling.

Secure the board between two chairs or tables so the board is level

Cut two lengths of string 60 cm long

Tie a heavy nut to one string and a light one to the other string

Put one string through the eye or staple and tape it to the stick so 15 cm of string hangs from the eye to the nut.

The pendulum string between the knot over the nut and the bottom of the eye is 15 cm. The extra string goes up through the eye, wraps around the pole and is taped in place.

Do the same on another eye with the other string

Pull the nuts up to one side even with the eyes

Released together the heavy and light pendulum nuts swing at the same time to begin with. The string shifted the direction of the swing and changed the timing.

Let the nuts go and watch how they move

Do they move together or is one faster than the other?

Pull one nut to the side level with the eye with the string tight

Pull the nut up level with the eye with the string tight before letting it go.

Start the stopwatch as you drop the nut

Count five times the nut comes back to where it started and stop the stopwatch

Do the same with the other nut

Lengthen the strings to 30 cm and repeat what you just did

Lengthen the strings to 45 cm and repeat these steps

Observations:

Compare how the two nuts swing

Times for five swings:

Five swings of the 15 cm pendulum does not take very long. it is hard to judge when the pendulum reaches the top of a swing.

Light nut, 15 cm:

Heavy nut, 15 cm

Light nut, 30 cm

Heavy nut, 30 cm

Light nut 45 cm

Heavy nut, 45 cm

Analysis:

Calculate the average time for one swing for each trial run

Light nut, 15 cm:

Heavy nut, 15 cm

Light nut, 30 cm

Heavy nut, 30 cm

Light nut 45 cm

Heavy nut, 45 cm

Conclusions:

How accurate do you think your times were? Why do you think so?

Is mass or string length what determines the time of a swing?

The two 30 cm long pendulums are set up.

Can you tie a string so the nut takes five seconds to complete one swing?

Do you think a pendulum will swing forever without being restarted? Why do you think so?

How could Galileo use this type of motion to make a clock?

What do you think would happen if you shook the board while one of the nuts was swinging? Try it and find out.

Would a pendulum clock always be accurate? Why do you think so?

What I Found Out:

I found it difficult to make the strings exactly the same length for the two different nuts. Another problem was when I released the nuts to swing like pendulums. For the first five or six swings they went back and forth then started shifting until they were swinging up and down the pole until they were swinging the opposite way across the pole. This was better when I tied the string off with a loose knot at the eye. It might improve how the nut swung if the string had been tied off each time instead of going through the eye.

The next difficulty was holding the nut up to exactly the same height each time. Putting another board or something else stiff across to bring the nut up to each time would make sure the height was the same each time.

Starting the stopwatch at the same time I released the nut was not as hard but I was probably not as accurate as it seemed I was.

The end result was that my times were probably not as accurate as I wanted them to be. In fact, it is surprising how similar each set of times were.

When I released the heavy and light nuts together, they swung at about the same time. This was the case until the strings shifted. That made me think the mass at the end of the pendulum was not the deciding factor in how fast the pendulum moved.

For my light nut the 15 cm string had an average time of 4.63 sec, the 30 cm string was 6.17 sec and the 45 cm string was 7.65 sec. For the heavy nut the 15 cm string had an average time of 4.75 sec, the 30 cm string was 6.44 sec and the 45 cm string was 7.81 sec.

The longest pendulums take the longest to make five swings. The time of a swing depends on the length not the mass.

Comparing the 15 cm strings gave me 4.63 sec and 4.75 sec. The 30 cm string gave me 6.17 sec and 6.44 sec. The 45 cm string gave me 7.65 sec and 7.81 sec.

This confirmed that the mass of the nuts did not determine the time of a swing. Instead, the longer the string was, the more time a swing took.

Since 5 sec is about half way between the times for the 15 cm and 30 cm strings, I would try a string 22 cm long for a 5 sec swing. I did not have time to test this idea.

I did notice that each swing was a little smaller than the previous swing. Part of this would be the shift in how the string was swinging. Part of this would be friction between the string and eye. Even tying the string to the eye did not stop the pendulum from slowing down. That means a pendulum would not continue swinging forever.

Since a pendulum can swing in the same time if friction is minimized or countered, Galileo could make a pendulum clock. Each swing of the pendulum would have to move a second hand which would move a minute hand which would move an hour hand.

In fact, Galileo did make such a clock. Clocks are still made with pendulums. They use weights to counter the friction and keep the pendulums swinging at the same speed. The pendulums turn gears that move the clock hands to show the time.

Shaking the pole would change how the nuts were swinging. Moving the chair made the swings change size and direction.

A pendulum clock would have to sit still to work properly. If the ground moved or it was on a ship, the pendulum swings would not stay the same so the clock would not be accurate.

# Physics 7 Motion and Vectors

For the Projects we’ve done so far we’ve accepted that the paper, the car, the balls and the jar moved. What is motion?

Look up motion in the dictionary. What does it say?

My dictionary says motion isthe act of changing place or moving.

We used vectors earlier to show the direction of a force. Vectors can also help us show where and how far something is moving.

Another concept in physics is displacement. This is how far something moves from its original position. This is not the same as the distance something moves.

Question: How can vectors show how something moves?

Materials:

Sheets of Grid paper [quarter inch is fine]

Pencil

Procedure:

Draw a line across a sheet of grid paper about ten squares from the top

The line is a street

Make a little mark across this line every second square

These marks show blocks

Draw a little house at the middle mark on the line

On a map east goes to the right, west to the left, north up and south down.

Trip 1:

You leave the little house and walk three blocks east to the market

Above the line you can make a fancy house and market. Below the line is room for the vectors. The first one goes from the house east to the market. It has an arrow on the tip pointing the direction you walked.

To show this draw a line from the mark in front of the house three blocks east or and put a little arrow at the end of the line.

Now you walk three blocks west back to the little house

You now walk back home so the vector arrow goes from the market to your house. The arrow is now on the end at your house as you walked that way.

Draw another line from the market to the little house and put a little arrow on the end

Conclusions:

How far did you walk?

This is distance. Your total distance is 3 blocks east plus 3 blocks west or 6 blocks.

What is your displacement?

Notice on your graph the arrows are equal and opposite. The vectors say you did not go anywhere.

Displacement is how far something moves away from where it started. In this case the displacement is 0 because you started and ended at the same place.

Trip 2:

Draw another line about ten squares below the first line and put a little mark in the middle

The long green line is the street running east and west with a mark showing your house in the middle. You can draw houses above the line if you wish.

This time each square is a block

You go to a friend’s house five blocks west of your house

The first vector is you going five blocks west so the line goes five squares to the left.

Draw this vector

The two of you decide to go to another friend’s house seven blocks east of where you are

Going seven blocks east means going past your house plus another two blocks and the vector shows this.

Draw this vector

Later you and your first friend go to your homes for dinner

You go only a short distance and your friend keeps going so two vectors are needed. I labeled them with a y for you and an f for friend so i would know which was which.

Draw these vectors

Conclusions:

Trip 2:

What distance did you walk?

What distance did your first friend walk?

What distance did your second friend walk?

What is your displacement at your first friend’s house?

What is your displacement at your second friend’s house?

What is your first friend’s displacement at your second friend’s house?

What is your total displacement?

What is your first friend’s total displacement?

Observations:

Your lines and vectors

Draw another line about ten squares below your last vector line

Mark your home in the center

Walk the five blocks west to your friend’s house

[Hint: This may be easier if you use more than one color for the vectors such as one to you alone, one for you and your first friend, one for the three of you and one for your two friends.]

The two of you walk seven blocks east to your other friend’s house

The three of you go five blocks east to a park for the afternoon

The three of you go to your house for supper

Your two friends go back to your first friend’s house for the night

Conclusions

What distance did you go?

What was your displacement?

What distance did your first friend go?

What was your first friend’s displacement?

What distance did your second friend go?

What was your second friend’s displacement?

What I found Out:

I used four different colors and labeled the vectors to keep track of them. Another way would be to do three graphs, one for each person. That method would make it easier to see how far and where each person went.

I walked 5 blocks W + 7 blocks E + 5 blocks E + 7 blocks W or 24 blocks. My displacement was 0 because I started and ended at home.

My first friend walked 7 blocks E + 5 blocks E + 7 blocks W + 5 blocks W or 24 blocks.  My first friend’s displacement is 0 because of starting and ending at home.

My second friend walked 5 blocks E + 7 blocks W + 5 blocks W or 17 blocks. My second friend’s displacement is 7 blocks because of starting at home and ending at my first friend’s house.