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Physics 16 How Far Does a Projectile Go?

When a projectile such as a ball is tossed or thrown, we saw the ball has two big vectors. One is gravity pulling the ball downward. The other is the force pushing the ball forward.

Finding how far a projectile goes is influenced by both of these vectors. But how?

Try this experiment [a friend observing helps]: Stand still and drop a ball catching it on the first bounce. Do not throw it. Ask your friend the path the ball followed down and up.

movement of a dropped ball graphic

A dropped ball goes straight down due to gravity then bounces straight up due to elasticity of the ball.

Next walk across the floor. As you walk, drop the ball and catch it on the first bounce. Ask your friend about the path this ball followed.

When you were standing still, the ball had to go straight down and up for you to catch it. When you were walking, if the ball dropped straight down and came straight up, you could not catch it because you were moving. The ball had to follow a curved or projectile pathway.

dropping a ball while walking graphic

When you walk forward, you have momentum. Even when you just drop a ball, it has some of the momentum from you so ti follows a curved path down and up so you can catch it instead of passing it by.

This shows the two movements of a projectile, although influenced by each other, work independently. This is important for finding out how far a projectile will go.

materials needed for Project

Question: How far does a projectile go?

Materials:

Rubber ball

Meter stick

Stopwatch

Procedure:

Repeat dropping and catching the ball as you walk to be sure you are dropping the ball not dribbling it. The only downward force is supposed to be gravity.

Measure the distance from where you will drop the ball to the floor

Mark a starting line on the floor. You will have to be walking as you cross this line so give yourself some room.

setting up the walking path

The meter stick will probably be long enough to show how far you walk dropping and catching the ball. Set is up from your starting line along the path you will follow.

Put the meter stick down with one end touching the starting line

Holding the ball, start walking toward the starting line

As you cross the starting line, drop the ball and start the stopwatch

Stop, stop the stopwatch when you catch the ball on the first bounce

Find the distance you went by looking at the meter stick

[You may want to have your friend work the stopwatch.]

Doing this can be difficult so you may want to repeat it a few times

Observations:

Describe the path the ball follows when you drop it:

Describe the path the ball follows when you drop it while walking:

Distance the ball is dropped:

For each trial with the ball write down the time and distance:

Analysis:

The falling projectile ball has two different movements so there are two different vectors.

vectors showing how the curved path happens

When you drop a ball while walking, ti follows a curved path. In vectors this is shown with two vectors, one going forward for the momentum and one going down for the gravity. Added up the two show where the ball will land.

Vector 1 – Distance

One of the vectors points forward because you are moving forward. How far forward will the ball go?

We’ve seen this already. The distance is the time multiplied by the speed. You want to know about the part when the ball is going to the floor. As we saw in the last Project, this is half of the total. Divide the distance and the time in half.

Now you can rearrange the formula to v = d/t. Put in your values for d and t to find the velocity for the first vector.

Vector 2 – Falling

We’ve seen this already. Gravity is acceleration so the distance down equals gravity’s acceleration multiplied by the square of the time.

Remember the acceleration is 9.8 m/s2 and the time is what you used before. Put your values in and calculate the distance the ball dropped.

Now compare the distance you dropped the ball to what you calculated.

Looking at What Makes Your Values Change

We used several measurements in our calculations. One was the value for gravity. We used an accepted and proven value of 9.8 m/s2 so this will not change.

vectors for dropping a ball while walking

There are three measurements you need for a projectile. One is time. One is the distance to the ground. The third is the distance from dropping to catching the ball.

Now we have several measurements we made. One was the distance you walked between dropping and catching the ball. We assumed we dropped and caught the ball at the same height.

How accurately did you measure the distance? It must be in meters. If you measured the distance and the time in different tests, can you be sure the distance was the same both times?

Another distance was how far you dropped the ball. When should we have measured this distance? Why? Is there a way to make sure you drop the ball from the same height each time?

We also measured the time it took to bounce the ball. My ball bounced up very fast making it hard to time this accurately. What about your time?

In the last Project we threw a ball upwards. The force we threw it with was countered by gravity until the two were equal and gravity took over causing the ball to fall down. Half the time was spent going up and half coming down.

When we drop a ball, gravity pulls it down. When the ball bounces, the force of the ball hitting the ground makes it come back up. Different kinds of balls will bounce differently.

What kind of ball did you use? I used one of those rubber balls that bounces back as high as the height I dropped it from for the first bounce. This kind of ball would come very close to taking the same amount of time coming up as it did going down.

If you used a different kind of ball, this may not be true. That would mean your time value would not be right. That would make your calculations off too.

Taking Another Look At How This Works

A projectile differs from a falling object because it moves from a starting to an ending place. The projectile or ball we looked at went out horizontally and fell as it traveled across this distance.

The arc of the falling projectile has two vector parts. One is falling because of gravity. The other is going forward due to some force pushing it forward.

With the balls we dropped, what was the forward push? When we walk forward, we have something called momentum. We will look at this more closely in a future Project. This momentum provided the force forward to our balls.

Calculating the time it takes for the ball to fall to the ground uses the formula d = at2 where a is 9.8 m/s2 for gravity and d is the distance we measure.

Calculating how far forward the ball will go uses the formula d = vt. If we know how far the ball will fall, we can calculate time as above or we can measure it.

We must know the distance to calculate velocity or velocity to calculate distance. We must know two values for the formula to calculate the third.

Giving It another Try

This time let’s try to keep our measurements much more accurate. The first one is how far we will drop the ball.

The farther the ball drops, the longer it will take making timing easier. However, we need to have some mark so we drop it and catch it at the same height. The waist is convenient but may make timing difficult.

Measure the height to your waist.

Next is the distance you walk while bouncing the ball.You need to be walking along before you drop the ball. Have a route and a marked starting line. It may help to have a line or something marked to keep walking in a straight line. Have a way to mark the ending spot.

The hardest measurement is the time. The ball will bounce back up quickly. Having a friend time the bounce may be easier than trying to walk a straight line, drop the ball while starting the stopwatch and catching the ball as you stop the stopwatch.

You can do several trials but keep each set of measurements separate as each trial may differ in  measurements from the others. They should be similar so you can pick a set that seems more accurate to use for your calculations.

What Can You Calculate?

You can use your distance and time measurements to calculate your walking velocity using v = d/t.

You can use d = at2 where a = 9.8 m/s2 to calculate the distance the ball falls to the ground or the time it takes to reach the ground. Because the time is squared, you will want to use a calculator to find the square root or the time that was squared.

What We Will Do Next

Next week the Project will be a projectile challenge. We will calculate the velocity of a ball traveling off a table and use it to calculate where to place a cup to catch the ball when it reaches the ground. You will need two long ramps, a ball, a meter stick and a stopwatch. Oh, you will need a cup to catch the ball in.

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.

There’s harmonic motion. A Slinky and springs showed us a little about this.

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

tossing a ball diagram

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

thrown ball diagram

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

Get your stopwatch ready. Stand ready to throw your ball straight up.

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?

vectors for a thrown ball

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?

vectors for tossing a ball

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.

diagram of a ball thrown hard

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 14 Gravitational Acceleration

As we’ve seen and used, gravity pulls things down to the ground. It causes what physicists call uniform acceleration. This means the object accelerates the same amount each second or unit of time.

Another way of saying this is that the object going speed in meters/second [m/s] per second moving [1/s] or acceleration [a] is m/s2.

In another Project we found gravitational acceleration is the same for large or small masses. Air can slow the object down due to friction. Remember the paper airplanes and the fan?

In this Project we will try to measure gravitational acceleration in two ways. This will require doing some math. Both ways require the stopwatch start when the ball is released so the ball starts from rest or velocity equal to zero.

materials for the project: ramp, ball, meter stick, stopwatch

Question: What is the value of gravitational acceleration?

Materials:

Ramp

Ball

Meter stick

Stopwatch

Procedure:

This is the hardest way. You drop the ball while timing how long it falls. The farther it falls, the easier it is to start and stop the stopwatch as the ball hits the ground. You must know exactly how far in meters the ball falls.

holding ball ready to drop it

The ball must be held at the tape mark each time before it is dropped.

Mark the height you will drop the ball from.

Measure the distance from the floor to the mark in meters

Stand with the ball in one hand and the stopwatch in the other hand or have a friend help

Start the stopwatch at the same time you drop the ball

Stop the stopwatch when the ball hits the floor

Do this at least three times

ramp on chair

The ramp was taped to the chair.

If you remember other Projects, running the ball down the ramp makes it take longer to get to the ground. This makes timing the ball easier. You must know exactly how far the ball rolls down the ramp to the ground.

Set up your ramp

I used a ramp two meters long propped and taped to a chair.

Mark your starting line on the ramp

Measure the distance from your mark to the floor in meters

Hold the ball in one hand at the starting line and the stopwatch in your other hand or have a friend help

Let the ball go at the same time you start the stopwatch

Stop the stopwatch when the ball reaches the floor

Do this at least three times

Observations:

Time for the ball to fall:

1st:

2nd:

3rd:

Time for the ball to go down the ramp

1st:

2nd:

3rd:

Analysis:

Find the average time for the ball to fall

Find the average time for the ball to go down the ramp

[Remember you add up all the times then divide by the number of times to find the average.]

To calculate the gravitational acceleration we will use the formula: a = v/t = d/t/t

The a is acceleration.

The v is the velocity of the ball when it hits the floor. You don’t know the velocity but velocity is distance divided by time and you do know these.

The d is the distance the ball travels in meters.

The t is the time in seconds.

Calculate the acceleration by dividing the distance in meters by the time in seconds then the quotient by the time in seconds again to get the acceleration for one second.

ball speeding down ramp

The ramp was steep so the ball sped down it quickly making timing difficult.

Use the same formula and the distance down the ramp and time for the ramp to calculate the acceleration down the ramp.

Conclusions:

Why is measuring the distance so important?

Why is measuring the time accurately so important?

Why do you use an average time?

Would it be better to have more times to use to get your average time? Why do you think so?

Why should the acceleration you calculate for the two methods of timing be about the same?

Were your two times the same? Why do you think this was the case?

The gravitational acceleration is thought to be 9.8 m/s2. Were your calculated accelerations close to this? Why do you think this was the case?

 

What I Found Out

This project seems so easy to do. I measured my ramp carefully so it was 2 m long. It was set up with a steep slope.

When I tried to time the ball going down the ramp, I had problems. It was easy to start the ball and the stopwatch at the same time. It wasn’t so easy to stop the stopwatch when the ball got to the floor.

Dropping the ball was even harder. Again it was easy to start the ball and the stopwatch at the same time. I’m positive the ball bounced before I got the stopwatch stopped.

This is definitely a project requiring two people to do it well.

The formula required two measurements. One was the distance the ball went. Since this distance is divided by the square of the time, a little mistake in measuring the distance can make a big difference in the answer.

The time is squared or multiplied by itself. Any mistake in the time becomes very big.

I measured the time four times each way the ball went. The times were very similar for going down the ramp with a span of only .03 sec between the lowest and highest times.

The times for dropping the ball had a range of .1 sec between the lowest and highest time. The range of the squares would be .19 sec2 to .29 sec2. That much difference would make a big change in the acceleration I calculated.

dropping the ball

My ball dropped 1.5 m faster than I could start and stop the stopwatch. This made getting good times difficult.

Using an average time smoothed out these extremes to give me a better time for my calculations.

The procedure said to use three time measurements. I chose to use four because my measurements were so different. If the three measurements had been more similar, I would have used only three.

I think the number of measurements you use depends on how similar they are.

When I calculated my accelerations I got 1.5 m/s2 for dropping the ball and 1.3 m/s2 for the ramp. Since the pull of gravity was the same for both methods, the acceleration should be about the same.

My calculated acceleration was very different from the accepted gravitational acceleration of 9.8 m/s2, not even close. I am not sure why my values were so different.

One possibility is the time. It was very hard for me to get a good time even though my values were similar.

What I would like to do is repeat this project with someone to help me. I would make two other changes.

First I would lower the angle of the ramp so the ball would go down a little slower making timing it easier.

Second I would lengthen the distance to at least two meters dropping the ball. This would give a little more time to stop the stopwatch before the ball bounced.

Physics 13 Acceleration and Speed

All forms of motion involve either speed or acceleration. What is the difference?

Speed in physics is how far something moves in a given time.

Acceleration in physics is a change in speed or direction or both.

Straight line motion is an easy way to look at both acceleration and speed.

This Project is easier with two people.

Project materials

Question: What is the difference between speed and acceleration?

Materials:

Stopwatch

Meter stick

Ball

Short ramp 1 to 1.5 m long

Long ramp 4 to 5 m long

Tape

Marker

Procedure:

Make the two ramps [Plastic car track will work, if you have it. Mark the long ramp with masking tape.]

I used stiff cardboard because it is smooth, easy to get and easy to work with. My piece was over a meter square. I cut long strips of cardboard about 15 cm wide.

folding the ramp pieces

My cardboard was thick and stiff making folding difficult. The fold does need to be fairly straight. Fold up one end so the ends are the same then start folding. Start the fold at the other end the same way then move each fold up toward the middle of the piece.

One piece was folded in half lengthwise for the short ramp.

overlapping the long ramp pieces

Each piece for the long ramp overlapped the other by 10 to 15 cm to add strength to the joint. Each overlap had to have the same top and bottom overlap so the ball would always run from the top piece to the bottom piece to minimize friction.

Several pieces were taped together to form the long ramp. First fold each piece in half lengthwise. Each piece must overlap 10 cm or so. The top piece always overlaps the next piece. The folds must be in the same place at each overlap. Tape each one top and bottom.

outside taping on long ramp

Because the long ramp would tend to sag down, I put extra duct tape over the joint to strengthen it.

Mark across the long ramp 20 cm from the end. Make a second mark 1 m from the first mark.

taping the inside of the ramp

In putting the duct tape on the inside of the ramp, I put it in the fold first then smoothed it upwards.

Make another mark 20 cm from the second mark. The next mark is 1 m from the third mark.

marking the meter areas on the long ramp

I numbered each marked meter on the long ramp with the top one being one. Each meter did span one of the taped areas but duct tape is smooth and few if any wrinkles were in the area the ball ran down minimizing friction and allowing the ball to run freely down the ramp.

Go down another 20 cm and make another set of marks 1 m apart.

Set up the short ramp so the top is 50 cm off the floor. The floor must be smooth, not carpeted.

setting up the short ramp

Masking tape holds the ramp in place. Tape keeps the ramp straight so the ball will go straight. The meter stick was moved after this as the ball hit it instead of going by.

Set the meter stick on the floor 10 cm from the end of the ramp so the ball will go past it

Get ready with the stopwatch

Let the ball go down the ramp and time how long it takes the ball to go the 1 m  past the meter stick

Do this three times

Move the meter stick so the end is 1 m from the end of the ramp

Time how long it takes the ball to go past the meter stick at least three times

Move the meter stick so the end is 2 m from the end of the ramp

Time how fast the ball goes past the meter stick at least three times

Set the long ramp up so the top end is 50 cm off the floor [If the ramp sags anywhere along its length, prop it up.]

setting up the long ramp

The long ramp was not quite straight. Only one prop was under it so the bottom sagged too much. It tried to tip over and required additional taping to the floor.

Get the stopwatch ready

Time how fast the ball goes the first meter at least three times

Time how fast the ball goes the second meter at least three times

Time how fast the ball goes the third meter at least three times

Place the meter stick on the floor 10 cm from the end of the ramp

Time how fast the ball goes this meter at least three times

Observations:

Short ramp-

1st meter:

2nd meter:

3rd meter:

Long ramp-

1st meter:

2nd meter:

3rd meter:

Floor meter:

Analysis:

Calculate the average time for each set of times for the short and the long ramps.

Draw a graph of time and which meter was run for the short ramp

Draw a line through the times

Add the times for the long ramp to the graph

Draw a line through the times

graph of times

The times from the short ramp for the different meter placements were very similar. They did gradually increase but all stayed between .3 sec and .38 sec giving a fairly straight line on the graph. This indicates we were measuring speed. The times from the long ramp changed a lot for the different meter sections giving a steeply curved line on the graph indication we were measuring acceleration.

Conclusions:

Does the speed of the ball seem to change for the short ramp? Why do you think so?

ball and short ramp

The ball sped down the short ramp and past the meter stick almost faster than I could start and stop the stopwatch.

Does the speed of the ball seem to change for the long ramp? Why do you think so?

Are you measuring speed or acceleration for the ball and short ramp? Why do you think so?

Are you measuring speed or acceleration for the ball and long ramp? Why do you think so?

If you could time the ball for the top and bottom halves of the short ramp, would the times be the same? Why do you think so? Is the ball accelerating on the short ramp?

Does the length of the ramp matter to the final speed of the ball? Why do you think so?

What could cause the ball to slow slightly from the short ramp?

 

What I Found Out:

I missed having Aiah to help with this Project. Two people working on it makes this much easier.

The short ramp was quick and easy to make and set up. My ball passed the first meter in .34 sec, .38 sec and .28 sec for an average of .33 sec. The ball ran the second meter in .41 sec, .25 sec, .31 sec and .28 sec. for an average of .31 sec. This was the hardest meter for me to time. The times for the third meter were .40 sec, .31 sec and .37 sec for an average of .36 sec.

The three average times for the short ramp were very similar. The speed does not seem to change for the distances from the ramp. This would be a measure of speed as the ball travels at about the same rate in the same direction.

The long ramp was harder to assemble. Duct tape holds it but I had to use a lot of it to keep the pieces from pulling apart. The prop under the ramp keeping it from sagging helped hold it together too.

ball on long ramp

The ball ran much slower down the long ramp making it easier to take a picture but the ball went faster for each meter and was going at the same speed when it got to the bottom as it had from the short ramp.

The first meter was the hardest to time for the long ramp. My times were .97 sec, .94 sec and .90 sec for an average of .94 sec. The times for the second meter were .59 sec, .56 sec and .50 sec for an average of .55 sec. The third meter times were .47 sec, .40 sec and .46 sec with an average of .44 sec. When I timed the meter on the floor, the times were .31 sec, .41 sec, .44 sec, .34 sec and .41 sec with an average of .38 sec.

While the ball is going down the long ramp, it goes faster each lower meter. The time it takes for the meters gets shorter so it must be going faster. This would be a measure of acceleration because the ball’s speed is increasing or changing.

If I could time the ball going down the short ramp, the ball would go faster on the bottom half of the ramp than on the top half. I think this because the ball has no speed when I first let it go and it is going very fast when it gets to the bottom. The ball’s speed is changing as it goes down the ramp so it is accelerating.

When I compare the average speeds of the ball for the first meter covered on the floor for the two ramps, they are similar. Even though the ball went much farther to get down the long ramp than on the short ramp, it accelerated the same amount. The length of the ramp does not matter.

What does matter is friction. This gradually slows the ball down as it rolls across the floor.

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.

Slinky, spring, wire

Question: What is harmonic motion?

Materials:

Slinky

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

Compressing a spring

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

wire around pencil

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

harmonic motion of a Slinky

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?

buckling compressed spring

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.

coiled wire

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 11 Circular Motion

Things move in different paths. So far we’ve looked at straight motion and pendulum motion. What if a pendulum didn’t swing back and forth but went all the way around? This is circular motion. How is circular motion different from pendulum motion?

string, nut, scissors, meter stick, stopwatch

Question: How does circular motion work?

Materials:

String

Nut

Procedure:

Cut a piece of string 1.5 m long

measuring 1.5 m of string

Measure off 1.5 m of string. My string unravels easily so I put a piece of tape over the end to hold it together.

Put a loop in one end big enough to fit on your wrist

loop in end of string

The loop at the end of the string needs to be big enough to slide over a hand but small enough to not slip off the wrist easily.

Tie the nut to the other end of the string [I taped the knot as my string doesn’t hold a knot well.]

nut on string

The nut is tied to the end of the string. Be sure to secure the knot so it will not come loose while you are swinging the nut around. I used tape.

Measure up the string 0.5 m and make a small knot

0.5 m knot

The first knot is tied 0.5 meter from the nut.

Measure up the string 1 m and make a small knot

1 m knot

The second knot is tied at 1 meter from the nut.

!Warning!: Getting hit by the nut can hurt. Hitting something else with the nut can get you into a lot of trouble picking up broken things off the floor.

Put the loop around your wrist

Hold the string at the first knot

Swing the nut back and forth like a pendulum but keep adding force until the nut goes all the way around

Swing the nut around in a circular path several times

Stop the string

Hold the string at the second knot

Swing the nut back and forth like a pendulum but keep adding force until the nut goes all the way around

Swing the nut around in a circular path several times

Stop the string

Observations:

How did you have to move your hand to add force to increase the swing of the nut?

nut moving in revolution

The nut swings at the end of the string. The hand holding the string keeps the nut moving at a fixed distance so it travels in a circular path.

Describe any differences for the longer string

Describe how it felt as the nut moved in a circular path

Describe any differences for the longer string

Conclusions:

Why do you loop the string around your wrist?

If you put a little bit of force into making the string swing, does the nut go all the way around?

Does the nut want to continue in a circular path or does it try to leave that path? Why do you think so?

What will the nut do if you let go of the string? If you decide to test this, be sure you are outside and not swinging the nut toward anything like a window. Take the loop off your wrist, swing the nut so it is going in a circle and let go of the string as it tops the circle. You can get a little idea of what it does by leaving the loop around your wrist, swing the nut by the first know and letting it go at the top of the circle. Be aware the nut could hit you when you do it this way.

Compare the speed of using a short string and using a long string. If you decide to time the swings, have a friend use the stopwatch. It would be easier to get an accurate time if your friend times three to five revolutions instead of one.

Try drawing the vectors to show how the nut travels in a circular motion. Remember one vector will follow the string as it holds the nut in the pathway. Which way will the nut’s forward vector point? Will it be curved or straight? Does gravity have much of an effect on this motion?

 

What I Found Out:

The nut was easy to put on the string. If it hits something breakable like a window, this is bad news. Keeping the string attached to my wrist and taping the knot holding the nut on the string made sure it couldn’t fly off and hit anything or anyone.

My hand swung back and forth to make the nut swing. This hand movement could turn the nut into a pendulum, even one that went very high. It did not make the nut go around in a circular pathway.

I had to move my hand in a circular path to get the nut to go around. With the short string, the nut went around very easily. It was very hard to slow down enough for the nut to not go around.

The longer string took more and bigger movements of my hand to get it started going around. If I slowed down at all, the nut would make only a partial circle and fall down toward the ground.

Once the nut was going around on the long string, I could make the same small movements with my hand to keep it going as long as I kept it going fast enough to go around.

I think gravity pulls on the nut. When the nut is going fast enough, gravity can’t pull hard enough to make it fall. If the nut slow down, gravity takes over and pulls it down.

I could feel the nut pulling on my hand as it went around. There was a bigger pull with the longer string.

When I let go of the string, the nut flew out away from the circular path. I had to keep the loop around my wrist doing this so the nut hit the end of the string and fell to the floor.

The nut was traveling fairly fast around the path making timing challenging. The short string gave me 3.09 sec and 3.06 sec for five times around. The long string times to 3.62 sec and 3.56 sec. The longer string seemed to give a longer time for each revolution. I would wonder how accurate this is because I could not measure the force used to make the nut go around so this may have been very different for the long and short strings.

circular motion vectors

There are three vectors interacting in circular motion. One points in to the center of the circle holding the object in its circular pathway. One is the pull of gravity. One is the straight line motion path the nut would take if the other two forces did not exist.

Drawing the vectors depends a little on where the nut is on the circular pathway. One vector arrow must point down toward my hand. I know this because I had to hold onto the string and felt the nut trying to pull free.

One vector arrow will point down toward the ground. This is gravity. It is a smaller arrow as the nut is going around, not falling straight to the ground.

The last vector arrow goes straight out from wherever the nut is. The nut is trying to go in a straight path. The vector arrow pointing to the hand keeps it from flying off so the straight vector is bigger than the gravity arrow and smaller than the one going to the hand.

Physics 9 Acceleration

Speed is the distance something goes in a certain amount of time. The speed stays the same. Except we know things go faster or slower and change direction. This is acceleration.
When Albert Einstein developed his Theory of Relativity, he made an assumption about gravity. He said it was a form of acceleration.
If gravity is a form of acceleration, it will make an object’s speed change over time.
Galileo worked with gravity too. He rolled balls down a ramp and found out something interesting about their final speeds.

setting up the acceleration project

I used the same set up I used for measuring speed. the ball ramp was taped to the chair with the meter stick on the floor.

Question: How does gravity change a ball’s speed?
Materials:
Ball ramp
Ball
Meter stick
Stop watch
Procedure:
Mark a place on the ramp to start rolling the ball
Measure the distance the ball will roll and divide it by four
Measure one fourth the distance and put a mark

marks on ball ramp

Each place on the ramp must be clearly marked. Will the ball go twice as fast from the top mark as from the half way mark?

Measure one half the distance and put a mark
Measure three fourths the distance and put a mark
Set up your ramp with the top mark0.5 m high
Set up the meter stick on the floor beside where the ball will roll with the beginning 10 cm from the end of the ramp
Write down how you think the ball’s speeds will compare for the four different starting points [Will the ball go half as fast when started half way down the ramp?]
Do at least three trials starting the ball from each mark.
You will start the stop watch when the ball reaches the beginning of the meter stick and stop it when the ball is at the end of the meter stick.
Observations:
Write down the four distances on the ramp:
Highest 1:
2:
3:
4:
How will the speed of the ball compare for each starting point?
Times for 1:
1:
2:
3:
Average
Times for 2:
1:
2:
3:
Average:
Times for 3:
1:
2:
3:
Average
Times for 4:
1:
2:
3:
Average

releasing ball on ramp

Aiya Taylor helped me with this project by letting go of the balls on the ramp. Help is important for these projects.

Analysis:
Calculate the average time for each starting point by adding up the times for the trials and dividing by the number of trials.
Draw a graph of speed and height. (Use 1/4, 1/2, 3/4 and 1 for the height.)
Conclusions:
Are you measuring final speed or acceleration? Why do you think so?
Is this measurement a good way to judge acceleration? Why do you think so?
Speed is constant so the line on your graph would be straight. Is your line straight?
Galileo decided gravity added acceleration at meters per second (speed) per second. This gives a curved line on a graph. Is your line curved?
Does your graph show speed or acceleration?

What I Found Out:
My ball had an average time of 44 seconds for the top mark. The time decreased to 39 seconds for the 3/4 mark. The time increased to 47 seconds for the 1/2 mark. The 1/4 mark had a time of 93 seconds.
It was hard to get good times for each trial run. But the time was definitely increasing as the height decreased. I think the 3/4 mark average was not accurate.
Because the ball was running on the level floor when I measured the time, I was measuring final speed not acceleration. The final speed was produced by the acceleration on the ramp so it was a good way to compare how much acceleration the ball gained at each height.
My graph was not a straight line so it showed acceleration.

Physics 8 Speed

So far we’ve seen vectors showing direction of a force and distance and direction of motion. Motion is a change in where an object is.

Sometimes that motion is very slow. Other times the change is very fast. The measurement of how fast something moves is speed.

Notice speed concerns two things. One is distance as the object is moving from one place to another over a distance. The other is time. It measures how much distance an object goes in a certain amount of time.

Measuring distance requires a meter stick. Measuring time requires a stop watch.

Although it is possible to do Projects using a stop watch by yourself, having help makes them much easier.

Scientists use the metric system. If you don’t have a meter stick, you can use a yardstick. You can convert yards into meters by multiplying the yards by 0.914 meters per yard. For measurements in inches you multiply by 2.540 centimeters per inch.

Remember our Project about forces and friction when getting ready for this Project. You need a smooth floor without carpet this time to minimize friction. If you can’t find a place like that, put down smooth cardboard so the ball rolls over it at least a meter.

Ball ramp, scale and balls for project

Question: Does mass affect speed?

Materials:

2 balls of different weights

Ramp 1 meter long for the balls

Meter stick

Stop watch

Scale

Procedure:

Mass the balls and record the masses

heavy ball mass 18.00 g

My heavy ball is a rubber ball with a mass of 18.00 g.

Set up your ramp so the end is 0.5 m high where you will start the balls

ball ramp in chair

I taped the ball ramp to a chair so it would remain the same for the entire project.

Put the meter stick on the floor 10 cm away from where the ball will roll onto the floor but not so the ball will hit it

Mark where you will start the balls

mark on ball ramp

Putting a mark on the ramp means the ball is released at the same point each time so it’s final speed will be the same each time.

Write down your prediction of whether speed is affected by mass or whether the light ball or heavy ball will be faster or if they will be the same.

You will start the stop watch when the ball gets to the meter stick and stop it when the ball gets to the end of the meter stick

Time how fast each ball covers the meter. Do each ball at least three times. Record the times.

Observations:

Mass ball 1

Mass ball 2

light plastic ball mass 3.07 g

My light ball is plastic with a mass of 3.07 g.

Your prediction about the speed of the two balls:

Times for ball 1

1:

2:

3:

Average t:

Times for ball 2

1:

2:

3:

Average t:

Analysis:

Average the times for each ball by adding up all the times then dividing by the number of trials.

Conclusions:

Compare the speeds of the heavy and light balls.

Do you think mass affects speed? Why do you think so?

Aiah Taylor releasing light ball on ramp

Aiah Taylor, 5, helped with this project by releasing the balls down the ramp so I could time them.

What I Found Out:

The first thing I found out was that it is impossible to let a ball go down the ramp, back up to take a picture and time it for 1 meter at the same time. Luckily for me I found someone to help. Aiah Taylor was home from kindergarten for the day and was happy to let the ball go down the ramp whenever I asked.

My light ball had a mass of 3.00 g. the heavy ball had a mass of 18.00 g.

When we dropped the two balls, one heavy and one light, they fell at the same rate. I think their speed will be the same too.

The heavy ball had .44 sec for all three trials. That gave an average of .44 sec.

The light ball had .44 sec, .48 sec and .35 sec. That gave an average of .42 sec which was almost the same.

I found it was very difficult to time the ball for the 1 meter as it was going so fast.

Since the speeds were so similar, I don’t think mass affects speed.

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

first vector

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

second vector

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

street line

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

first vector

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

second vector

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

final vectors going home

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

 

On Your Own

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:

vector graph for the 3rd trip

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.

Physics 1 What Is a Force

Be sure to start a Physics Journal to keep track of all your physics projects. Sometimes one Project will ask you to take another look at a Project you did earlier. A Journal makes this easy to do.

Physics journal

A physics journal doesn’t have to be fancy, just full of paper to write on. That way all or your observations are in one place, easy to find.

Physics can be very hard with lots of difficult math. But some parts of physics are much easier. Those are the ones we will be doing this year.

Physics tries to explain forces. What is a force? The easiest definition of a force is: A force is a push or a pull.

Since physics is about forces, we will start with some simple forces and how they work.

Physics Project 1 materials

Question: What is a force?

Materials:

2 Small blocks of wood

Ball

Scale

Procedure:

Open your Physics Journal and write the Project number

Physics Journal entry

In my Physics Journal I put only the Project number and question. then I list the observations, analysis and conclusions. If I did not have the materials and procedure on the computer, i would put those in my Journal too.

Set a block of wood on a table then leave the room

wood block on table

Left setting on a table a wood block sits there not moving.

Come back in the room and look at the block of wood

Did the block of wood move?

Push on the block of wood with a finger

Does the block of wood move?

pushing the block

Pushing on the wood block caused the block to move in the direction of the push.

Pull the block of wood using a finger

Does the block of wood move?

Hold the ball in your hand

Does the ball stay in your hand?

Drop the ball

What does the ball do?

Place one block of wood on the scale

Weighing Block 2

Block 2 has a weight of 57.57 g. It wavered between 57.56 g and 57.57 g but finally settled on 57.56 g.

Place the second block of wood on the scale

Put both blocks of wood on the scale

 

Observations:

Did the block of wood move?

What happens when you push the block of wood?

What happens when you pull the block of wood?

What does the ball do in your hand?

What does the ball do when you drop it?

How much does one block of wood weigh?

Weighing Block 1

Block 1 had a weight of 32.13 g.

How much does the second block of wood weigh?

How much do both blocks of wood weigh?

 

Analysis:

Add up the masses of the two blocks of wood

weighing both blocks

Together the wood blocks have a weight of 89.69 g.

Conclusions:

What makes the block of wood move?

Why doesn’t the block of wood float off the table?

Why does the ball sit in your hand?

ball in hand

A ball sits in the hand as long as it is held there.

Why does the ball drop when you let it go?

A contact force is a force you apply directly to an object. A non-contact force is a force applied to an object without touching it. Which of the forces applied to the block of wood and the ball were contact forces and which were non-contact forces? Explain why you think this.

Compare the masses of the two blocks on the scale and the two masses you added up. Do masses combine? Why do you think so.

Weight is a measurement of the pull of gravity. Do you think forces combine? Why do you think so?

 

What I Found Out

My block of wood didn’t move by itself. It did move when I pushed or pulled it. Pushing or pulling the block makes it move. It sits on the table because of gravity.

pulling the block

Pulling on the wood block caused the block to move across the table in the direction it was pulled in.

The ball sat in my hand because I was holding it until I dropped it. Then it fell down to the table. Gravity pulled the ball to the table.

dropped ball

This was not a bouncy ball. It fell to the table with a thud when I let go of it.

Pushing and pulling the block of wood were contact forces because I had to touch the block to make it move. Gravity is a non-contact force because it works without touching the block or the ball.

The total mass of the two blocks was 89.69g and the added mass of the two blocks was 89.69g which is the same so I think masses can be combined or added together. Gravity creates weight and is a force so I think forces can be combined.