# 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.

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.

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.

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.

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.

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.

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.

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

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.]

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.

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

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?

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.

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 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.

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

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

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.

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

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

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

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

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

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, 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.