Tag Archives: acceleration

Physics 22 Force and Mass

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

materials for project

Question: How are acceleration, force and mass related?

Materials:

Spring scale

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

String

2 Masses about the same

Stopwatch

Tape

Meter stick

Procedure:

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

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

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

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

Put the masses in the cups

Zero the spring scale

massing Cup 1

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

Use the scale to mass Cup 1 and Cup 2

Remove the mass from Cup 1

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

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

Put a loop in the loose end of the string

Put the cup 10 cm before the starting line

Put the mass in the cup

Hook the spring scale to the loop

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

mass and force stay the same

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

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

Record the force needed

Try pulling the cup faster recording the time and force

Remove the mass from Cup 2

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

Put the second mass in Cup 2

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

Record the force needed

Pull the cups faster recording the times and force needed

Observations:

Masses

mass on spring scale

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

Cup 1:

Cup 2:

Times:

One mass:

Force needed:

Both masses:

Force needed:

Conclusions:

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

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

How are force and mass related?

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

Why do you think this is the case?

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

How could you use greater force to move the cups?

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

pulling two masses

Doubling the mass being pulled does double the force needed.

What I Found Out:

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

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

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

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

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

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

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

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

Physics 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 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.