# Physics 18 Momentum

We met Newton’s First Law of Motion some time ago when we ran the little cars down a ramp with pennies on their roofs. The car stopped. The penny didn’t. Inertia was the reason but the penny also had momentum. Where did that momentum come from?

Recently we dropped a ball while walking. Even though we didn’t try to push the ball, it still moved forward as it fell. The ball had momentum. Where did it come from?

When a moving object hits another motionless object, some of the momentum must transfer to the other object. Think about what happens when a bowling ball hits the pins. Think about catching a ball and how your hand feels especially the difference between a fast ball and a slow ball.

Question: How do mass and velocity affect momentum?

Materials:

Ramps [1 with marked meter]

2 identical balls [Ball 1 and Ball S]]

1 smaller, lighter ball [Ball L]

1 heavier ball [Ball H]

Stopwatch

Meter stick

Scale

Procedure:

Mass the balls

Ball 1 has a mass of 18 g. It’s momentum will change with its velocity.

Set up the ramps so one ends at the edge of a table [like in Project 17]

Mark 2 starting lines so one is twice the height of the other

The sloped ramp accelerates the ball. The flat ramp sets up the collision.

Use the stopwatch to find the velocity of Ball 1 released from each of the starting lines

Remember to do several times for each

Timing is important for determining velocity of Ball 1.

Set Ball L at the end of the ramp

Release Ball 1 at the lower starting line

Mark where Ball L lands [You may want to use a long box with towels in it to catch the balls.]

Observe what Ball 1 does after the collision

Measure the distance

Repeat this several times

Put Ball L back at the end of the ramp

Release Ball 1 at the higher starting line

Mark where Ball L lands

Observe what Ball 1 does after the collision

Measure the distance

Repeat this several times

Repeat this using Ball S and then Ball H

Observations:

Mass of balls

Ball 1

Ball L

Ball S

Ball H

Velocity (m/s):

Low starting line

High starting line

Distances:

Ball L

Low starting line:

High starting line

Ball S

Low starting line

High starting line

Ball H

Low starting line

High starting line

What Ball 1 does after the collision

Ball L

Low starting line:

High starting line

Ball S

Low starting line

High starting line

Ball H

Low starting line

High starting line

Analysis:

Calculate the average time for the low and the high starting line to get the velocities

Momentum is the mass (in grams) of an object times its velocity (m/s). Any moving object has momentum because it is moving.

Ball 1 accelerates down the ramp. Increased velocity turns into momentum transferred to the ball at the end of the ramp when the two collide.

Calculate the momentum of Ball 1 for each starting line.

Make a graph of the distances for the balls [ball vs. distance]. Do the three low starting line distances in a group and the three high starting line distances in a group.

Conclusions:

Which starting line provides the most velocity to Ball 1? Why?

Which starting line provides the most momentum to Ball 1?

Which starting line transfers the most momentum to the other ball? Why do you think so?

Which ball, L, S or H, had the most momentum? Why do you think so?

How does mass affect momentum?

How does velocity affect momentum?

If you are riding in a car going 60 MPH [2.5 m/s], what is your momentum? [1 pound is about 2.2 kg]

If you divide the momentum by 2.2, you get your relative mass if the car suddenly stops as in a crash and you continue on like the pennies did. Why are seat belts useful in a car crash?

What I Found Out:

I set up my ramps a little longer than for Project 17 so I would have a little more time to do the timing for the velocity. This helped a lot since I work alone.

My ball masses were 18 g for Balls 1 and S, 2.08 g for Ball L and 53.78 g for Ball H.

From my low starting line my velocity was 1 m/.68 s. This gave me a momentum of 26.4 g-m/s. The high starting line had an average velocity of 1 m/.47s giving a momentum of 36.1 g-m/s.

Gravity pulls the ball down the ramp. The more time and height. The more gravity pulls making the ball go faster. Since the mass remains the same from either line, the velocity affects the momentum. The greater the velocity, the greater the momentum.

The lightest ball was one ninth the mass of Ball 1. When hit by Ball 1, it almost flew out of the ramp.

When Ball 1 hit Ball L from the low line, Ball 1 bounced out of the ramp and Ball L went an average of 68.5 cm. When Ball 1 started at the high line, both balls went off the ramp but Ball L went an average of 106 cm and Ball 1 mostly fell straight down.

When Ball 1 hit Ball S from the low line, it bounced back inside the ramp. Ball S went an average of 17.8 cm. From the high line Ball 1 bounced back less and Ball S went an average of 29.9 cm.

When Ball 1 hit Ball H from either line, it stopped. Ball H went an average of 10 cm from the low line and 22.4 cm from the high line.

The higher starting line gave Ball 1 more momentum so it could give more to the other balls. This showed as the average distances for the high line were greater for all the balls than the average distances for the low line.

Ball L went the farthest both times so it got the most momentum from Ball 1. I think this was because the ball had the least mass so more force was used to create velocity than to make the ball move. The greater the velocity, the greater the momentum.

Once a ball is moving, if all the balls moved at the same velocity, the heaviest ball would have the most momentum.

If I were in a car moving 60 MPH, I would have a momentum of 605 kg-km/s. this would give me a relative mass of 275 pounds. A seat belt keeps me from hitting the front of the car that hard.

# Physics 17 Projectile Challenge

Do you like a challenge?

We are going to set up a slanted ramp leading to a level ramp ending at the edge of a table. When we release the ball at the top of the first ramp, it will accelerate as it comes down into the second ramp which will launch it out in an arc from the edge of the table until it hits the floor.

Where will the ball land on the floor? That’s the challenge. Can you calculate where the ball will land?

Question: Where will the ball land?

Materials:

Two ramps [one must be over a meter long]

Meter stick

Stopwatch

Pan 10 to 15 cm across

Ball

Procedure:

Mark out 1 m on the long ramp

Knowing the velocity of the ball is critical in your calculations. Using a 1 meter section is long enough so timing can be done but not so long the ball will slow down much due to friction.

Set up the long ramp level on the table top so it ends at the edge of the table

Set up the second ramp on a slant so the bottom end leads into the long ramp

The ramps are set up and appear straight. I found the ball itself would cause the ramps to shift a little. I didn’t tape the central part in place and should have.

Make sure both ramps are secured in place

Put a barrier at the edge end of the long ramp to stop the ball [a cloth will work]

Why stop the ball? So you won’t know where to put the bucket without calculating the distance using your measurements.

Mark a starting line near the top of the slanted ramp

Release the ball at the starting mark

Time how fast the ball goes over the marked meter in the long ramp

Repeat this at least three times or until each time is close to the others

Take the barrier out of the long ramp

Measure the distance from the edge of the long ramp to the floor in meters

Calculate the distance the ball will go before hitting the floor [See analysis]

Place your pan with a cloth or sand in it to keep the ball from bouncing where you think the ball will land [Make sure it is straight out from the ramp.]

Note: Be sure you measure from straight down from the edge of the ramp. Why?

Release your ball at the starting mark

If your ball does not land in your pan, try the challenge again

Observations:

Velocity times:

Timing a ball for one meter is difficult. It covers the meter in about half a second.

Distance to the floor:

Analysis:

You have two formulas to work with: d = vt and d = at2.

Remember a is due to gravity and is known to be 9.8 m/s2.

Look back at Physics Project 16 to see which formula tells you how the ball moves, forward or downward. Which values do you know?

Give it a try on your own.

If you have trouble:

When you measure the time it takes for your ball to travel one meter on the long ramp, you have the v for the first equation. The d will be how far the ball goes when it leaves the ramp which you don’t know yet. The time is how long the ball will be in the air when it leaves the second ramp which you also do not know yet.

The height from the edge of the ramp to the floor is the d in the second equation. You also know the a. Use a calculator to solve for t as you must find the square root.

Now you know the t for the first equation and can calculate the d.

Notice the jag in the ramp. I had to correct this then place my bucket to catch the ball.

Conclusions:

What I Found Out:

I will admit I do these Projects in a hurry and am often a bit careless in my measurements. That is a recipe for disaster in this challenge.

First problem: The ramps must line up in a straight line or the ball will wobble from side to side or even jump out of the ramp.

Second problem: Both releasing the ball and working the stopwatch. It helps a lot to work with a friend.

Third problem: Measuring the height at which the ball is released accurately if this is not the very top of the ramp. My first measurement was off by almost 2 cm. Also note this measurement is not to the top edge of the ramp but the place the ball is set.

Will the ball land in the bucket? It took several measurement corrections and calculations, but it finally did.

In case you haven’t figured it out by now, my ball missed my bucket for several tries. I redid my height measurement first. This helped. Then I retimed the ball and found I was off by over half a second.

My ball did finally land in the bucket.