# Labs from Chicago, Fall 1993 : Conservation of Momentum.

Dr. Rich Kron, Dr. Heidi Newberg, and Luisa Rebull
Labs written for the CARA Space Explorers, Fall 1993

This is meant to be handed out to the students.

## I. Introduction

Velocity - Speed is a measure of the time it takes to move a given distance. Velocity is the same thing as speed, except you also specify what direction. For example, if you drove to a store that is 50 miles away, and it took you one hour to get there, then you were traveling at a speed of 50 miles per hour, on the average. If the store is directly north from your home, then your average velocity was 50 miles/hour to the north. If on the way home you were stuck in slow traffic and it took 2 hours to get home, then on the average you went 25 miles per hour on the second trip. Your average velocity was 25 miles per hour towards the south.

We calculated the average velocity (which we can represent by the letter v) by dividing the distance (represented by d) by the time (represented by t). It is often clearest to represent this relationship by an equation. In this case, the equation is:

v = d / t

(NOTE: read this equation as "velocity equals distance divided by time".)

Using this equation, we can calculate the velocity in the first example by putting 50 miles, which is the distance, where the "d" is, and putting 1 hour, which is the time, where the "t" is. Then, we do the division to find the average velocity.

v = (50 miles) / (1 hour) = 50 miles/hour

The second example is represented by:

v = (50 miles) / (2 hours) = 25 miles/hour

Using this formula, we can calculate the average velocity of anything if we know how far it went in how much time. To make it really velocity instead of speed, we should also specify which direction the object is going.

In our lab, we will be measuring velocities in centimeters per second (cm/s). An inch is about 2.5 centimeters long.

inch: centimeter:

mass - Mass is a measure of how much stuff is in an object. Most people associate it most closely with weight, since our best method for measuring mass is to find out how hard gravity pulls the object towards the ground. The more an object weighs, the more massive it is.

In our experiment, we will measure masses in grams. A gram is the mass of a container of water that is one centimeter tall, one centimeter wide, and one centimeter thick.

momentum - In physics terms, momentum is an object's mass multiplied by its velocity. For example, if a 30 gram mouse is crawling at 10 centimeters/second to the south, then the momentum is 30 x 10 = 300 gram-centimeters/second. (We will be careful to attach such units to measured quantities. Something like "gram-centimeters/second" may seem unfamiliar, but it is really just like "miles/hour" or "dollars/gallon.") Momentum is traditionally not represented as an "m". This is because mass is represented as an "m". We usually use a "p". So, keeping this oddity in mind, the equation for momentum is:

p = m * v

(NOTE: Read this as "momentum equals mass times velocity".)

Momentum is an interesting quantity because it is conserved. This means that if you start out with a momentum of 300 gram-centimeters/second, and nothing disturbs you, then you will continue to travel at 300 gram- centimeters/second forever. This might seem absurd to you. That mouse surely will stop, change directions, and eventually die and decay. How can there be conservation of momentum?

The tricky part is that we specified that "nothing disturbs you." In the case of a mouse on the floor, it can change directions by pushing on the floor, thus interacting with something outside the system. Imagine trying to change directions when you are walking on something that is hard to push against, like ice. The only place that conservation of momentum is easy to observe is in space, where there is no air, no floor, no stray objects to interact with the system we are studying.

When I use the word system, I mean all of the objects we are considering - for example, just the mouse. We could have several objects that interact with each other, but with nothing else. In that case, one object could transfer some or all of its momentum to another object, but the sum of all of the momenta in this system would remain the same. In the laboratory, we will measure the momentum of little cars that are on air tracks. The air coming out of the holes in the air tracks forms a small layer of air that will keep the cars a little bit above the metal air track. That will help keep the cars from interacting with the air track the way mice interact with the floor. We will use a system that is just one car first, then we will look at a couple of systems that have just two cars. In principle, we could make systems that have more than two cars, but that would just complicate the experiments and the calculation. Remember, if the cars bump into anything, like the ends of the track, momentum is no longer conserved, since the car has interacted with something outside the system. In later laboratories, we will understand more about what happens in these interactions with things that are outside the system.

## II. Activities

### Velocity

Push all of the cars except one off to the ends of the track. Position your car so that it is to the left of both of the timers. Make sure the timers have been set to zero. Gently push the car towards the timers. The timers will operate the whole time the metal sheet is passing it. So, the time on the timer will be the number of seconds it took the metal sheet to pass the timer. The metal sheet is exactly 10 centimeters long.

Time from first timer: _____________ seconds

Time from second timer: _____________ seconds

Now, find the speed the car had when it passed the first timer, and the speed the car had when it passed the second timer. The speed is 10 centimeters divided by the number of seconds on the timer. Write down the velocity, which is the speed, plus the words "to the right," since the car was traveling to the right.

Velocity when the car passed the first timer:

______________________________________________________

Velocity when the car passed the second timer:

______________________________________________________

Was momentum conserved? __________

### Inelastic Collision

Select two cars, and put the velcro attachments in so that they face each other (you can do this without removing the cars from the tracks). Place one of the cars to the left of both of the timers, and the other car between the two timers. Make sure the car between the timers is not moving. Make sure the timers are set to zero. Then, slide the car on the left so that it hits the second car. They should stick together after they hit.

Time on the first timer: ______________ seconds

Time on the second timer: _______________ seconds

Now calculate the velocity of the car before the collision, and the velocity of the two cars together after the collision. (REMEMBER: TWO CARS PASSED THE SECOND TIMER, SO 20 CENTIMETERS OF CAR WENT BY. ONLY TEN CENTIMETERS OF CAR WENT BY THE FIRST TIMER.)

Velocity before collision:

____________________________________________________

Velocity after collision:

____________________________________________________

Now you have to weigh the two cars in the collision on the scale. There is a scale at each end of the room. The mass before collision is the mass of the first car, and the mass after collision is the mass of the two cars together.

Mass first car: _____________ grams

Mass of two cars together: ______________ grams

Finally, calculate the momentum before and after the collision.

Momentum before collision:

______________________________________________________

Momentum after collision:

______________________________________________________

Is momentum conserved? ______________

### Explosion

Choose two more cars. Put the spring mechanism in the facing ends of the cars. Push the cars together so that the suction cup holds the cars together. Place the cars between the timers. Make sure the timers are zeroed. Release the cars. (THE CARS SHOULD NOT BE MOVING BEFORE THEY ARE RELEASED.) The cars should spring apart and fly in opposite directions.

Time on first timer: ___________ seconds

Time on second timer: ___________ seconds

Again, calculate the velocity of the two cars.

Velocity of first car: (don't forget direction)

______________________________________________________

Velocity of second car:

______________________________________________________

Again, measure the mass of each car:

Mass of first car: ___________ grams

Mass of second car: ___________ grams

Calculate the momentum of each car:

Momentum of first car:

______________________________________________________

Momentum of second car:

______________________________________________________

Is momentum conserved? ___________

## III. Examples of possible quiz questions for next week

1.If it takes 1 hour to drive to Fermilab, which is 30 miles west of Chicago, what is the average velocity on the trip?

2.If the car you drive in to Fermilab weighs 500,000 grams, what is the average momentum during the trip?

3.A car on an air track is not moving. Another car crashes into it and sticks. Do the two cars together move faster, slower, or the same speed as the original moving car?

4.Two cars that have the same mass are stuck together with a spring, and can move freely on an airtrack. If the cars start out motionless, then explode apart, then:

• (a) Their velocities will be the same but in opposite directions.
• (b) Their velocities will be the same and in the same direction.
• (c) The one on the left will move faster than the one on the right.
• (d) Although the cars have the same momentum, their velocities depend on their mass.
5.If momentum is conserved, then how can a mouse stop, thus reducing its momentum to zero?
• (a) Momentum is not conserved for mice.
• (b) The mouse interacts with the floor, so conservation of momentum does not apply to the system of just the mouse.
• (c) Mice can't stop, they keep moving forever.
• (d) Momentum is not conserved for one mouse, but it would be conserved if there were two mice.