This is meant to be handed out to the students.
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.
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.
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? __________
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? ______________
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? ___________
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:
Important Disclaimers and Caveats