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Conservation of Momentum: Cart Collision
By Richard Duong and Heather Wolfe
Purpose: Two momentum carts collide with an inelastic collision. You are asked to determine the mass of one of the carts.
Video: Click on the picture above to load the movie in a new window. This is a 1.23 Mb file. To save the movie: Mac users: control click. PC users: right click then Save As. For help with the movie or how to get measurements, click here.
Introduction:
In our clip you will see the collision of two wooden carts (labeled #1 and #2), which stick together. The carts, although they appear to be identical, have different masses. Extra mass has been stuck to one of the carts to make it a different mass.
When you play the movie, the carts will collide. This type of collision is called an inelastic collision. This type of collision, through the conservation of momentum, is expressed by the equation:
Given that m1 = 0.90 kg, your objective is to find the mass of m2.
1. The first step to this problem is to find the distance cart #1 and cart #2 travel separately BEFORE the collision. Note that the dark marker strips that are placed along the ruler are at every 10 centimeters. (10 cm = 0.1 m). You should start from the first frame of the movie where the carts are rolling freely without being touched until the frame just before the carts collide. Count the frames as you go.
Distance cart #1 travels before the collision:
Distance cart #2 travels before the collision:
2. Once the distance traveled is found for cart #1 and cart #2, the time can be calculated given the fact that the movie plays at 30 frames per second. Calculate the travel time for both carts before the collision.Time cart #1 travels before the collision:
Time cart #2 travels before the collision:
3. Given the equation: v = d/t, find the velocity of both cart #1 and cart #2. Note that one direction must be denoted as positive while the other is negative. We recommend making motion to the left negative. (Velocity is measured in m/s.)
Velocity of cart #1 before the collision (v1):
Velocity of cart #2 before collision (v2):
4. Now you need the time it took from when the carts crashed into each other until they stopped moving was not timed, that information can be found by counting the number of frames from the moment of collision until the movie ends. Note that, like above, every 30 frames equals 1 second. Once you find the time it took for both carts moving together, find the distance using the ruler markingsand use the same equation as part 2 to find the final velocity. (Hint: since the carts bounce and oscillate when they collide, you might be better off using the portion of the motion when they are rolling but not bouncing.)Distance carts travel after collision:
Time carts spend travelling this distance:
Velocity of joined carts after the collision (v3):
5. Now you have all the information to solve for m2. Plug in your answers from the previous parts and solve for m2. Note that it might be easier if you have m2 on just one side of the equal sign. (your distance in part 1 needs to be in meters for your answer to come out correctly)
Questions:
1. What possible sources of error are there in this exercise?
2. In general, if the carts have equal masses, what will V3 turn out to be?
3. If one cart is not moving and the other one is prior to the collision of identical carts, what will be the ratio of V1 to V3?
Jeff Adkins, Director
astronomyteacher@mac.com
Cheryl Domenichelli, Assistant Director
cheryldomenichelli@antioch.k12.ca.us
4700 Lone Tree Way
Antioch, CA 94531
The ESPACE Academy is sponsored in part by a grant from the California Department of Education's Specialized Secondary Program.
