LINEAR MOMENTUM

Film Loop: Colliding Freight Cars

Length: 2:45 min., Black and White, No sound

This film shows a test of freight-car coupling. The collisions, in some cases, were violent enough to break the couplings. The "hammer car" coasts down a ramp, moving about 6 miles per hour. The momentary force between the cars is about 1,000,000 pounds. The slow-motion sequence allows measurements to be taken of the speeds before and after impact, and thus tests conservation of momentum. The collisions are partially elastic, as the cars separate to some extent after collision.

The masses of the cars are: hammer car: m1 = 95,000 kg, target car: m2 = 120,000 kg. To find velocities, measure the film time for the car to move through a given distance. (It may be necessary to run the film several times.) Use any convenient unit for velocities.

Simple timing will give v1 and v2. The film was made on a cold winter day and friction was appreciable for the hammer car after collision. One way to allow for friction is to make a velocity-time graph, assume a uniform negative acceleration, and extrapolate to the instant after impact.

An example might help. Suppose the hammer car coasts 3 squares on graph paper in 5 seconds after collision, and it coasts 6 squares in 12 seconds after collision. The average velocity during the first 5 seconds was v1 = (3 squares)/ (5 sec) = 0.60 squares/sec. The average velocity during any short, interval approximately equals the instantaneous velocity at the mid-time of that interval, so the car's velocity was about v1 = 0.60 squares/sec at t = 2.5 sec. For the interval 0-12 seconds, the velocity was v1 = 0.50 squares/sec at t = 6.0 sec. Now plot a graph: The graph shows that v1 = 0.67 squares/sec at t = 0, just after the collision.

Compare the total momentum of the system before collision with the total momentum after collision. Calculate the kinetic energy of the freight cars before and after collision. What fraction of the hammer car's original kinetic energy has been "lost?" Can you account for this loss?