Question

Two coupled boxcars are rolling along at 4.0 when they collide with and couple to a third, stationary boxcar.

1.) What is the final speed of the three coupled boxcars?

2.) What fraction of the cars' initial kinetic energy is transformed into thermal energy?

Answer 1

Assume that the boxcars all have the same mass.

Use conservation of momentum:

2*m*vi = 3*m*vf

where m is the mass of one boxcar, vi is the initial speed, vf is the final speed.

2*m*4 = 3*m*vf

vf = 8/3

Initial kinetic energy is ki

1/2*(2*m)*vi^2 = m*4^2 = 16*m

Final kinetic energy kf is

1/2*(3*m)*(8/3)^2 = 1/2*(3*m)*(64/9) = (32/3)*m

The fraction of the car's initial kinetic energy that is transformed into thermal energy is (ki - kf)/ki