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?
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?
Answers
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
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