The kinetic energy of a trolley moving on rails without friction is 12 J. After loading, the mass

The kinetic energy of a trolley moving on rails without friction is 12 J. After loading, the mass of the trolley increases by 3 times, but its momentum does not change. Find the kinetic energy of a loaded minecar.

Data: Ek1 (kinetic energy of an empty trolley) = 12 J; m2 (trolley weight after loading) = 3m1 (trolley own weight); P (trolley impulse) = const.

1) Determine the speed of the loaded trolley: since P = const, then m1 * V1 = m2 * V2 = 3m1 * (V1 / 3) and V2 = V1 / 3.

2) Change in the kinetic energy of the trolley: Ek2 = m2 * V2 ^ 2/2 = 3m1 * (V1 / 3) ^ 2/2 = 3m1 * V1 ^ 2 / (2 * 9) = m1 * V1 ^ 2 / (2 * 3) = Ek1 / 3 = 12/3 = 4 J.

Answer: The kinetic energy of a loaded trolley is 4 J.