Question

Two objects moving with a speed v travel in opposite directions in a straight line. The objects stick together when they collide, and move with a speed of v/6 after the collision.

(a) What is the ratio of the final kinetic energy of the system to the initial kinetic energy?



(b) What is the ratio of the mass of the more massive object to the mass of the less massive object?

Answer 1

initial kinetic energy = 0.5 * m1 * v^2 + 0.5 * m2 * v^2

initial kinetic energy = 0.5 * v^2 * (m1 + m2)

final kinetic energy = 0.5 * (m1 + m2) * (v/6)^2

final kinetic energy / initial kinetic energy =  0.5 * (m1 + m2) * (v/6)^2 / 0.5 * v^2 * (m1 + m2)

final kinetic energy / initial kinetic energy = (v/6)^2 / v^2

final kinetic energy / initial kinetic energy = 1 / 36

by conservation of momentum

initial momentum = final momentum

m1 * v - m2 * v = (m1 + m2) * v / 6

m1 - m2 = (m1 + m2) / 6

m1 - m2 = m1/ 6 + m2 / 6

m1 - m1/ 6 = m2 / 6 + m2

5m1 / 6 = 7m2 / 6

5m1 = 7m2

m1 / m2 = 7 / 5