An object with m₁ = 5kg is attached to a spring of negligible mass. This mass/spring combination is then slid horizontally on a frictionless surface with a velocity of 5m/s towards a stationary object with m₂ = 6kg. Upon impact, the spring compresses, then we examine two cases. First, find the velocities of the two objects assuming the spring completely relaxes again after the interaction. Second, assume that m₂, after they separate, slides up a frictionless incline.

(a) What is the relative speed of the masses when the spring is maximally compressed?

(b) When the spring is completely compressed, how much potential energy does it have?

(c) If the spring constant is k = 2000 N/m, by how much (what distance) is the spring compressed at that point?

(d) If the spring relaxes while still on at the ground, what is the kinetic energy of m₂ just before it slides up the hill?

(e) If there is no friction on the hill, how high up the hill does m₂ go?

(f) If there is friction on the hill, and m₂ goes up the hill to a height of 0.5 meters, how much energy was dissipated?