An elevator (mass M = 2000 kg) is moving downward at v₀ = 1.5 m/s. A braking system prevents the downward speed from increasing. 

(a) At what rate (in J/s) is the braking system converting mechanical energy to thermal energy?

(b) While the elevator is moving downward at v₀ = 1.5 m/s, the braking system fails and the elevator is in free fall for a distance d = 5 m before hitting the top of a large safety spring with force constant k = 1.5 × 10⁴ N/m. After the elevator cage hits the top of the spring, we want to know the distance ∆y that the spring is compressed before the cage is brought to rest. Write an algebraic expression for the value of ∆y in terms of the known quantities M, v₀, g, k, and d, and substitute the given values to find ∆y.