Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 33_H

In Fig. 8.29, a spring with \( k = 170 \text{ N/m} \) is at the top of a frictionless incline of angle \( \theta = 37.0^\circ \). The lower end of the incline is distance \( D = 1.00 \text{ m} \) from the end of the spring, which is at its relaxed length. A \( 2.00 \text{ kg} \) canister is pushed against the spring until the spring is compressed \( 0.200 \text{ m} \) and released from rest. (a) What is the speed of the canister at the instant the spring returns to its relaxed length (which is when the canister loses contact with the spring)? (b) What is the speed of the canister when it reaches the lower end of the incline?