Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 67_SSM

A spring (\(k = 200 \text{ N/m}\)) is fixed at the top of a frictionless plane inclined at angle \(\theta = 40^{\circ}\) (Fig. 8.42). A \(1.0 \text{ kg}\) block is projected up the plane, from an initial position that is distance \(d = 0.60 \text{ m}\) from the end of the relaxed spring, with an initial kinetic energy of \(16 \text{ J}\). (a) What is the kinetic energy of the block at the instant it has compressed the spring \(0.20 \text{ m}\)? (b) With what kinetic energy must the block be projected up the plane if it is to stop momentarily when it has compressed the spring by \(0.40 \text{ m}\)?