A 3.0kg crate is released from rest at the top of a rough, frictionless ramp that is 4.0m long and inclined 30∘ above the horizontal. At the bottom of the ramp the crate slides onto a horizontal track and immediately compresses a light spring that is fixed to a wall. The spring has force constant 600Nm−1. Friction is negligible everywhere.
parts:[{"content":"(a) Calculate the speed of the crate just as it leaves the ramp and first makes contact with the spring."},{"content":"(b) Determine the maximum compression of the spring."},{"content":"(c) While the spring is being compressed, find the speed of the crate at the instant when the compression equals one-half of the maximum value you found in part (b)."},{"content":"(d) At the instant described in part (c), state the amount of each of the following energies present in the system: gravitational potential energy (relative to the bottom of the ramp), elastic potential energy, and kinetic energy."}]