A package is released from rest at the top of a rough chute inclined at to the horizontal
PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power
Problem
A 4.0kg package is released from rest at the top of a rough chute inclined at 25∘ to the horizontal. After sliding 3.5m down the chute, the package reaches a horizontal spring with spring constant 450Nm−1. The coefficient of kinetic friction between the package and the chute (and between the package and the horizontal surface in front of the spring) is 0.18. The package compresses the spring and momentarily comes to rest.
Take g=9.8ms−2. Ignore any rotational motion or air resistance.
(a) Determine the speed of the package at the bottom of the chute just before it contacts the spring.
(b) Calculate the maximum compression of the spring.
(c) Compute the total thermal energy generated by friction from the moment the package is released until it momentarily comes to rest at maximum spring compression.
(d) If the spring subsequently pushes the package back up the chute, qualitatively describe how the maximum distance travelled up the incline compares to the initial 3.5m and explain your reasoning.