A block of mass is initially at rest at the top of a frictionless incline of length…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A block of mass m is initially at rest at the top of a frictionless incline of length L that makes an angle θ with the horizontal. The bottom of the incline meets a horizontal surface where an ideal spring with spring constant k is attached. The block slides down the incline, continues onto the horizontal surface, and compresses the spring a maximum distance x before momentarily coming to rest.
(a) Derive an expression for the maximum compression x of the spring in terms of m, g, L, θ, and k.
(b) Evaluate x numerically for m=0.80kg, L=2.5m, θ=30∘, and k=550Nm−1.
(c) Determine the speed of the block just as it makes first contact with the spring.
(d) Describe, in words, the sequence of energy transformations that occurs from the moment the block is released until it is instantaneously at rest after compressing the spring.