A block is released from rest at the top of a high frictionless ramp
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A 2.0kg block is released from rest at the top of a 1.5m high frictionless ramp. At the bottom of the ramp the block moves onto a horizontal, frictionless surface and collides with an ideal spring of force constant 600N⋅m−1 that is initially at its relaxed length. The block compresses the spring and comes momentarily to rest.
(1) Derive an algebraic expression for the maximum compression xmax of the spring using the bottom of the ramp as the position where gravitational potential energy is zero.
(2) Derive a second algebraic expression for xmax if the reference position for potential energy is instead chosen at the point of maximum spring compression.
(3) Show explicitly that both expressions obtained in parts (a) and (b) lead to the same numerical value of xmax. Provide a clear sequence of mathematical steps.
(4) Briefly discuss the physical significance of your result in part (c) with respect to the choice of potential–energy reference level in combined gravitational–elastic systems.