A block oscillates horizontally on a frictionless surface

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Oscillations · Oscillations

Problem

A 0.40 kg0.40\,\text{kg} block oscillates horizontally on a frictionless surface, attached to an ideal spring. A coordinate axis is chosen so that the origin is located 0.080 m0.080\,\text{m} to the right of the spring’s relaxed length; displacements to the left of the origin are positive. When released from rest, the block is located at x=+0.060 mx=+0.060\,\text{m} (that is, 6.0 cm6.0\,\text{cm} left of the origin) and the spring is compressed relative to its relaxed length. (a) Determine the magnitude and direction (as left or right) of the restoring force on the block at the instant of release if the spring constant is 75 N m−175\,\text{N\,m}^{-1}. (b) Calculate the instantaneous acceleration of the block at that moment. (c) State whether the block will initially move toward or away from the origin, and justify your answer using your results from parts (a) and (b).

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