A vertical ideal spring with spring constant is suspended from a rigid support

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A vertical ideal spring with spring constant

120\,\text{N}\!/\!\text{m}

is suspended from a rigid support. A small block of unknown mass is attached to the free end of the spring, and the system is pulled downward so that the spring is stretched

0.12\,\text{m}

from its unstretched length. The block is momentarily held at rest in this position and then released upward at

t=0

. A motion sensor records the block’s initial upward acceleration to be

1.5\,\text{m}\!/\!\text{s}^2

. Air resistance is negligible. (a) Derive an expression for the mass of the block in terms of the measured acceleration

a

, the stretch

\Delta y

, the spring constant

k

, and

g

. (b) Calculate the numerical value of the block’s mass. (c) Suppose instead the block were released from a stretch of

0.060\,\text{m}

under otherwise identical conditions. Predict qualitatively how the magnitude of its initial acceleration would compare with

1.5\,\text{m}\!/\!\text{s}^2

and provide a brief explanation.

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