Springs A and B are mounted horizontally on a low-friction track

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

Problem

Springs A and B are mounted horizontally on a low-friction track. Each spring is compressed

0.10\,\text{m}

from its relaxed length by an identical

0.250\,\text{kg}

glider that is initially held at rest against the spring. When released, the glider leaves spring A with a speed of

2.5\,\text{m}\,\text{s}^{-1}

and leaves spring B with a speed of

3.5\,\text{m}\,\text{s}^{-1}

. Neglect any dissipative effects. (a) Develop an expression for the stiffness constant of a spring in terms of the block’s mass

m

, the compression distance

x

, and the speed

v

of the block as it loses contact with the spring. (b) Using your expression, calculate the stiffness constant for each spring. Include units and show all steps. (c) Compute the ratio

k_B/k_A

and explain what this ratio indicates about the relative stiffness of the two springs. (d) Discuss one experimental limitation or assumption in this procedure that could affect the accuracy of the calculated stiffness constants, and propose a modification that would reduce its impact.

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