A block of mass rests on a frictionless horizontal surface and is attached to an…

PHYSICS · Multi-part · AP · Physics C: Mechanics · Force and Translational Dynamics · Force and Translational Dynamics

Problem

A block of mass

m

rests on a frictionless horizontal surface and is attached to an ideal spring of force constant

k_s

. Starting at

t=0

, an external horizontal force that increases linearly with time,

F_{\text{ext}}(t)=Ct

, is applied to the block in the direction that compresses the spring. The block is observed to remain at rest during the interval of interest. (a) Derive an expression for the spring’s compression

x(t)

in terms of

C

k_s

, and

t

while the block remains at rest. (b) For

k_s = 200\,\text{N}\!\cdot\!\text{m}^{-1}

and

C = 10\,\text{N}\!\cdot\!\text{s}^{-1}

, calculate the time required for the spring compression to reach

0.10\,\text{m}

. (c) Determine the elastic potential energy stored in the spring at the instant found in part (b), and explain how the work done by the external force up to that time is partitioned among the system’s energy forms.

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