A certain spring has a spring constant of and can safely be compressed or stretched…

PHYSICS · Single correct · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics

Problem

A certain spring has a spring constant of

120\,\text{N/m}

and can safely be compressed or stretched by no more than

5.0\,\text{cm}

from equilibrium without permanent deformation. Engineers need the spring to generate at least

8.0\,\text{N}

of restoring force on a test mass. Which of the following evaluations is correct? (a) The requirement can be met: compressing the spring by

4.0\,\text{cm}

will produce the needed

8.0\,\text{N}

within the safe limit. (b) The requirement cannot be met: even at the maximum safe displacement the spring provides only

6.0\,\text{N}

, so a spring with

k \ge 1.6 \times 10^{2}\,\text{N/m}

is needed. (c) The requirement can be met by using the full

10\,\text{cm}

range from maximum stretch to maximum compression; this yields

12\,\text{N}

and stays within the allowed displacement. (d) The requirement can be met: a

6.7\,\text{cm}

compression gives

8.0\,\text{N}

, which is still less than the

5.0\,\text{cm}

safety limit.