Question

How far must you stretch a spring with k = 1000 N/m to store 200 J of energy?

Short answer

As the all we solve above from that we have , the spring's stretched distance is$0.63m$.

Step-by-step solution

Introduction

You must exert effort in order to compress or stretch a spring. You must apply a force to the spring that is the same magnitude as the force the spring applies to you, but in the opposite direction. Fext = kx is the force you apply in the direction of the displacement x from its equilibrium position.

Explanation

In a compressed or extended spring, the potential energy stored is,

$U_{\mathrm{s}}=\frac{1}{2}k(\Delta s{)}^2$

We have, $k$= spring constant and$\Delta s$is the length of the spring compressed or stretched.

Rewriting equation $\Delta s$,

$\Delta s=\sqrt{\frac{2U_{\mathrm{s}}}{k}}$

Putting $200\mathrm{J}$for $U_{\mathrm{s}}$and $1000\mathrm{N}/\mathrm{m}$for $k$, solve for $\Delta s$.

$\Delta s=\sqrt{\frac{2(200\mathrm{J})}{1000\mathrm{N}/\mathrm{m}}}$

$=0.63\mathrm{m}$

As the all we solve above from that we have , the spring's stretched distance is $0.63\mathrm{m}$.