Chapter 10, Problem 1P

A hand exerciser utilizes a coiled spring. A force of $89.0 \text{N}$ is required to compress the spring by $0.0191 \text{m}.$ Determine the force needed to compress the spring by $0.0508 \text{m}.$

To determine

The force needed to compress the spring by $0.0508$ m.

Answer to Problem 1P

  $236.7\text{N}$

Explanation of Solution

Given:

Force $(F)=89\text{ N}$ ,

Extension $\left(X_1\right)=0.0191\text{ m}$

Extension $\left(X_2\right)=0.0508\text{ m}$

Formula used:

First, find the spring constant which is given by,

  $\begin{array}{l}k=\frac{F}{X_1}\\ k=\frac{89}{0.0191}\\ k=4659.0191\text{ N/m}\end{array}$

Calculation:

So, now find the required force using the same formula,

  $\begin{array}{l}{F}_2=k{x}_2\\ F_2=4659.0191\times 0.0508\\ F_2=236.7\text{ N}\end{array}$

Conclusion:

Hence, the force required force will be $236.7\text{ N}$ .