Chapter 8.5, Problem 34E

To determine

To check : Whether the statement is true or false.

Answer to Problem 34E

The statement is false.

Explanation of Solution

Given information :

A force is applied to compress a spring several inches. Assume the spring obeys Hooke’s law.

Formula used :

The work spent compressing n^th inch is given by ${\displaystyle \underset{n-1}{\overset{n}{\int }}kxdn}$ . K is constant of spring.

Calculation :

The given statement is false.

For any spring with constant k, the work spent compressing it the first inch is given by ${\displaystyle \underset{0}{\overset{1}{\int }}kxdn}={k\frac{x^2}{2}]}_0^1=\frac{k}{2}$ and the work spent compressing it the second inch is given by ${\displaystyle \underset{0}{\overset{1}{\int }}kxdn}=\frac{3k}{2}$

  $\therefore$ Three times the amount of work required.