Chapter 8.5, Problem 8E

a.

To determine

To find the force constant.

Answer to Problem 8E

The force constant is 200 lb/inches.

Explanation of Solution

Given information: A spring has a natural length of 10 in. An 800-lb force stretches the spring to 14 inches.

Calculation:

As per the given problem,

  $800/4=200$

Hence, The force constant is 200 lb/inches.

b.

To determine

To find the work done in stretching the spring from 10 inches to 12 inches.

Answer to Problem 8E

400 in-lb work is done in stretching the spring from 10 in. to 12 in.

Explanation of Solution

Given information: A spring has a natural length of 10 in. An 800-lb force stretches the spring to 14 inches.

Calculation:

As per the given problem,

The amount of work can be calculated by solving the integral,

  $\begin{array}{l}{\displaystyle {\int }_0^{2}200xdx}\\ =400\end{array}$

Hence, 400 in-lb work is done in stretching the spring from 10 inches to 12 inches.

c.

To determine

To find distance far beyond its natural length will a 1600-lb force stretch the spring.

Answer to Problem 8E

8 inches far beyond its natural length will a 1600-lb force stretch the spring.

Explanation of Solution

Given information: A spring has a natural length of 10 inches. An 800-lb force stretches the spring to 14 inches.

Calculation:

As per the given problem,

The 1600 lb force will stretch the spring $\left(4-1600\right)/800=8$ inches beyond its natural length.

Hence, 8 inches far beyond its natural length will a 1600-lb force stretch the spring.