A spring has a natural length of 8 in. If it takes a force of 16 lb to compress the spring to a length of 6 in., how much work is required to compress the spring from its natural length to 7 in.? (Round your answer to four decimal places.)

Explanation:

Work in a Spring

Suppose we have a spring of constant k and natural length xo. When it's unstretched, the force exerted by the spring is 0. When the spring is stretched to a length x1, the spring exerts a force given by the Hooke's law:

Where

We have the following data

Solving the first equation for k

Plugging in the given values

When the sping is compressed to 7 inches:

The work required to compress the spring is

seeing the graph would