$\"\"$

\

Work required to stretch a spring $\"\"$ inches from its natural length is $\"\"$ foot-pounds.

\

Work done by the object in moving from $\"\"$ to $\"\"$ is $\"\"$ .

\

Hooks law: $\"\"$ .

\

$\"\"$ .

\

Here $\"\"$ , $\"\"$ and $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Find the work required to stretch the spring an additional one-half inch.

\

Thus $\"\"$ , $\"\"$ and $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Therefore, work required to stretch the spring an additional one-half inch is $\"\"$ .

\

$\"\"$

\

Work required to stretch the spring an additional one-half inch is $\"\"$ .