9.
A force of 20 pounds is needed to stretch a 10-inch spring by 5 inches. Find the work done in stretching the spring from a length of 25 inches.
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Hooke's Law
A force of 50 pounds stretches a spring 1 inch from its natural position. Find the work done in stretching the spring from its natural length of 10 inches to double that length.
In Exercises 9-14, use Hooke’s Law to determine the work done by the variable force in the spring problem.
Eighteen foot-pounds of work is required to stretch a spring 4 inches from its natural length. Find the work required to stretch the spring an additional 3 inches.
15. Use integrals to solve
a) A spring has a natural length of 10 inches. An 800lb force stretches the spring to 15 inches. How much work is done in stretching the spring form 10 inches to 12 inches?
b) A 20-foot chain, weighing 5 pounds per foot, is hanging from a winch 12 feet above the ground. How much work is done in winding up the chain until the bottom is 4 feet above the ground?