help-application-integrals[work]?

Question

Answer 1

(2)

Step 1:

The spring has a natural length of 25 cm = 0.25 m.

Force required to stretch a spring to length of 32 cm is 3.5 N.

Assume that the spring obeys Hooke's law.

Hooke's law : where x is the extension of the spring.

Therefore the spring constant is k = 50.

Step 2:

Find the work done to stretch a spring of length of 30 cm to 45 cm.

Work done by the spring : .

Force required in moving an object to a distance of x is .

Work done to stretch a spring of length of 30 cm to 45 cm.

Natural length of the spring is 25 cm.

Now calculate work done to stretch a spring of length of 5 cm to 20 cm from its natural length.

Work done to stretch a spring of length of 30 cm to 45 cm is 0.9375 J.

Solution:

Work done to stretch a spring of length of 30 cm to 45 cm is 0.9375 J.