A light spring obeys Hooke\'s Law. It takes 29.8 J of work to stretch this sprin

Question

A light spring obeys Hooke's Law. It takes 29.8 J of work to stretch this spring from an elongation of 4.59 cm to an elongation of 5.59 cm.

(a) Is the amount of work required to increase the elongation of the spring from 5.59 cm to 6.59 cm greater than, less than, or equal to 29.8 J?

greater thanless than    equal to

(b) Verify your answer to part (a) by calculating the required work.

How is the work done on a spring related to its potential energy? How is the potential energy of a spring related to the stretch of the spring? J

Explanation / Answer

Here ,

for the spring to stretch from 5.59 cm to 4.59 cm

a) the work done required for 5.59 cm to 6.59 cm will be greater than 29.8 J

b)

for the spring for calculating the work done

W1/W2 = (6.59^2 - 5.59^2)/(5.59^2 - 4.59^2)

W1/29.8 = (6.59^2 - 5.59^2)/(5.59^2 - 4.59^2)

solving for W1

E1 = 35.7 J

the work done required is 35.7 J

for the spring ,

work done = - change in potential energy

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