how much work W

Question

A spring has a natural length of 22 cm. If a 20-N force is required to keep it stretched to a length of 32 cm, how much work W is required to stretch it from 22 cm to 27 cm? (Round your answer to two decimal places.)

Answer 1

The force due to a stretched spring (Hooke's Law) is:

 

F = kx

 

Use the given data point (32 cm, 20 N) to find the value of the constant k:

 

20 N = k(32-22)

20 N = k*10

2 = k

 

Work is given by:

 

dW = F*dx = 2x dx

 

To find the work done is stretching the spring 5 cm (27 cm - 22 cm = 5 cm):

 

         ₅

W = ∫ 2x dx

        ⁰

               ₅

W = x²  |   =  5² - 0² = 25 N-m

               ⁰