Question

The force required to stretch a Hooke's-law spring varies from 0N to 70.4N as we stretch the spring by moving one end 5.35cm from its unstressed position. What is the work done?

a) 0.375 J
b) 1.88 J
c) 3.76 J
d) 7.52 J

Answer 1

The work done by the spring force can be calculated using the formula W = ½kx², where W is the work done, k is the spring constant, and x is the displacement of the spring. By finding the spring constant and plugging it into the formula, we can calculate the work done to be approximately 0.375 J.

Step-by-step explanation:

The work done by a spring force can be calculated using the formula:

W = ½kx²

Where W is the work done, k is the spring constant, and x is the displacement of the spring from its unstressed position. In this case, the force required to stretch the spring varies from 0N to 70.4N as the spring is stretched 5.35cm. To calculate the work done, we need to find the spring constant. Using the given formula, we can set up the equation:

70.4N = k * 0.0535m

k = 70.4N / 0.0535m

k ≈ 1313.08 N/m

Now we can calculate the work done:

W = ½ * 1313.08 N/m * (0.0535m)²

W ≈ 0.375 J