Question

A spring has a natural length of 4m. It requires 180J of work to stretch the spring to 10m. Calculate the work required to stretch the spring from 7m to 11m. Round your answer to the nearest hundredth if necessary.

Answer 1

Answer + Explanation:

First, we need to find the spring constant, k, using the given information. We can use Hooke's Law:

W = (1/2)kx^2

Where W is the work done, k is the spring constant, and x is the distance the spring is stretched or compressed from its natural length.

When x = 6 m (the stretch from 4m to 10m), we have:

180 J = (1/2)k(6m)^2

Solving for k, we get:

k = 5 J/m

Now we can use this spring constant to find the work required to stretch the spring from 7m to 11m:

W = (1/2)k(11m^2 - 7m^2)

W = (1/2)(5 J/m)(144 m^2)

W = 360 J

Therefore, the work required to stretch the spring from 7m to 11m is 360 J.