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.