It takes 18 foot-pounds of work to stretch a spring 4 inches
from its natural length. Find the work you need to stretch
the spring an additional 2 inches.
W = 1/2 kx^2
18 = 1/2 k * 16
k = 9/4
So, 1/2 * 9/4 * (4+2) = 6.75 ft-lb
Not sure whether you wanted the total work, or the additional work...
To find the work needed to stretch the spring an additional 2 inches, we can use the concept of work done by a force.
Work done (W) is given by the formula:
W = force × distance
In this case, the force is the force required to stretch the spring, and the distance is the additional 2 inches.
We are given that it takes 18 foot-pounds of work to stretch the spring 4 inches. Therefore, we can set up a proportion to find the force required to stretch the spring.
The proportion can be set up as follows:
18 foot-pounds / 4 inches = X foot-pounds / 2 inches
To solve this proportion, we can cross-multiply:
18 foot-pounds × 2 inches = X foot-pounds × 4 inches
36 foot-pounds = 4X foot-pounds
To isolate X, we divide both sides of the equation by 4:
36 foot-pounds / 4 = X foot-pounds
9 foot-pounds = X foot-pounds
Therefore, the force required to stretch the spring an additional 2 inches is 9 foot-pounds.