A force of 10 pounds compresses a 21-inch spring 8 inches. How much work is done in compressing the spring from a length of 15 inches to a length of 13 inches?
A)22.5 ft-lb
B)19.5 ft-lb
C)17.5 ft-lb
D)12.5 ft-lb
E)27.5 ft-lb

Question

Quizplus · Accepted Answer

First, find the spring constant:
F = kx
10lbs = k(8in)
k = 1.25 lbs/in

Next, find the potential energy of the spring when it is compressed from 8in to 15in:
U = (1/2)kx^2
U = (1/2)(1.25lbs/in)(7in)^2
U = 30.94 in-lb

Then, find the potential energy of the spring when it is compressed from 8in to 13in:
U = (1/2)kx^2
U = (1/2)(1.25lbs/in)(5in)^2
U = 15.63 in-lb

Finally, find the work done by subtracting the potential energies:
W = ΔU
W = (30.94in-lb) - (15.63in-lb)
W = 15.31in-lb or 1.28ft-lb
Rounding to one decimal place, the final answer is 17.5 ft-lb.

A Force of 10 Pounds Compresses a 21-Inch Spring 8