Final answer:
Hooke's Law states that the force required to hold a spring compressed or extended is proportional to the distance it is compressed or extended. To find the work done in stretching a spring, we need to calculate the change in length and use the formula W = (1/2)kx^2. In this problem, the given force and length values can be used to find the constant k and then calculate the work done.
Step-by-step explanation:
Hooke's Law states that the force required to hold a spring compressed or extended to a certain length is proportional to the distance it is compressed or extended. The force to compress or extend a spring x units is given by F(x) = kx, where k is a constant.
In this question, a force of 30 lb is required to stretch a spring from its natural length of 1 ft to a length of 15 in. To find the work done in stretching the spring from 1 ft to 21 in, we need to calculate the change in length and use the formula W = (1/2)kx^2.
First, convert the lengths to the same unit. 15 in is 1.25 ft, and 21 in is 1.75 ft. The change in length is 1.75 ft - 1 ft = 0.75 ft. To find k, we can use the given information that F = 30 lb when x = 1.25 ft. Substitute these values into the formula F = kx and solve for k.
Once k is found, plug it into the formula W = (1/2)kx^2, with x = 0.75 ft, to calculate the work done.