Question

Hooke's law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 13 lb stretches a certain spring 9 in., how much will a force of 52 lb stretch the spring?

Answer 1

Using Hooke's Law and the provided measurements, we calculate the spring constant with the initial force and stretch, then use it to determine the stretch resulting from the larger force.

Step-by-step explanation:

Hooke's Law states that the distance a spring stretches varies directly as the force applied to it. In equation form, Hooke's law is F = kx, where F is the force applied, k is the spring constant (a measure of the spring's stiffness), and x is the change in the spring's length (its deformation). Using the information given that a force of 13 lb stretches the spring 9 inches, we can calculate the spring constant, k, and then use it to determine how much the spring will stretch under a force of 52 lb.

First, we find the spring constant k by rearranging the formula to k = F/x. We know the force, F, is 13 lb, and the deformation, x, is 9 inches. So, k is 13 lb/9 in.

Then, with a force of 52 lb, the amount of stretches can be found by using the spring constant k we just calculated. By rearranging Hooke's Law, we find x by x = F/k. The spring will stretch by x when subject to a force of 52 lb.