Question

elastic potential energy depends on the spring constant and the distance the spring is stretched or compressed. by what factor does the elastic potential energy change if the springs stretch is (a) doubled or (b) tripled?

Answer 1

The elastic potential energy of a spring quadruples when the stretch is doubled, and it increases ninefold when the stretch is tripled, due to the square relationship between displacement and stored energy.

Step-by-step explanation:

The elastic potential energy (EPE) stored in the spring is governed by the spring constant (k) and the square of the displacement (x).

This relationship is described by the formula for the potential energy of a spring, EPE = ½ kx².

Therefore, if the stretch of the spring is doubled, the elastic potential energy changes by a factor of 2² = 4, and if the stretch is tripled, the potential energy changes by a factor of 3² = 9.