Chapter 7, Problem 10MCQ

You pull on a spring, which obeys Hooke’s law, in two steps. In step 1, you extend it by distance $x_s$. In step 2, you further extend it by the same distance $x_s$

Choose the answer that correctly compares the elastic potential energy of the spring after the first step $\left(U_{s1}\right)$ with that after the second step $\left(U_{s2}\right).$

$U_{S}2=2U_{s1}$ because the extension of the spring at the end of step 2 is two times larger than the extension of the spring at the end of step 1.

$U_{s2}\text{= }2U\text{ s1}$ because the more the spring is stretched, the larger the force that is needed to extend the spring for a unit distance.

$U_{S2}>2U\text{ s1}$ because the average force exerted on the spring in step 2 is more than two times larger than the average force exerted on the spring in step 1.

$U_{S2}>2U\text{ s1}$ because the average force exerted on the spring in step 2 is more than two times larger than the average force exerted on the spring in step 1.