Answer to Question #156405 in Physics for Yoshi

Question

A rubber band has a force constant of 45 N/m. When the rubber band is pulled by a force of 9.8 N, how far will it stretch and what is its potential energy?

Answer 1

The elongation of the band is given by the Hook's law:

$$x = \dfrac{F}{k}$$

where $k = 45N/m$ is the force constant, and $F = 9.8N$ is the applied force. Thus, obtain:

$$x = \dfrac{9.8N}{45N/m} \approx 0.22m$$

The potential energy is given as follows:

$$W = \dfrac{kx^2}{2}\\ W = \dfrac{45\cdot 0.22^2}{2} \approx 1.1J$$

Answer. 0.22 m, and 1.1J.