Question

A force of 6 N will stretch a rubber band 4 cm ​(0.04 ​m). Assuming that​ Hooke's law​ applies, how far will an 18​-N force stretch the rubber​ band? How much work does it take to stretch the rubber band this​ far? How far will an 18​-N force stretch the rubber​ band?

Answer 1

Explanation:

First, we need to calculate the constant force, that is, the ratio between the applied force and the rubber stretch due to the application of the force:

$k=\frac{F}{d}(1)\\k=\frac{6N}{0.04m}\\k=150\frac{N}{m}$

Now, we can know how far will an 18​N force stretch the rubber​. From (1):

$d=\frac{F}{k}\\d=\frac{18N}{150\frac{N}{m}}\\d=0.12m=12cm$

The work done by the external force on the rubber is equal to its elastic potential energy:

$W=\frac{kd^2}{2}\\W=\frac{150\frac{N}{m}(0.12m)^2}{2}\\W=1.08J$