Question

A mass is connected to a spring on a horizontal frictionless surface. The potential energy of the system is zero when the mass is centered on x = 0, its equilibrium position. If the potential energy is 3.0 J when x = 0.050 m, what is the potential energy when the mass is at x = 0.10 m?

Answer 1

U = 12 J.

Step-by-step explanation:

The potential energy in a spring is given by the following formula

`U = (1)/(2)kx^2`

where k is the spring force constant and x is the displacement from the equilibrium.

If U = 3 J when x = 0.05 m, then k is

`3 = (1)/(2)k(0.05)^2\\k = 2400~N/m`

Using this constant, we can calculate the potential energy at x = 0.10 m:

`U = (1)/(2)(2400)(0.1)^2 = 12 ~J`