Question

A single conservative force Fx = (6.0x – 12) N (x is in m) acts on a particle moving along the x axis. The potential energy associated with this force is assigned a value of +20 J at x = 0. What is the potential energy at x = 3.0 m? a. +11 J

Answer 1

`29 J`

Explanation:

We know that `F=-(du)/(dx)` for a conservative force acting,or, `du=-F dx` (where `du` is change in potential energy and `F` is the amount of force applied)

Given, `F= 6x-12`

So, `du = -6x dx +12 dx`

Integrating the above equation in the range of `u=[0,U]` and `x=[0,3]`

We get, `U = 20+9 J` or `29 J`