A single conservative force F_x = (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 B) +29 J C) +9.0 J D) −9.0 J E) +20 J

Question

Quizplus · Accepted Answer

We can find the potential energy associated with the conservative force by integrating the force over the distance moved. ∆U = -∫F_x dx ∆U = -∫(6.0x - 12) dx Since we know that the potential energy at x = 0 is +20 J, we can use this to find the constant of integration. U(0) = +20 J ∆U = -∫(6.0x - 12) dx + 20 ∆U = [-3.0x^2 + 12x] + 20 At x = 3.0 m, ∆U = [-3.0(3.0)^2 + 12(3.0)] + 20 ∆U = +29 J Therefore, the potential energy at x = 3.0 m is +29 J, which is choice (B).

A Single Conservative Force Fx = (6

A Single Conservative Force F_x = (6