A single conservative force F = (8.0x - 12)i N where x is in meters, acts on a p

Question

A single conservative force F = (8.0x - 12)i N where x is in meters, acts on a particle moving along an x axis. The potential energy U associated with this force is assigned a value of 25 J at x = 0. What is the maximum positive potential energy? At what negative value of x is the potential energy equal to zero? At what positive value of x is the potential energy equal to zero?

Explanation / Answer

Potential energy from 0 to x is given by the work done by the force F(x).so by integrating U(x)=Int.(0--->x)F(x).dx =S (8x-12).dx =4x^2-12x+C at x=0 U(0)=25 so C=25 hence PE U(x)=4x^2-12x+25 for maxima dU/dx=0 8x-12=0 so at x=1.5 we get u(1.5)=16 but this is minima. There is no +ve or -ve value of x at which U=0

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