A single conservative force vector F = (6.0x - 12)i hat N where x is in meters,

Question

A single conservative force vector F = (6.0x - 12)i hat 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 29 J at x = 0. (a) Write an expression for U as a function of x, with U in joules and x in meters. U(x) = Correct: Your answer is correct. (b) What is the maximum positive potential energy? 41 Correct: Your answer is correct. J (c) At what negative value of x is the potential energy equal to zero? m (d) At what positive value of x is the potential energy equal to zero? m

Explanation / Answer

U = 29 - integral(6x -12)dx = 29 - 3x^2 +12x

maximum U occurs at dU/dx = 0; -6x +12 = 0 or x = 2

U(2) = 29 - 12+24 = 41J

roots of function U(x) are -1.69, +5.69

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