A particle is moving along the x axis under the influence of a conservative forc

Question

A particle is moving along the x axis under the influence of a conservative force given by

If U(x) = 0 when x = 0, determine the following as the particle travels from xi = 1.10 m to xf = 4.10 m.

(a) The potential energy function U(x). (Use the following as necessary: x. Do not enter units in your expression.)
U(x) =____________J

(b) Change in potential energy of the particle.
________________J

(c) Change in kinetic energy of the particle.
_____________ J

(d) Work done on the particle by the force

______________J

Explanation / Answer

a) F = -dU/dx

du = -F*dx

U = integral of (-F*dx) = integral of [4x - 9x^2]*dx

U = 4*x^2/2 - 9*x^3/3 = (2x^2 - 3x^3 ) J

B) change in potential energy is given by

[(2*4.1*4.1)-(3*4.1*4.1*4.1)]-[(2*1.1*1.1)-(3*1.1*1.1*1.1)] = -173.143-1.573 = -174.716 J

C) change in kinetic energy is 174.716 J

D)Work done on the particle is -change in potential energy = 174.716 J

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