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 F = [(4.00 N/m)x + (9.00 N/m2)x2]i hat. If U(x) = 0 when x = 0, determine the following as the particle travels from xi = 2.80 m to xf = 5.50 m.

A particle is moving along the x axis under the influence of a conservative force given by F = [-(4.00 N/m)x + (9.00 N/m2)x2]i. If U(x) = 0 when x = 0, determine the following as the particle travels from x1 = 2.80 m to Xf = 5.50 m. (a) The potential energy function U(x). (Use the following as necessary: x. Do not enter units in your expression.) U(x) = (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 F. J

Explanation / Answer

F = -4x + 9x^2

U = -F.dx= -(-2x^2 + 3x^3 + C)

U(0) = 0 So C=0

a)So U(x) =-(2x^2 + 3x^3) =2x^2 - 3x^3 (ans)

b)Change in potential energy =U(5.5) - U(2.8)= -438.625 - (-50.176) = -388.449 J (ans)

c)Change in energy due to conservative field = 0

So change in Kinetic energy= 388.449 J (ans)

d) Work done by force = F.dx from 2.8 to 5.5

=388.449 J (ans)

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