A single conservative force acting on a particle within a system varies as F = (

Question

A single conservative force acting on a particle within a system varies as F = (? Ax + Bx5)i N, where A and B are constants, F is in newtons, and x is in meters.
(a) Calculate the potential energy function U(x) associated with this force, taking U = 0 at x = 0. (Use any variable or symbol stated above as necessary.)

U(x) =
.

(b) Find the change in potential energy and change in kinetic energy as the particle moves from x = 2.50 m to x = 3.70 m. (Use any variable or symbol stated above as necessary.)

?U =

?K =

Explanation / Answer

a)u(x)=int(-F.dx) [0,x] =Ax^2/2 - Bx^6/6 b)u(3)-u(2)=del K =A/2*(3.7^2-2.5^2)-B/6*(3.2^6-2.5^6) =3.72A -387 B

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