Answer to Question #85238 in Classical Mechanics for Furqan shah

Question

Find the potential energy function associated with the force
(1) F=–YZ i–XZ j–XY k
(2). F=cx³

Answer 1

1)

∂U/∂x=-(-yz)=yz

U=∫▒yzdx=xyz+f(y,z)

∂U/∂y=-(-xz)=xz=xz+∂f/∂y→∂f/∂y=0

Thus,

U=xyz+g(z)

∂U/∂z=-(-xy)=xy=xy+∂g/∂z→∂g/∂z=0

Therefore,

U=xyz+C.

2)

U=-∫▒Fdx

U=-∫▒〖cx^3 dx〗=-(cx^4)/4+C.