Daniel B. answered • 12/16/20

A retired computer professional to teach math, physics

(a)

The force F is the negative gradient of the potential energy U:

F = (4x+2, -1, 0)

At point A:

F = (6, -1, 0)

(b)

In general, work W is the integral of the force F over a path.

I do not know whether you are expected to actually compute the integral;

if so you can pick any convenient path, as the force is conservative.

Otherwise, the work is simply the difference in potential energy:

W = U(A) - U(B)

Note the sign: any decrease of potential energy when going from A to B

implies positive work.

Substituting actual values:

W = (1 - 2 - 2) - (2 - 8 - 4) = 7J

(c)

By conservation of energy, ΔE = 0,

and ΔK = 7J, namely the reduction in potential energy calculated in (b).

Craster V.

Thanks a lot!12/16/20