Question

The force exerted by gravity on a refrigerator of mass m is vectorF = -mg vectork. Is F conservative (that is path independent)? Give a reason for your answer. How do I find potential function?

Answer 1

For this one, the potential function is easy to find. Just integrate the \(\hat{k}\) component. Since the other components are zero, we know that our potential function is constant with respect to \(x\) and \(y\).

Answer 2

The \(\hat{k}\) component is integrated with respect to \(z\) by convention.

Answer 3

Since \[
\nabla f(x,y,z)= \frac{\partial f}{\partial x}\hat{\imath}+\frac{\partial f}{\partial y}\hat{\jmath}+\frac{\partial f}{\partial z}\hat{k}
\]

Answer 4

oh, got it, so the function is going to look like f(x, y, z) = -mgk + C

Answer 5

Well, \(\hat{k}\) is just a unit vector. The potential function is not a vector, so there should be no \(\hat{k}\) in it. You're integrating with respect to \(z\) because conventionally the \(z\) variable is associated with the \(\hat{k}\) direction.