Question

As shown in Figure, a person pulls a vacuum cleaner at speed $v$ across a horizontal floor, exerting on it a force of magnitude $F$ directed upward at an angle $\theta$ with the horizontal. (a) At what rate is the person doing work on the cleaner? (b) State as completely as you can the analogy between power in this situation and in an electric circuit.

Answer 1

a) The person is doing work at a rate of $P=Fv\cos \theta$.
(b) Compare the previous equation to $P=\Delta V_{rms}{I}_{rms}\cos \varphi$. One can consider the emf as the "force" that moves the charges through the circuit, and the current as the "speed" of the moving charges. The $\cos \theta$ factor measures the effectiveness of the cause in producing the effect. $\theta$ is an angle in real space for the vacuum cleaner and $\varphi$ is the analogous angle of phase difference between the emf and the current in the circuit.