Question

Find the power necessary to move a 28.5 kg block up a frictionless 32.5 degrees incline at 4.65 m/s.

Answer 1

In order to move a block up a frictionless incline one should apply force $\mathbf{F}$ against the projection of the gravity force $m\mathbf{g}$ on the x-axis. Here $m = 28.5kg$ is the mass of the block and $g = 9.81m/s^2$ is the gravitational acceleration.

In order to maintain constant speed $v = 4.65m/s$ , this force should be:

$$F = mg\sin32.5\degree$$

The power is, then:

$$P = Fv = mgv\sin32.5\degree\\ P = 28.5\cdot 9.81\cdot 4.65\cdot \sin32.5\degree \approx 698.5\space W$$

Answer. 698.5 W.