A lift is used to raise objects to the back of a moving truck.If the maximum power the lift is capable of delivering is 98 W,what is the maximum constant speed with which this lift can raise a 5.0 kg crate straight up from the ground to the back of the moving truck? The back of the moving truck is 5.0 m above the ground.

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Quizplus · Accepted Answer

The maximum speed can be found using the formula for power, $P = \frac{W}{t}$, where $W$ is work done and $t$ is time. Work done can also be expressed as $W = Fd$, where $F$ is force and $d$ is distance. Since the force needed to lift the crate is equal to its weight ($F = mg$), we can substitute to find $P = \frac{mgd}{t}$. Rearranging for speed ($v = \frac{d}{t}$), we get $v = \frac{P}{mg}$. Substituting the given values ($P = 98\,W$, $m = 5.0\,kg$, $g = 9.8\,m/s^2$), we find $v = \frac{98}{5.0 \times 9.8} = 2.0\,m/s$.

A Lift Is Used to Raise Objects to the Back