An empty lift has a mass of 500 kg. How much work must be done to lift it a height of 20 m? This is done in 40 s. How much power must the motor supply?

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Answer 1 · 2016-11-09T07:43:05

Work $\approx 100000 J$ $~~ "100000 J"$

Power $\approx 3000 W$ $~~ "3000 W"$

Work is force in Newtons times distance in meters.

Notice we have the mass of the lift but not the force, which is its weight. Multiply the mass by the acceleration due to gravity, $g$ $g$ .

$500 kg \times {9.8 m/s}^{2} = 4900 N$ $"500 kg"xx"9.8 m/s"^2="4900 N"$

Now we can calculate work.

$W = F \times d$ $W=Fxxd$

$W = 4900 N \times 20 m = 98000 N\cdotm = 98000 J = 100000 J$ $W=4900 "N"xx20"m"="98000 N·m"="98000 J"="100000 J"$ to one significant figure

Now we can calculate power, which is the rate of work done over time in seconds. The equation for power is $P = \frac{W}{t}$ $P=W/t$ .

$P = \frac{W}{t} = \frac{98000 J}{40 s} = 2540 J/s = 2540 W = 3000 W$ $P=W/t="98000 J"/"40 s"="2540 J/s"="2540 W"="3000 W"$ to one significant figure