Question

A machine operates with a power of 1500 Watts. the machine lifts one steel beam, of 500 N, vertically upward 15 meters. How long does it take for the machine to lift 20 beams

Answer 1

QUESTION:

A machine operates with a power of 1500 Watts. the machine lifts one steel beam, of 500 N, vertically upward 15 meters. How long does it take for the machine to lift 20 beams

SOLUTION:

The power of the machine is

$$P = \frac {A}{t}$$

According to the work-energy theorem:

$$A = mgh \text{ (for one beam)}$$ $$\mathrm{mg} = 500 \mathrm{N}$$

Hence,

$$P = \frac {A}{t} = \frac {\mathrm{mg} \cdot \mathrm{h}}{\mathrm{t}}$$ $$t = \frac {\mathrm{mg} \cdot \mathrm{h}}{A}$$ $$t = \frac {500 \cdot 15}{1500} = 5 \mathrm{s}$$

So, it takes

$$t_1 = 20t$$ $$t_1 = 20 \cdot 5 = 100 \mathrm{s}$$

to lift 20 beams

ANSWER:

$$t_1 = 100 \mathrm{s}$$