Question

A person having mass 60 kg lifts a load of 20 kg and climbs up 20 steps of a ladder in 10 s. If the height of each step is 0.2m. Find the power of the person.

Answer 1

Answer on Question#40533 – Physics – Mechanics

A person having mass $60\,\mathrm{kg}$ lifts a load of $20\,\mathrm{kg}$ and climbs up 20 steps of a ladder in 10 s. If the height of each step is $0.2\,\mathrm{m}$. Find the power of the person.

Solution:

Power is the rate at which work is done. It is the work/time ratio.

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

Work done by person:

$$W = F \cdot S$$

Person acts on the mass and raises itself:

$$F = Mg + mg = (M + m)g$$

Traversed distance:

$$S = N \cdot h$$

(4)in(3):

$$W = (M + m)g \cdot Nh$$

(5)in(1):

$$P = \frac{(M + m)g \cdot Nh}{t} = \frac{(20\,\mathrm{kg} + 60\,\mathrm{kg}) \cdot 9.8\,\mathrm{\frac{N}{kg}} \cdot 20 \cdot 0.2\,\mathrm{m}}{10\,\mathrm{s}} = 314\,\mathrm{Watts}$$

Answer: power of the person is equal to 314 Watts.