Question

A boy whose mass is 40kg runs up a flight of 30 steps, each 150mm high, in 6 seconds. Find the average power developed. (Take g as 10m/s2).

Answer 1

Answer on Question 74275, Physics / Mechanics | Relativity

Question

A boy whose mass is $40\,\mathrm{kg}$ runs up a flight of 30 steps, each $150\,\mathrm{mm}$ high, in 6 seconds. Find the average power developed. (Take g as $10\,\mathrm{m/s}^2$).

**Solution.** Lifting to the height $h$ the boy doing work against gravity which is

$$W = F \cdot h$$

where $F = mg$ is the force equal to the weight of the boy. The height $h$ is equal to the step height $d$ multiplied by the number of steps, $h = d \cdot 30$. The step height in meters is

$$d = \frac{150\,\mathrm{mm}}{1000\,\mathrm{mm/m}} = 0.15\,\mathrm{m}$$

Then the work done is

$$W = mg \cdot h = 40\,\mathrm{kg} \cdot 10\,\frac{\mathrm{m}}{\mathrm{s}^2} \cdot 0.15\,\mathrm{m} \cdot 30 = 1800\,\mathrm{J}$$

The average power is the rate at which work is done, that is

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

Substituting $W = 1800\,\mathrm{J}$ and $t = 6\,\mathrm{s}$ we get

$$P = \frac{1800\,\mathrm{J}}{6\,\mathrm{s}} = 300\,\frac{\mathrm{J}}{\mathrm{s}} = 300\,\mathrm{W}$$

**Answer:** the developed average power is $P = 300$ watt.

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