Question

A boy whose mass is 40kg Finds that he can run up to 50 steps each of 15cm high in 5 seconds. How much power is required for the boy to run up the flight assuming g = 10m/s

Answer 1

To find the power is required for the boy, we need to evaluate the work done by the boy. The equation for the work is

$$W=F\cdot h$$

- F is the force that the boy exert to run up, which is equal to its mass, m, multiplied by the acceleration due to gravity, g,

$$F=mg=40\,\text{kg}\,\cdot \text{10}\,\frac{\text{m}}{{{\text{s}}^{\text{2}}}}=400\,\frac{\text{kg}\cdot \text{m}}{{{\text{s}}^{\text{2}}}}=400\,\text{N}$$

- h is the height of the staircase equal to the product of the height of one step by the number of steps

$$h=0.15\,\text{m}\cdot 50=7.5\,\text{m}$$

Then work equals

$$W=400\,\text{N}\cdot \text{7}\text{.5}\,\text{m=3000}\,\text{N}\cdot \text{m=3000}\,\text{J}$$

Now we find power is required for the boy. Power is calculated by dividing the work done by the time it took to do the work

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

Substituting the known values, we get

$$P=\frac{3000\,\text{J}}{5\,\text{s}}=600\,\frac{\text{J}}{\text{s}}=600\,\text{W=0}\text{.6}\,\text{kW}$$

So, the power is required for the boy to run up the flight is 600 W=0.6 kW