Question

In an experiment to measure his power, a student records the time taken by him in running up a flight of steps on a staircase. Use the following data to calculate the power of the student:
Number of steps = 28
Height of each step = 20 cm
Time taken = 5.4 s
Mass of student = 55 kg
Acceleration due to gravity = 9.8 m s⁻²

Answer 1

Power is energy consumed per unit time.

When the student runs up on a staircase, his energy is consumed in doing work against the force of gravity.

Work done by the student against the force of gravity = $mgh=55\mathrm{kg}\times 9.8{\mathrm{ms}}^{-2}\times (28\times 20\times {10}^{-2}\mathrm{m})=3018.4\mathrm{J}$

Time taken by the student = 5.4 s

Power of the student = $\frac{\mathrm{Energy}}{\mathrm{Time}}=\frac{3018.4\mathrm{J}}{5.4\mathrm{s}}=559\mathrm{J}/\mathrm{s}$