A student of mass 60 kg climbs a flight of stairs of total vertical height 4.5 m in a time of 12 s. Take gravitational field strength g = 10 N/kg. (a) Calculate the useful work done by the student in raising her own body up the stairs. [2] (b) Calculate the useful power develope…

IGCSE Physics 0625: Work, Power and Muscle Efficiency Climbing Stairs

A student of mass $60\text{ kg}$ climbs a flight of stairs of total vertical height $4.5\text{ m}$ in a time of $12\text{ s}$ . Take gravitational field strength $g = 10\text{ N/kg}$ .

(a) Calculate the useful work done by the student in raising her own body up the stairs. [2]

(b) Calculate the useful power developed by the student while climbing the stairs. [2]

(c) The student's muscles are only $25\%$ efficient at converting chemical energy into this useful mechanical work; the rest is wasted. Calculate the total chemical energy transferred from the student's internal chemical energy store during the climb. [2]

(d) State the main form in which the wasted energy is transferred away from the student's body. [1]

Part (a): Useful work done

Climbing the stairs raises the student’s own weight through a vertical height, so the useful work done equals the gain in gravitational potential energy, $W = mgh$ :

$W = 60 \times 10 \times 4.5$

$W = 2700\text{ J}$

Part (b): Useful power developed

Power is the useful energy transferred per unit time:

$P = \frac{W}{t} = \frac{2700\text{ J}}{12\text{ s}}$

$P = 225\text{ W}$

Part (c): Chemical energy transferred

Efficiency compares the useful energy output with the total energy input:

$\text{efficiency} = \frac{\text{useful energy output}}{\text{total energy input}}$

Rearranging for the total (chemical) energy input, with efficiency $= 25\% = 0.25$ :

$\text{total energy input} = \frac{\text{useful energy output}}{\text{efficiency}} = \frac{2700}{0.25}$

$\text{total energy input} = 10800\text{ J}$

Part (d): Where the wasted energy goes

The $8100\text{ J}$ ( $10800\text{ J} - 2700\text{ J}$ ) that is not usefully transferred to gravitational potential energy is mostly dissipated as heat, mainly through sweating and the warming of the skin and surrounding air as the muscles work.

Final answers

(a) Useful work done $=$ $2700\text{ J}$
(b) Useful power developed $=$ $225\text{ W}$
(c) Chemical energy transferred $=$ $10800\text{ J}$
(d) Wasted energy is mostly transferred as heat