Question

What average horsepower is developed by a man of 80 kg while climbing in 10 s flight of stairs that rises 6 m vertically?
A. 0.63 hp
B. 1.26 hp
C. 1.8 hp
D. 2.1 hp

Answer 1

Hint: The average power is defined as the work done or energy spent in doing the work divided by time. The energy spent is equal to the gravitational potential energy. 1 hp is equal to the 746 watt.

Complete step by step answer:
A man of mass $m=80kg$ climb upstairs which is 6 m high in time $t=10\sec$. The work done against force of gravity when the man goes upwards is equal to the potential energy of the man at the highest point i.e., $h=6m$ .
The potential energy is defined as the energy possessed by a body by virtue of its specific position or changed configuration. The gravitational potential energy of a body (man) at a height above the ground is measured by the amount of work done in lifting it up to that height against the force of gravity.
Gravitational potential energy $\left(P\right)=mgh$
$P=80\times 10\times 6$ where g is acceleration due to gravity.
$P=4800J$
The rate of doing work is called power i.e.,$Power={\displaystyle \frac{Work}{time}}$
$Power={\displaystyle \frac{4800}{10}}$
$Power=480W$
Horsepower is another unit of power same as watt but it is largely used in mechanical engineering. It is used when a large unit of power is being measured. $1hp=746W$
Thus, 480W in hp = ${\displaystyle \frac{480}{746}}=0.643hp$
Therefore, option (A) is correct.

Note:The power spent by a source is measured by the amount of work done per unit time i.e., the energy spent in doing the work per unit time. The average power is the same as the power in this case.