Daily Physicist

Today is the birthday of

• James Watt (1736-1819).

Today’s Problem

Determine the power output in watts of a 75 kilogram person climbing up 400 meters from the Earth’s surface in one hour.

Answer

A watt is a joule per second. The number of joules required to lift a 75 kilogram person up by 400 meters is

\[E=mgh=(75\mathrm{kg})(9.8\mathrm{m/s}^2)(400\mathrm{m})=294,000\,\mathrm{J}\]

So the person’s power output is

\[\frac{E}{t}=\frac{294,000\,\mathrm{J}}{1\,\mathrm{hour}}\left(\frac{1\,\mathrm{hour}}{3,600\,\mathrm{sec}}\right)=81.7\,\mathrm{W}\]