Question

a) Show that one British horsepower is equal to 746 W. (b) What is the horsepower rating of a 75-W light bulb?

Short answer

1. One horsepower is equal to 746 Watts. (b) The horsepower rating of the light bulb is 0.10 hp.

Step-by-step solution

Definition of power

Power, P is defined as the rate at which work is done and is obtained by dividing the time taken to perform that work.

$P=\frac{\mathrm{W}\mathrm{o}\mathrm{r}\mathrm{k}}{\mathrm{T}\mathrm{i}\mathrm{m}\mathrm{e}}=\frac{W}{t}$

Units of power:

The SI unit is Watt (W) and the imperial unit is horsepower (hp).

Definition of Horsepower

Horsepower is a unit of power that compares the power of a machine to the horse muscle power. The power of turbines, heavy engines, and other machinery is usually measured in horsepower.

(a) Conversion of horsepower into Watt

One horsepower is equal to$550\mathrm{f}\mathrm{t}-\mathrm{l}\mathrm{b}/\mathrm{s}$.

Also,

$1\mathrm{l}\mathrm{b}=4.45\mathrm{N}$

$1\mathrm{m}=3.38\mathrm{f}\mathrm{t}$

Therefore, one hp can be converted into Watts as:

$\begin{array}{rl}1\mathrm{h}\mathrm{p}& =\left(\frac{550\mathrm{f}\mathrm{t}-\mathrm{l}\mathrm{b}/\mathrm{s}}{1\mathrm{h}\mathrm{p}}\right)\left(\frac{4.45\mathrm{N}}{1\mathrm{l}\mathrm{b}}\right)\left(\frac{1\mathrm{m}}{3.28\mathrm{f}\mathrm{t}}\right)\\ & \approx 746\mathrm{W}\end{array}$

Thus, one horsepower is equal to 746 Watts.

(b) Determination of horsepower rating

It is given that the input power of the bulb is 75 W. The rating of the bulb in hp is:

$\begin{array}{rl}{P}^{\prime }& =\left(75\mathrm{W}\right)\left(\frac{1\mathrm{h}\mathrm{p}}{746\mathrm{W}}\right)\\ & =0.10\mathrm{h}\mathrm{p}\end{array}$

Thus, the rating of the light bulb in terms of horsepower is 0.10 hp.