Question

A horse exerts a pull on a cart of 300 N so that the house-cart system moves with a uniform speed 18 km/h on a level road. Calculate the power developed by the horse in watt and also find its equivalent in horsepower.

Answer 1

Step 1: Given data

Force exerted on the cart is, $F=300N$

Speed of the cart is, $v=18km/hr=\left(18\times \frac{5}{18}\right)m/s=5m/s$

Step 2: Obtaining an equation for power in terms of force and speed

Power is given as,

$P=\frac{W}{t}$

where, $W$ is work done and $t$ is time.

Now, work done is given as,

$W=Fd$

where, $F$ is force and $d$ is distance.

Therefore, the equation for power can be written as,

$P=\frac{Fd}{t}$

Now, we know that speed is given as,

$v=\frac{d}{t}$

where, $d$ is distance and $t$ is time.

Hence, the equation for power can also be written as,

$P=Fv$

Step 3: Calculating power

Substituting the known values in the above equation for power, we get,

$$\begin{gathered} P=300N\times 5m/s \\ P=1500W \\ P=2hp[1hp=746W] \end{gathered}$$

Therefore, the power developed by the horse is $1500W$ or $2hp$.