Question

The maximum frictional force on a motor bike of $2.5{\text{ }}H.P$ is $1000{\text{ }}N$. What is the maximum possible speed of the bike?

Answer 1

Hint: We know that Power is defined as the work done per unit of time. In this problem we first change the value of power from horsepower to watt as per conversion.The SI unit of Power is Watt. The industrial unit is “horse power, hp”. So, $1{\text{ }}hp = 746{\text{ }}watts$.

Complete step by step answer:
As given in problem:
$P = 2.5{\text{ }}HP$
Change the unit horsepower into Watt
$P = 2.5{\text{ }} \times {\text{746 W}}$
And, $F = 1000{\text{ }}N$
We have to find the maximum possible speed of the bike.
$\text{Power} = \text{Force} \times \dfrac{\text{Displacement}}{\text{Time}}$
As, $\dfrac{\text{Displacement}}{\text{Time}} = \text{velocity}$

So,
$\text{Power} = \text{Force} \times {\text{ Velocity}}$
We can write,
$\text{Velocity} = \dfrac{\text{Power}}{\text{Force}}$
Put the values in above equation
$\text{Velocity} = \dfrac{{2.5 \times 746}}{{1000}}$
$\Rightarrow \text{Velocity} = \dfrac{{1865}}{{1000}}$
$\Rightarrow \text{Velocity} = \dfrac{{1865}}{{1000}}$
By solving, we get
$\therefore \text{Velocity} = 1.865{\text{ }}m{s^{ - 1}}$

Therefore, the maximum possible speed of the bike is $1.865{\text{ }}m{s^{ - 1}}$.

Note: In order to solve this question we have assumed there will be no loss of power of the motor bike. If we go practically then there will be loss of some part of power in the form of heat due to frictional force and hence we cannot apply the above method to find the maximum velocity of the bike.