Question

A cycle together with its rider weighs 100kg. How much work is needed to set it moving at 3m/s?

Answer 1

Hint: In this question, we need to find out the amount of power that is required to make the cycle move at the given speed. We know that power is equal to the product of force applied on a body and the velocity of the body. We have the value of velocity given and the force required is equal to the force due to the weight of the cycle and its rider together.

Formula used:
The power can be defined by the following expression:
\[P = F \times V\]
Here F is the force applied on a body and v is the velocity attained by the body due to the applied force. The force due to weight of a body can be defined by using Newton’s second law of motion given as
$F = mg$
Here m is the mass of the body while g signifies the acceleration due to gravity whose value is given as
$g = 10m/{s^2}$

Complete step-by-step answer:
We are given that a cycle together with its rider weighs 100kg. Therefore the mass of the cycle with its rider is given as
$m = 100kg$
The force due to the weight of the cyclist can be calculated by using the formula given for force in the Formula used section. It is given as
$F = mg = 100 \times 10 = 1000N$
Now it is asked how much work is required to be done on the cycle so that the cycle moves with a velocity of 3m/s.
$V = 3m/s$
We know that the product of force and velocity gives us power which is equal to the rate of doing work. Therefore, the power required to move the cycle at a velocity of 3m/s is given as
$P = F \times V = 1000 \times 3 = 3000W$
This is the required answer.

Note: It should be noted that we have calculated power in this question because it gives us the rate of doing work. The obtained value of power signifies that in order to make the cycle move at a speed of 3m/s, the rider needs to do 3000J of work per second.