Question

When a motor car of mass 1500kg is pushed on a road by two persons, it moves with a small uniform velocity. On the other hand, if this car is pushed on the same road by three persons, it moves with an acceleration of $0.2m/{s^2}$. Assume that each person is producing the same muscular force. Then force of friction between the tyres of the car and the surface of the road is:
A) 300N
B) 600N
C) 900N
D) 100N

Answer 1

Hint: Friction is also known as opposing force, it is always opposite to the force applied. It is a fundamental force without which the earth cannot function. The frictional force is a force that is kept to a minimum to minimize the loss of energy.

Complete step by step solution:
Find out the friction between the two surfaces:
The first case: Here, in the first case two people are pushing a motor car of mass 1500kg, which means that we need to resolve horizontal forces.
Force applied by one person on the car: F;
Force applied by two persons on the car: 2F;
Now, the horizontal force applied by the two persons will be equal to the frictional force which would be:
f = 2F;
Here,
F = Force applied;
f = Frictional Force;
Here, the force applied by three persons produces an acceleration of $0.2m/{s^2}$, we know the mass of the car is 1500kg. Also the force applied by the three persons would be equal to the frictional force.
$F = ma$ ;
Put the value and find out the force:
$\Rightarrow F = 1500 \times 0.2 = 300N$;
Now, the force applied is 300N.
We have found out that f = 2F:
$\Rightarrow f = 2 \times 300$;
So, the frictional force would be:
$\Rightarrow f = 600N$;

Final answer is option B. Therefore, the force of friction between the tyres of the car and the surface of the road is 600N.

Note: Here, there is no need to apply the formula for friction. Just equate the horizontal forces with each other. In this question there are two horizontal forces which are being applied to the motor car one is of friction and another is push force.