Question

Two persons manage to push a motorcar of mass ${\text{ }}1200{\text{ }}kg{\text{ }}$at a uniform velocity along a level road. The same motorcar can be pushed by three persons to produce an acceleration of ${\text{ }}0.2{\text{ }}m{s^{ - 2}}.$ with what force does each person push the motorcar? (Assume that all persons push the motorcar with the same muscular effort.)

Answer 1

Hint: The mass of the car and the acceleration produced is given in the question. According to the second law of motion, the force is the product of mass and acceleration. It is also given that all persons are pushing the car with the same effort. We have to find the force exerted by one person and it is the same for all.

Formula used
$F = ma$(Where${\text{ }}F{\text{ }}$ stands for the force acting on an object, ${\text{ }}m{\text{ }}$stands for the mass of the object, and ${\text{ }}a{\text{ }}$stands for the acceleration of the object)

Step by step solution
The mass of the car is given by, ${\text{ }}m{\text{ }} = {\text{ }}1200{\text{ }}kg$
In the question, it is given that two people are pushing the car. The acceleration of the car increases if a third person joins them.
The acceleration produced by the car when the third person pushes,
$a = 0.2m{s^{ - 2}}$
We know that, the force
$F = ma$
Substituting the values of mass and acceleration in the above equation, we get
$F = ma = 1200 \times 0.2 = 240N$
The force applied by one person is ${\text{ }}240{\text{ }}N$
It is given that all people are pushing the car with the same muscular effort. So the force applied by each person is${\text{ }}240{\text{ }}N$

Note
$1{\text{ }}N$is defined as that force that will produce an acceleration of ${\text{ }}1{\text{ }}m{s^2}{\text{ }}$on a body having a mass of ${\text{ }}1{\text{ }}kg{\text{ }}$. Newton is the unit of force. We know that the force acting on a body is directly proportional to the rate of change of momentum. Momentum of a body can be defined as the product of its mass and velocity. A body with greater mass will produce more momentum and hence the force will be greater. For two bodies with the same mass, the body with greater velocity will have greater momentum.