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

Question

Philoid · Accepted Answer

Let, the force applied by each person be F.

So,

Total force applied by two persons = F + F

= 2F (i)

Force of friction, f = 2F (ii)

Now, when three persons apply force to push the motorcar, then:

Total force applied by three persons = F + F + F

= 3F (iii)

Now, the total force applied by three persons is 3F whereas the opposing force of friction is f.

Force that produces acceleration = 3F – f (iv)

As from equation (ii),

f = 2F

Force that produces acceleration = 3F – 2F

= F

Now, Force = Mass × Acceleration

F = m × a

= 1200 × 0.2

= 240 N

Therefore, each person pushes the motorcar with a force of 240 N