Question

Two persons manage to push a motorcar of mass`1200kg` at a uniform velocity along a level road. The same motorcar can be pushed by three persons to produce an acceleration of `0.2m//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

Suppose each person applies a force F to push the motorcar.
So, Total force applied by two persons=F+ F
=2F ....(1)
Since this force (2F) gives a uniform velocity to the motorcar along a level road (where work is done only against the force of friction), so the force 2F can be taken as being equal to the force of friction f between the motorcar and the road. That is,
Force of friction, f=2F ....(2)
Now, when three persons apply force to push the motorcar, then:
Total force applied by three persons=F+ F+F
=3F .....(3)
Now, the total force applied by three persons is 3F whereas the opposing force of friction is f. So,
Force that produces acceleration=3F-2F ...(4)
But from equation (2), we have f=2F.So,
Force that produces acceleration=3F-2F
or Force that produces acceleration=F
Now, Force =mass `xx` acceleration
F=m`xx`a
F=`1200xx0.2N`
F=240 N
Thus, each person pushes the motorcar with a force of 240 newtons.