According to Newton's third law, the force acting on object is equal and opposite to the other object that is applying the force. If I push a table with 5N force then table is doing the same. But the table and I have different masses, so how could the force be same? Isn't $F=ma$?
[Physics] Newton’s third law.. please explain here
forcesnewtonian-mechanics
Best Answer
Suppose you and the table are floating in space. If you push the table it will go in one direction and you will go in the other direction. Your and the table's acceleration will be different so you will end up travelling at different speeds. This is obvious from conservation of momentum. The momentum in the centre of mass frame is initially zero, so after the push your velocity $v$ and the table's velocity $V$ are related by:
$$ MV = mv $$
where $M$ is the mass of the table and $m$ is your mass. Your velocity will therefore be:
$$ v = \frac{M}{m} V $$
If you walk up to a table in your living room and push it then other forces come into play. These include the force on the table legs exerted by the living room floor and the force on your feet exerted by the living room floor. You would need to take these into account to analyse the situation properly.