# Newton 3rd law of motion

If I took both hands and hold as I am greeting someonei.e.namaste. Now, I push both hands with same force say 10N , there is no change in position.But Newton 3rd law has said,equal and opposite forces are on different bodies and they never cancel each other (action reaction). So, why they don't move? (Here , they- hands)

• Why do you think the force acting on one hand from the other hand is the only force acting on that hand? Apr 6 '20 at 19:25

I think you are confusing two ideas (commonly confused). Equilibrium forces (which cancel) and reactive forces, which may or may not cancel depending on the situation.

Think of a book on the table. You push on the book. The book pushes back on you with an equal and opposite reactive force. If you push hard enough, the book will move. According to Newton's second law, the movement of the book depends only on the force you apply to the book, not to the reactive force which the book applies to you.

Now at the same time as you push on the book, your friend pushes back with an equal and opposite force. The book does not move. But your friend is applying a force to maintain equilibrium, not a reactive force. The book applies a reactive force to you, and another reactive force to your friend. These are equal and opposite, but strictly they don't cancel because they are applied to different bodies. The reason the book does not move is because of the forces you and your friend apply, not because of the reactive forces applied by the book.

The situation you describe is essentially the same, but without the book. The force you apply to your friend's hand cancels with the force your friend's muscles apply to his hand.

• You push on the book. The book pushes back on you with an equal and opposite reactive force. How does the book push back?
– Gert
Apr 4 '20 at 20:27
• It just does. That is the nature of a reactive force as described by Newton's third law. If one wants to go deeper, this is a consequence of conservation of momentum, which can be proven from particle interactions in relativistic quantum theory. Apr 4 '20 at 20:36
• @Gert The push of the book is due to strong repulsive force exerted by the book's atoms on our hands' atoms.
– user258881
Apr 11 '20 at 6:04

When you push on your right hand with your left you feel a force back on your right hand. This is the 'equal and opposite' force that comes from Newton's third law. However, at the same time you are pushing with your right hand you are also pushing with your left and feel a force back on your left hand, again due to Newton's third law. While it is true that the equal and opposite forces act on different bodies and as such can't cancel there are actually two pairs of Newton's third law forces with a force and its reaction force (equal and opposite force) from each hand. These can cancel. If you were to stop pushing actively with one hand, say the left, then both hands would move left as the only forces now are the force to the left from the right hand and the reaction force from the left hand on the right hand.

On each hand, you really have two forces: one from the other hand (10N, pushing out) and one from the arm (10N, pushing in).

These are the equal and opposite forces, hence your hands do not move.