# Confusion with Newton’s third law

Suppose i push a box with my hand which has a mass=1kg. I apply a force of 2 newtons and it will accelerate at 2m/s^2. But, according to the third law, the box applies a force on me, which is also equal to 2 newtons, in the opposite direction which will cause ME to accelerate in the backward direction. But this is not the case, i am accelerating forward ( my hand ) but that force ( the reaction of the box ) is forcing me to move backward, and that force is equal to 2 newtons. So i MUST apply a force larger than 2 newtons to move forward, but i am not doing this, i am still applying a force of 2 newtons and accelerating forward.

Why?

PS- I know the forces donnot cancel out as they act upon different objects.

• The force you apply is the force you apply, but the resulting movement is less than the distance that you move your arm forward because the center of mass of your body moves backwards a little. It is this lapse in movement that you perceives as "inefficient" rather than a change in force. If you calculate this formally then you end up with what is known as the "rocket equation", which basically tells you that rockets incur an exponentially rising "fuel cost" as we try to boost the payload to ever higher velocities. Jan 23, 2016 at 6:54