# Confusion about an application of Newton's third law

If I apply a force F on a block with my hand, the block in return applies the same force on my hand. But my hand is in contact with the block and moves with it. On who does this opposite force act on exactly in this scene ? I am standing on rough ground without sliding. What I think is, it ultimately causes a same force F on ground, i.e., the earth (because of friction on my legs) . Am I right about this ? Is this how momentum is also conserved ?

If I apply a force F on a block with my hand, the block in return applies the same force on my hand.

Yes.

But my hand is in contact with the block and moves with it. On who does this opposite force act on exactly in this scene?

You just answered that in the former sentence.

• The block feels a force caused by the hand, and
• the hand feels a force caused by the block.

These two forces then happen to be equal but opposite, and this is what we call Newton's 3rd law.

I am standing on rough ground without sliding. What I think is, it ultimately causes a same force F on ground, i.e., the earth (because of friction on my legs). Am I right about this?

Yes, you are right. We can continue the stepwise thought-process above:

• Your hand exerts a force on the block.
• The block then exerts a force (equal but opposite) on the hand.
• The hand is then exerting this force on the body, because the body tries to prevent the hand from accelerating backwards.
• The body then exerts this same force on the Earth, because the Earth tries to prevent (by friction) the body from accelerating.

The force propagates through and eventually, when nothing is there to restrict the object anymore then acceleration will happen. And nothing prevents the Earth from accelerating, so it will. But naturally, from Newton's 2nd law we know that for this same force it will accelerate very, very little due to its enormous mass.

Is this how momentum is also conserved?

Yes, Newton's 3rd law brings along the momentum conservation law. Many sources show the connection / derivation, for example here.

To understand this problem, you must consider two applications of Newton's Third Law. The first is between your hand and the block. The second is between your feet and the ground.

For simplification, we'll treat you as a rigid object and neglect vertical forces. The principles are similar in any case.

So you push on the block with force F, horizontally. The block accelerates, and a balancing force -F is exerted on your hand, pushing you backwards.

Then, static friction between your feet and the ground causes you to exert the same force -F on the ground. The ground, being rigid and extremely high mass, moves only negligibly, but exerts the balancing force F on you.

Thus there is both an F and a -F exerted on you, summing to zero, and you remain still. The block and the ground are accelerated in opposite directions, but due to the extreme ratio of masses (about a septillion to one), only the block moves an easily measurable distance.

As you said. You are standing on rough ground without sliding. If you pushed the block in outer space, you would be accelerating in the opposite direction to the block. In the case of standing on planet earth, in a very simplified hypothetical sense, to an extremely small and undetectable scale, you and the planet earth are accelerating in the opposite direction. Of course, there is virtually zero acceleration of the planet earth. The force applied to earth will a cause small pressure wave that travels at the speed of sound, so it is rather a pressure wave that dies out quickly.