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$(a)$ Let's say A person is pushing an object. Then the object will put a force on the person equal to the force the person is putting on the object (because of Newton's third law). Then the person should move backward because of the opposing force. But clearly, the person moves in the same direction as the object while the person pushes it. Is there something wrong with my reasoning?

$(b)$ Let's say I am pushing against a wall with force $F$, then the wall will push me with force $F$ (because of newtons 3rd law). Because The wall is pushing me with force F, then I will (because of newtons 3rd law), push the wall with force $F$, this will add up with my previous force to $2F$. If I keep doing this indefinitely, then I can say that I am pushing this wall with a force of $\infty$ $N$ and the wall is pushing me with a force of $\infty$ $N$. That would mean I will get crushed and the wall will get destroyed. But clearly, that does not happen. Again, where am I using Newton's 3rd law in the wrong way?

DanielC
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Kripke Platek
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2 Answers2

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(a) You have to consider all of the forces acting on you. In addition to the force from the object being pushed, there is a frictional force on your feet. If you were in deep space and pushed on the object, it would move forward and you would move backward.

(b) You pushing on the wall with force F and the wall pushing on you with force F is the end of the story. The force of the wall on you is the reaction to the force you exert on the wall. For every force there is an equal and opposite force i.e. one of each. I suppose you could think of your force on the wall as being the reaction of the wall's force on you. There is no extra force created beyond those two.

Not_Einstein
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  • In The wikipiedia the third law is stated like this ,"When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body." How do I define which one is the first body and which one is the second ? Also , the statement doesn't say anything about why I cant have things like reaction of reaction reaction of reaction force etc .Shouldn't the statement for the 3rd law be more precise? – Kripke Platek Nov 10 '20 at 15:37
  • You don't have to define a first and second. The earth exerts a force on the moon and the moon exerts an equal and opposite force on the earth...or...the moon exerts a force on the earth and the earth exerts and equal and opposite force on the moon. Either statement is correct. – Not_Einstein Nov 10 '20 at 19:35
  • As with first and second, either force in a pair can be identified as the action or reaction. As I mentioned, you pushing on the wall is the "reaction" to the wall pushing on you. – Not_Einstein Nov 10 '20 at 19:38
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To add a bit to Not_Einstein's excellent answer. The force of friction keeps you from sliding and allows you to move the object forward; the maximum force of friction on you is proportional to the normal force pushing up on you from the ground. To increase this force of friction, you push down against the ground to increase the normal force. As an earlier answer suggests, see answer by Bob D on [Friction when walking] : https://physics.stackexchange.com/a/480867/277960

The total external force forward on the system defined as the person and the object, is the force of friction on the person forward minus the force of friction on the object backwards. The heavier the object, the greater its normal force and its resisting force of friction; hence, the harder you must push down against the ground to increase the forward force of friction.

The force you provide on the object produces a torque about the center of mass of the object, tending to tip the object; the effective position of the normal force from the ground on the object moves forward from the center of mass in the direction of motion to provide a counter torque.

John Darby
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