Newton's Third Law of Motion? [duplicate]

Question

Newton's third law of motion states that every action has an equal and opposite reaction. But, on punching a wall, I feel much greater force than on punching an inflated balloon. So, what does it mean? Is the balloon not applying an equal and opposite force. Or, what else is going on here?

Answer 1

You are dealing with two different scenarios here;

1. When I punch a wall
2. When I punch a balloon

Newton's III Law of motion doesn't say that the force applied on the wall should be equal to the reaction of the balloon or viceversa. I think you are mixing both scenarios. Indeed the force is different in both situations but action and reaction in each of those obeys Newton's III Law.

Ballons have less mass than walls and thus they have less inertia (resistance to a change in their movement). When you want both objects to accelerate in the same way (just as your fist moves) what you need is a huge force applied on the wall and a smaller one on the balloon since according to Newton's II Law of motion for an equal acceleration on a different mass object you need different mass forces:

$\vec{a}_{balloon} = \vec{F}_{balloon}/m_{balloon}\;\;$ and $\;\; \vec{a}_{wall} = \vec{F}_{wall}/m_{wall}$

If $\;\; \vec{a}_{balloon} = \vec{a}_{wall}\;\;$ then $\;\;\ F_{balloon}/F_{wall} = m_{balloon}/m_{wall}$

Which means that the force to be applied on the wall is to the force to be applied to the balloon as large as the ratio of the masses. So, if you want to accelerate the wall in the same way as the balloon and the wall is, let's say, $10000$ times more massive than the balloon, then the force on the wall should be $10000$ times larger than the force on the balloon.

What you really feel in each scenario is the reaction of the wall (or the baloon). Since according to Newton's III Law the reaction is equally intense as the action you should expect the wall to react $10000$ times stronger to your punch than in the case of the balloon.

All of that would happen if you expect the wall and the baloon to move when you punch them at the same rate as you move your fist. This means that we are considering you hitting the wall with more enthusiasm than the balloon (with more muscular force).

But let's say that you hit both with exactly the same muscular force. Then the explanation is different. The balloon is not a rigid object (or at least not as rigid as the wall), this means that if your fist is moving at a velocity $\vec{v}$ you have plenty of time for your fist to decelerate as the baloon deforms. That change in the speed of your fist from $\vec{v}$ to zero will occur in a relatively large timespan and thus the acceleration is low, and thus the force on your fist is small. On the contrary for the wall your fist will transition from a speed of $\vec{v}$ to zero in just a fraction of the time, meaning that there is a larger acceleration imposed on your fist and thus a larger force.

So as you can see it doesn't matter if you punch one with more force to see it moving at the same acceleration as the other or if you punch both with same force to see them moving at different accelerations; the result is the same, you feel a more intense reaction when hitting the wall than when hitting the balloon.

This is even more noticiable in reality when you consider the fact that usually the wall would trully stop your fist but the balloon would probably gain some momentum and then keep moving in the air with the same speed as your fist after the collision without further accelerating, or in other words; the ballon would never absorb all the momentum of your fist since it would fly away before that, something that the wall is not expected to do, and thus the acceleration considered for the fist against the ballon is even smaller than the acceleration considered before.