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# On Newton's Third Law

11/12/2010 12:24 PM

This is about Newton's Third Law. Newton's third law viz. that every action has an equal and opposite reaction is something I have probably misunderstood in its detail or not understood properly.

In an example of say a hand hitting a table, we see that there is an opposite force on the hand. Now in the case of say a hand hitting a pillow, how does someone experience the same reaction as hitting the table?

From what I can understand, the force applied is the same (considering identical movement of hand), but why doesn't the reaction force seem the same?

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#1

### Re: On Newton's Third Law

11/12/2010 12:28 PM

The pillow is not a solid object. It moves with the hand and absorbs the energy over a longer period of time.

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#2

### Re: On Newton's Third Law

11/12/2010 12:40 PM

Newton's law still holds. Whatever force your hand exerts on the pillow, the pillow must exert on your hand. I think the reason it seems different in the case of the pillow versus the table is because the force is different!

Force by definition is the change in momentum through time ( in math terms d (mv)/dt) or when mass is constant, as most people put it.. m*a).

Let's assume your hand starts at the same velocity and comes to a rest in both cases. (This means that the change in velocity will be the same in both)

In the case of the table, it stops in a shorter time than with the pillow. So in math terms the "m*v" term stays the same but the "dt" (change in time term) is different. (The table slows down your hand much faster than the pillow so it must exert a greater force!)

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#3

### Re: On Newton's Third Law

11/12/2010 11:07 PM

If an object of weight W rests on a table, the table reacts with an upward force of W. If the table is very strong, the deflection is not noticeable.

If an object of weight W rests on a pillow, the pillow compresses, but when the object finally comes to rest, the pillow reacts with an upward force of W. The deflection may be substantial and the pillow is noticeably deformed, but the reaction is the same as it was on the rigid table.

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Bruce
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#4

### Re: On Newton's Third Law

11/13/2010 10:40 AM

@ ChaoticIntellect

Well explained. So wouldn't the explaination (if I actually understood it correctly) also lead us to infer that its quiet difficult (or impossible) for our hand to apply above a certain force to the pillow due its material nature?

Btw, thanks to all of you

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#5

### Re: On Newton's Third Law

11/13/2010 11:38 AM

If the load is static, there is no limit to its magnitude. It simply compresses the pillow until it comes to rest.

If the load is dynamic, there is an impact upon collision. The impact will feel more painful on a hard table than a soft pillow because the pillow acts as a shock absorber causing a slower deceleration as stated by lynlynch.

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Bruce
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#6

### Re: On Newton's Third Law

05/11/2011 10:26 AM

How is this explained in terms of Newton's laws? After all a compressing collision in terms of the pillow, is a collision too.

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