Force Questions -- Snooker ball collision and a rock through a window

[Gulfstream757]

Homework Statement

These are two conceptual questions we were given recently. It's strange how mathematically I regularly do much harder problems but these caught me out a bit

Q1.
If a one snooker ball hits another ball moving at constant speed, why does the second ball move? Surely due to Newton's second law as it is not accelerating there is no force?

Q2.
If by Newton's third law every action has an equal and opposite reaction, why does a stone thrown at a window go through it if thrown hard enough and not simply bounce off?

Homework Equations

F=ma

The Attempt at a Solution

For the first one I think perhaps it's due to imparting an impulse?

For the second one something to do with net forces?

These are confusing me more than they should I know!

 

[kuruman]

Q1: Impulse is one way of looking at it. More simply, while the balls are in contact in time $dt$, the target ball, which is initially at rest, experiences a force from the other ball. What does an object at rest do when a force acts on it?

Q2: If you place a book on a table, the table will exert a normal force and the book will be at rest. If you place a second book, the table will exert a larger force to keep both of them at rest. If you place a battleship on the table, the table will collapse. So somewhere between two books and a battleship there is a threshold force that the table can exert before it collapses. With the window, think impulse again as $\int{F~dt}$ and how much force the window pane can exert in time interval $dt$ when the stone is moving fast.

Mathematical equations can do more for you than just give you numerical answers. They often tell you more about the physical world than you might think at first glance.

 

[Nidum]

Mathematical equations can do more for you than just give you numerical answers. They often tell you more about the physical world than you might think at first glance.

+ 1 +1 +1 .....+ 1 .

Very few people using mathematical equations ever seem to understand that or the significance of it in solving practical problems .

 

[Delta2]

For Q1 (this also relates to Q2 as there are contact forces there too), if your next step is to ask :

"Why when two objects come in contact there is a force generated between them?" (actually two forces , one force $F_{12}$ from object 1 to object 2 and the opposite but equal force $F_{21}=-F_{12}$ from object 2 to object 1)

the answer is that it is due to EM field interactions(in simple words the EM fields from outer electron clouds of the two objects interact electromagnetically and this interaction results in a dominant repulsive force) or due to the Pauli Exclusion Principle (PEP), or both. This is an open debate in these forums.

 

[haruspex]

If by Newton's third law every action has an equal and opposite reaction, why does a stone thrown at a window go through it if thrown hard enough and not simply bounce off?

I'm not sure what they are after here. No reasoning is given for why this should be paradoxical.
The paradox I can think of would apply in the simpler context of, say, pushing on a box. If the box pushes equally back on you, why should it move? Can you answer that?
Introducing the potential breakage of the object may be drawing attention to our common simplification of dealing with "rigid bodies". To explain how a window breaks you need to consider it as multiple bodies with forces between them.

 

[Delta2]

I think the purpose of these two questions is centered around the contact forces that will appear, that the contact forces are actually a pair according to Newton's 3rd law and each component of this pair is exerted on different bodies (for example one force from the stone to the window and another one opposite and equal from the window to the stone), and that they can become large enough to affect the structural integrity of one body (window) , yet no matter how strong, leave mostly unaffected the second body (stone).

 

[haruspex]

I think the purpose of these two questions is centered around the contact forces that will appear, that the contact forces are actually a pair according to Newton's 3rd law and each component of this pair is exerted on different bodies (for example one force from the stone to the window and another one opposite and equal from the window to the stone), and that they can become large enough to affect the structural integrity of one body (window) , yet no matter how strong, leave mostly unaffected the second body (stone).

Perhaps, but I still do not see how that connects with the sugestion in the question that Newton's third leads to some kind of paradox. The paradox, surely, is that anything should be moved by a force if it exerts an equal and opposite force back.

 

[kuruman]

f by Newton's third law every action has an equal and opposite reaction, why does a stone thrown at a window go through it if thrown hard enough and not simply bounce off?

I think the implied paradox is that if the reaction force is always equal to the action force, the pane will always be able to oppose the force that the stone is exerting on it and therefore it will not break and the stone will always bounce off. That is simply not true with contact forces that have an upper limit.

 

[haruspex]

the implied paradox is that if the reaction force is always equal to the action force, the pane will always be able to oppose the force that the stone is exerting on it

I agree, but this same reasoning leads to the paradox that a pushed box should not move, so it is not really anything to do with whether an object will break.

 

[kuruman]

If one views Q1 and Q2 as independent questions, then this in another example of the "pushed box" so called paradox. If, however, the questions are meant to be related to impulse, then Q2 is not appropriate.

 

[haruspex]

If one views Q1 and Q2 as independent questions, then this in another example of the "pushed box" so called paradox. If, however, the questions are meant to be related to impulse, then Q2 is not appropriate.

I did not understand Q1. Where does "the ball is not accelerating" come from? Viewed as an instantaneous change, there is an infinite acceleration.

 

[kuruman]

Where does "the ball is not accelerating" come from?

I think it is a leap of (bad) faith based on the same misconception as the pushed box. If the target ball is always exerting an equal and opposite force to the one exerted by the projectile ball, then the net force on it is zero at all times, therefore it does not accelerate.

 

[RedDelicious]

I did not understand Q1. Where does "the ball is not accelerating" come from? Viewed as an instantaneous change, there is an infinite acceleration.

They are referring to the first ball before the collision.

I think it is a leap of (bad) faith based on the same misconception as the pushed box. If the target ball is always exerting an equal and opposite force to the one exerted by the projectile ball, then the net force on it is zero at all times, therefore it does not accelerate.

The intention was to address the misconception that accelerating objects carry force. If the first ball is moving at a constant velocity, then F = ma = 0, and so how can it exert a force the second ball? To resolve this, you have to understand that Newton's second law is talking about the forces acting on the object and not accelerating objects carrying force. Ideally, you would then begin thinking of what it is that objects actually do possess, which is momentum, and how the interaction can be thought of as a transfer of momentum, not an accelerating object transferring a force F = ma.

 

[haruspex]

The intention was to address the misconception that accelerating objects carry force. If the first ball is moving at a constant velocity, then F = ma = 0, and so how can it exert a force the second ball?

You may be right, but if so I would say the wording is woefully inadequate.