Why Does a Pool Ball Stop Dead When Hit at a Straight Angle?

[kaloyan5]

Hi. I'm having trouble understanding Newton's third law. It states that: To every action there is an equal and opposite reaction. Then howcome if you hit a pool ball with the cue ball, at a straight angle, it'll stop dead. Isn't it supposed to go backwards the same distance as the second ball (because the reaction is supposed to be equal and opposite to the action)?

 

[rcgldr]

I'm having trouble understanding Newton's third law. It states that: To every action there is an equal and opposite reaction. Then how come if you hit a pool ball with the cue ball, at a straight angle, it'll stop dead.

This requires you put a bit of backspin on the cue ball so there's zero spin at the point of collision. Each ball experiences the same magnitude of force and each ball compresses the same amount. During the collision, the rate of acceleration of the pool ball and the rate of deceleration of the cue ball are the same, since the forces are equal and opposing, and the masses of the balls are the same. The end result is the cue ball ends up stopped and the pool ball ends up with the same speed as the cue ball originally had (ignoring losses). The cue ball doesn't instantly stop though, during the collision, both balls are moving forwards, but the duration of the collision is a very small amount of time.

 

[K^2]

For objects in an equal mass in collision, Newton's 3rd leads to the CHANGE of velocity being the same in magnitude opposite in direction. For the cue ball it means going from motion to dead stop. For the struck ball it means going from rest to moving at the original velocity of the cue ball.

After that, yes, spin takes over, but the instant after collision, it hasn't had any affect yet.

 

[MagnetDave]

Let me put this a bit more simply:

The cue ball imparts a force on the target ball equal to the force you hit it with (ignoring friction, of course). Let's call it X Newtons. X Newtons accelerates the target ball from 0 to the speed of the cue ball. In turn, the target ball imparts an equal force of X Newtons on the cue ball in the opposite direction, with accelerates the cue ball from it's speed exactly to 0.

To make the cue ball go in the opposite direction, it would that 2X Newtons, enough force to accelerate the ball to 0, and accelerate it again up to speed in the opposite direction.

 

[K^2]

That is absolutely wrong. A force applied over time gives you change in momentum, and collision times are going to be different. You absolutely cannot claim that both will be X Newtons. And that's skirting the issue of these forces not being constant during the collision either.

 

[MagnetDave]

That is absolutely wrong. A force applied over time gives you change in momentum, and collision times are going to be different. You absolutely cannot claim that both will be X Newtons. And that's skirting the issue of these forces not being constant during the collision either.

yes yes yes...however, to be responsive to the OP in as direct a manner as possible as to why the cue doesn't fly back as far as the target ball, it is reasonably fair to ignore friction, spin, and elasticity.

I was simply trying to say, to OP, WHY a cue ball squarely striking an object of equal mass does not, from its equal and opposite reaction, fly off in the opposite direction, by trying to put what the forces actually do in perspective.

 

[kaloyan5]

I think I get it now, thanks.

 

[sophiecentaur]

. . . . and collision times are going to be different. You absolutely cannot claim that both will be X Newtons. And that's skirting the issue of these forces not being constant during the collision either.

Does that make sense? How can one ball be pushing at the other ball for a different time to being pushed back at? If they're in contact, they're in contact - no?

 

[sophiecentaur]

Ah - I see now what you may mean. Too terse, perhaps? The two forces to which you refer are cue-ball and ball-ball. In that case, the force times time (impulse, as you say) will be the same in each case.

 

[K^2]

Average force, yes. Otherwise, you have to integrate. But ball-ball collision is going to be much shorter than ball-cue.

 

[Danger]

I speak now as a fairly good pool player rather than as a scientist. There are so many variables in the real world that it is hard to generalize.
For instance, in a "normal" shot, the cueball follows the object ball in the same direction (for a straight shot). It is delivered with 1/4 to 1/2 tip-width of top spin, and you always want to "stroke through" (follow through) the cueball with the stick for a at least 4" to 6".
The texture of the felt makes a tremendous difference, as well.

 

[cobrastrike]

It also has conservation of energy.

 

[Danger]

It also has conservation of energy.

Absolutely, but the game in quesion is still strictly defined by the refs and coaches and observers of the game.

 

[sophiecentaur]

I speak now as a fairly good pool player rather than as a scientist. There are so many variables in the real world that it is hard to generalize.
For instance, in a "normal" shot, the cueball follows the object ball in the same direction (for a straight shot). It is delivered with 1/4 to 1/2 tip-width of top spin, and you always want to "stroke through" (follow through) the cueball with the stick for a at least 4" to 6".
The texture of the felt makes a tremendous difference, as well.

Yes. In reality, the game is far from'ideal'. If there were no friction effects it would be really boring as you'd only have angles to play with.
The "stroking through" you refer to must, presumably, work because pushing the ball along with a smooth, chalked cue, over the drag of the cloth must get the cue ball rolling rather than skidding along, as it would with a brief blow from the cue. Once the nearly ideal, nearly instant' collision with the target ball has happened, the cue ball will still have some angular momentum and will drive itself forward, rather than remaining still.
I imagine there must be some really good slow mo movies of this sort of thing somewhere. I'll have a look at U tube.

 

[Danger]

Maybe try TSN, Sophie. They're the ones who broadcast our misbegotten attempts at taking Vegas by storm. I still feel honoured to have won the trip down there to play in the world finals 5 years in a row, but the first thing that you learn after arriving is that you don't know a damned thing about playing pool.