A question for math and science people

[FIRST JerseyKid]

What angle and position would be idle for applying the least amount of force on a que ball and sinking all 9 balls in a pool table in with 1 hit? This would be with idle conditions. Where would you apply force on the ball and in what direction?

[Denman]

a), spell checker is also an enemy, it should be ideal i think?
b) do you mean when they are all in the starting positions or where?
c) I'll help as much as i can

[jdiwnab]

Do you mean 10 balls? Usual pool tables have 10 balls in the rack aranged in a triangle:
O
OO
OOO
OOOO
But there is 9 ball pool. I don't know how their arranged.

When you say that you want to strike all of the balls, do you want the cue to hit them all, or to cause all of them to move? Do you want them to move to the holes, or just move out?

[Denman]

9 ball is in a diamond shape
O
OO
OOO
OO
O
Whilst 8 ball has 15 in a triangle...

[jdiwnab]

Originally Posted by Denman

Whilst 8 ball has 15 in a triangle...

I guess I miss counted. It didn't sound right.

[Denman]

its 8ball because you have to pot 8 balls, 7 of your colour (i suppose spots or stripes for you lol) and the black

[Greg Ross]

Originally Posted by jdiwnab

Do you mean 10 balls? Usual pool tables have 10 balls in the rack aranged in a triangle:

   O
  O O
 O O O
O O O O

That's the arrangement of the pins for bowling.

[mathking]

Pool uses 15 balls (7 solids, 7 stripes and the 8 ball). They are arranged in a triangle.

There is no ideal angle and force. The system is too sensitive to changes in the initial conditions. A minor change in the surface of the pool table or a millimeter change in the position of one ball can greatly change the "correct" angle of incidence. So the correct answer requires statistical mechanics and has a variey of solutions. In general, a firm strike which is a few degrees off of head on the lead ball is the "best" option.

As for minimum force to sink all 15 balls, again there is not one best answer. The minimum force to maximize your chance of sinking all of the balls is likely to be whatever force won't shatter the queue ball and the first ball it strikes. To sink all of the balls, they would have to be bouncing around a LONG time. It is such an unlikely event that it would be essentially impossible to do a real statistical mechanics study. You would not experience success often enough to get any decent conclusions.

[Denman]

not necessarily, 9ball is in a diamond...
it might be that there is a set up he means for....

[mathking]

Yeah, I thought of nine ball as I was driving home today. The answer about the force and angle will still be pretty much the same.