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General Science => General Science => Topic started by: Ron Maxwell on 12/01/2015 04:15:25

Title: When Pool Balls Collide
Post by: Ron Maxwell on 12/01/2015 04:15:25

I know that when a pool ball hits another ball, if there is no spin involved, they should move away at an angle of 90 degrees. The cue ball is often smaller than the other balls though. How would this change the angle at which they move away from each other?

Title: Re: When Pool Balls Collide
Post by: alancalverd on 12/01/2015 08:35:46

Quote from: Ron Maxwell on 12/01/2015 04:15:25

I know that when a pool ball hits another ball, if there is no spin involved, they should move away at an angle of 90 degrees.

Not true. Consider the case of two identical balls. If the line of approach is aligned with the centers, they will move off in the same direction. As the skew angle increases, so does the departure angle.

Quote

The cue ball is often smaller than the other balls though. How would this change the angle at which they move away from each other?

Same principle applies, because the balls are constrained to move in two dimensions only, but the arithmetic is changed slightly.

The underlying principle is conservation of momentum. if the balls have mass m and velocity v then

m₁v₁ + m₂v₂ = m₁'v₁' + m₂'v₂'

where ' indicates "after collision". The important point is that v is a vector so the components in any two orthogonal directions (say the speed along and across the table) must be conserved.

The fact that the cue ball is smaller than the target simply alters the true angle of approach, means that m₁ ≠ m₂, and in practice adds a bit of spin.

Title: Re: When Pool Balls Collide
Post by: Ron Maxwell on 13/01/2015 02:33:22

In simple terms then, if you use the line of travel of the cue ball as a base line, is the angle between the two balls after collision twice the value of the angle from that line to the centre of the object ball upon contact?

Title: Re: When Pool Balls Collide
Post by: syhprum on 16/01/2015 19:10:26

Although simple theories such as the conservation of momentum work fine in an idealised case the collision of pool balls in the real world is much more complex.
The balls are not of zero size upon collision some of the kinetic energy converts to a wave of compression within the ball which reaches the centre then in a slightly weakened and delayed form bounces back out to the surface during which time the balls may have moved to some extent or had some spin imparted to them.
There is always some spin imparted to the first ball due to friction between it and the table although a skilled player tries to pre-empt this.
A robot snooker playing computer would be quite difficult to program !