How Fast

[Steve_ref]

Posted this on a snooker forum, but I'm not sure how many mathematicians/physicists there are who play snooker.

Is it possible to calculate the fastest speed a snooker ball can travel on a standard 12 x 6 snooker table, given the weight of the ball, the resistance of the cloth, air temperature/humidity, etc.?

[mjd]

I suspect that the answer will have little to do with rolling resistance or the viscosity of the air but will be limited by the materials used in the manufacture of the balls.

As you strike the ball harder and harder with the cue it will travel faster and faster, until you strike it so hard that it shatters.

[Teddio]

Hitting a snooker ball really hard with a cue will cause it to slide across the cloth. Air viscosity and table friction are negligible factors. The cue transfers momentum to the ball. The ball's maximum velocity can be much greater than the cue-tip velocity. The collision time is quite long due the lateral elasticity and deformation of the cue. There is no simple way of calculating the ball's maximum speed because of the complex nature of the collision.

[Muppit]

yeah, try f x t = (m1 x v) - (m2 x u)

where f = force, t = collision time, m1 = mass of cue, v = initial velocity of cue, m2 = mass of ball, u = velocity of ball

rearrange to get: [(m1 x v) - (f x t)] / m2 = u

i think that a typical cue weighs about 0.6kg
a ball weighs about 0.1kg
average human could apply a force of say 75N?
with a cue speed of 5m/s
call the collision time 0.1s

then with these made up numbers, you have a ball speed of 72m/s.

no need to worry about friction and stuff, as the maximum speed will be as the ball leaves the cue.

[Steve_ref]

Many thanks. I thought it could be done.