Work
The Work involved in any aspect of physics relates force to distance in the following equation:
W = F * d ; where W is work, F is force, and d is distance.
Knowing this relationship the force necessary to move the ball a desired distance can be found by the
initial force. In pool the initial force is added to the system by the person through the cue stick when
striking the cue ball. However, the force is a function of two variables: the mass and acceleration of the
cue stick striking the cue ball.
F = m * a ; where f(i) is force, m(stick) is mass of the stick, and a(stick) acceleration of the stick
To account for the frictional force in the shot, the work of the cue ball on the other ball is the F(i)
multiplied by the distance between the cue ball and other ball d(i) minus the work done by the frictional
force F(f) over the same distance all multiplied by the ratio of the angle(Ø) between the two balls .
F(i) * d(i) - F(f) * d(i) = (90/(90-Ø)) * F(ball) * d(ball)
Knowing the above equations, the values from the properties page, and the distance one wants the ball
to travel the needed acceleration of the cue stick can be calculated by the following:
a(stick) = [(90 / (90-Ø)) * (F(ball) * d(ball) - F(f) * d(i))] / [*m(stick) * d(i)]
*the mass of the cue stick varies but can usually be found printed on the stick.
This site was created by:
Erik Crawford
Physics 212 - Spring 2005
University of Alaska Fairbanks