According to Biddulph (2014), cue sports is the wide variety of games of skills usually played using a cue stick which is then used to strike a billiard ball. It has a very long history, stretching all the way back to the 15th century. There are three major types of cue sports that are the most popular: Carom billiards, pool and snooker.
We are focusing on pool for our experiment. Pool has originated from carom billiards somewhere in the United States. Even after that, there are still many variations of pool, like eight-ball, nine-ball, straight pool, etc. We particularly chose pool as it has a smaller table than snooker, and it actually has pockets to shoot the balls into, fulfilling some form of purpose.
According to Shepard (1997), when the cue tip strikes the cue ball exactly in the centre, there is no angular velocity imparted directly to the cue ball. Also according to Shepard (1997), as the two balls collide in an off-center hit, the frictional forces acting tangential to the surfaces are relatively small so all of the remaining force is directed along the line between the centres of both the cue ball and the coloured ball.
According to Walker (1983), the friction of the ball with the table serves only to diminish the spin. Also, when the cue ball comes in contact with a coloured ball, if the cue ball has any side spin, it will affect the net force of the coloured ball and make it change directions.
According to Normani (2014) the height of the sweet spot on the cue ball is 7r/5 where r is the radius of the cue ball. At this height, no friction will develop between the initial area of contact between the cue ball and the pool table. Also according to Normani (2014), the speed of the cue ball will affect the final velocity of the two balls and it can be calculated by the Pythagoras Theorem.
According to Karl Hamlin (n.d.), after exerting a force on the cue stick, the force translates into momentum which is transferred through the cue stick, into the cue ball, and then into the object ball. The momentum can be calculated by multiplying the mass and speed of the object.
1.2 Research Question
How does the initial velocity of the cue ball affects the final velocity of the coloured ball?
If there is a constant relationship between the initial velocity of the cue ball and the final velocity of the coloured ball when they hit straight on, then it is possible to derive a formula to predict the speed of the coloured ball.
1.3.1 Independent variable
The independent variable for this experiment would be the initial velocity of the cue ball.
The dependent variable would be the final velocity of the coloured ball after it was hit by the cue ball.