COOPER CITY HIGH
STUDY OF THE COLLISION BETWEEN BILLIARD BALLS:
In this activity, we will study the collision between two billiard balls: the cue (white) ball, and another (blue) ball. Initially, both balls are at rest with a small distance between them. We have to hit the cue ball using the stick with a force F. We will assume that the time of interaction between the stick and the cue ball is 0.10 s. The cue ball will get some initial momentum and will move without friction hitting the blue ball.
After the collision both balls will move in different directions losing energy because of the friction with the green cloth. The coefficient of kinetic friction will be considered μK = 0.20. The blue ball will move in direction to the corner where it will arrive with speed 0 (zero) under an angle θB while the cue ball will move under the angle θC and will stop at some point with coordinates (xC, yC).
Initially, the blue ball will be centered on the baulk line (white line) at a distance X from the upper cushion. The baulk line is located at 0.737 m from the left cushion and 2.845 m to the right cushion. The width of the table is 1.791 m.
After the collision, the blue ball will move in direction of the upper right pocket, and will get there with speed zero. The cue ball will move in direction of the lower cushion and depending on the initial position of the blue ball X, will stop before touching the lower cushion, or after performing an elastic scattering with the lower cushion. We will consider no lose of energy during this collision, and we will consider that the angle of incidence will be equal to the angle of reflection.
The values of the masses of the cue and blue ball are: MC=0.17 kg, and MB=0.16 kg. The value of X will be different for different students and it will be given individually before starting the exercise.
As a result of the calculations, it is expected that the student will get the following information:
1. The initial speed of the blue ball right after the collision VB=
2. The angle of the blue ball θB=
3. The initial speed of the cue ball VC0=
4. The speed of the cue ball after the collision VC=
5. The angle of the cue ball after the collision θC=
6. The coordinates of the point where the cue ball stops (xC, yC) =
7. The magnitude of the force (F) that gives the impulse to the cue ball F=
SHOW YOUR CALCULATIONS: