4. Discussion

4.1       Key findings

The black ball travels faster than the cue ball.

Velocity of black ball/Velocity of cue ball = 1.26 (average)

4.2       Explanation of key findings
The black ball weighs 5.5 oz (155.9 g) while the cue ball weighs 6.0 oz (170.1g). As the cue ball is heavier, when the black ball gets hit by it directly through its line of motion , it will travel faster than the cue ball.

Using the equation for kinetic energy,
Kinetic Energy = 0.5 x mass x velocity^2
Ratio of the kinetic energy of the black ball to the kinetic energy of the cue ball
= (0.5 x 6.0 x velocity^2)/(0.5 x 5.5 x velocity^2)
= 6.0/5.5
= 1.090 (4 significant figures)

From the equation for kinetic energy, we will also know that
velocity^2= kinetic energy/(0.5 x mass)
velocity = sqrt(kinetic energy/(0.5 x mass))

Thus,
Ratio of velocity of black ball to the velocity of cue ball
= sqrt(1.090/0.5 x 5.5)/sqrt(1/0.5 x 6.0)
= 1.090 (4 significant figures)

This shows that kinetic energy of black ball/kinetic energy of cue ball= velocity of black ball/velocity of cue ball= 1.090 (3 significant figures)
The values are not equal and are off by 0.136, due to errors such as the area of the ball hit, air resistance, friction against carpet of the pool table and fps of camera. However, the point remains the same, the black ball travels faster than the cue ball.

4.3       Evaluation of hypothesis
Keeping all other constants the same, the black ball will travel 1.26 times faster than the cue ball that hits it directly through its line of motion.

4.4       Areas for improvement
A camera with higher FPS (frames per second) would have been better to track the motion of the ball even more precisely, but with the short amount of time we ended up using our own camera. We could have also used a better cue bridge or buy it. We could have more aluminium profile so the camera is more stable to film better. We could have a better camera holder for the camera that holds the camera in place.

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