Challenge: To design and build a device that measures the impulse given to a dropped golf ball as it hits an angled fixed surface . Using height to vary impact speed, you will find the coefficient of restitution (COR) of the collision. Then you will use what you have learned to find the relative COR of a ball made of a different material.
Parameters: Your system should be designed to fit into your locker, and cannot be stored in the room. Your system needs to allow you to vary and measure the drop height and the dx and dy as the ball bounces off the angled surface.
Scoring: Your system will be scored on your ability to accurately determine the ratio of the COR of the unknown ball to that of your golf ball.
Score = % difference between your ratio and the accepted value
Lowest score will receive highest rank.
Physics: The raised ball has potential energy. (∆Ep = mg∆h)
As it falls, it converts into kinetic energy. (Ek = 0.5mv2)
During the collision the ball will experience a large unbalanced force for a brief time. (∆p = Fnet•∆t) This impulse will change the velocity and momentum of the ball. (∆p = m•∆v) After, the ball will follow a parabolic course, whose dimensions can be used to find the velocity after the collision.
In a collision with a fixed, immovable object, the coefficient of restitution is simply the ratio of velocity after collision to velocity before collision. (COR = v’/v)
Total kinetic energy is not conserved during the collision because the collision is not perfectly elastic.
Extensions: The contact forces during the collision depend on the speed of impact, and can be ten to hundreds of times the weight of the ball. Even with slow-motion video, it will be difficult to measure the time of contact with any precision. However, try with lots of light, and 240 fps, nice and close. If you can estimate ∆t, you can estimate the net force on the ball during the collision.
Help/Hints: Keep track of your golf balls! Try to use the same one each time, or at least the same model. Make sure you're able to release the ball from a precise height with no initial velocity or spin. Angle the fixed plane at around 20-25° to see if you can get the balls to bounce with an initial "launch" angle of about 45°, although it does not have to be perfect. Use the centre of the golf ball upon impact as the vertex of your coordinate plane for measuring dx and dy for the projectile motion.
Use Google Sheets to do the math for you, although I expect you to show your steps for at least one trial.
Quiz Topics: Energy and Momentum
Online Text: 7.1 - 7.7, 8.1 - 8.6