Challenge: To design and build a device that measures the impulse given to a dropped golf ball as it hits an angled metal surface provided by Mr. J. The drop height can vary from 25 cm to 95 cm. The “strike plate” angle should be between 20° and 25°. You will measure the impulse experienced by the golf ball by video analysis of its rebound. Your device with its metal plate must experience a measurable change as a result of the strike by the golf ball, which you can use to calibrate it as an impulse measurer. Once calibrated, Mr. J will drop the golf ball from an unknown height, which you will need to determine without video analysis.
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 so you can calibrate the effect of the impact on the device itself.
Scoring: Your system will be scored on your ability to accurately determine the original drop height of the golf ball.
Score = % difference between your estimate of the height 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 (dx and dy) can be used to find the velocity (v’) after the collision.
Total kinetic energy is not conserved during the collision because the collision is not perfectly elastic.
However, Newton’s third law does apply. Your device will experience the exact same impulse as the golf ball in exactly the opposite direction. It must experience a change in proportion to this impulse in order to be used as an impulse measuring device that can be calibrated with strikes from a golf ball previously dropped from known heights.
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