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3.2 Bouncing Balls !!!

3.2 Bouncing Balls !!!. New ideas for today. Coefficient of restitution Bats and racquets. Basketball. Air. Approaching energy = “Collision” energy Rebounding energy = “Rebound” energy. Some energy is converted into thermal energy. Bouncing from Stationary, Rigid Surfaces.

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3.2 Bouncing Balls !!!

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  1. 3.2 Bouncing Balls !!!

  2. New ideas for today Coefficient of restitution Bats and racquets

  3. Basketball Air Approaching energy = “Collision” energy Rebounding energy = “Rebound” energy Some energy is converted into thermal energy

  4. Bouncing fromStationary, Rigid Surfaces • Approaching ball has kinetic energy. • Bouncing ball has elastic potential energy. • Rebounding ball has kinetic energy. • Some energy is lost to thermal energy. • Lively (happy) balls lose little KE, dead balls (sad) lose a lot of KE. Approaching energy  “Collision” energy Rebounding energy  “Rebound” energy

  5. Happy/Sad Ball Which ball is “happier”? on ramp Why, the one with this highest Coefficient of Restitution, of course!

  6. Clicker question Why doesn’t an under-inflated basketball bounce as well as an inflated one? (A) Air is a “better” spring than the rubber (B) The rubber is a “better” spring than air (C) An under-inflated ball exerts a bigger impulse on the floor, therefore wasting more of its energy

  7. Outgoing Speed Incoming Speed Coefficient of Restitution = Coefficient of Restitution • Measure of a ball’s liveliness. • Ratio of outgoing to incoming speeds. superball: 0.90 golf ball: 0.82 tennis ball: 0.75 baseball: 0.55 Hard surface:

  8. Clicker question Which way is this ball bouncing and why? (A) From left to right, because it looks like it’s going to bounce higher on the right side. (B) From right to left, because the speed is higher on the right side. (C) From left to right, because the speed is higher on the right side. (D) From right to left, because the speed is higher on the left side.

  9. Regulation tennis balls must rebound 53-58 inches when dropped from a height of 100 inches onto a concrete slab. Why? KE = ½ mv2 = mgh 0.752 = 0.56 1.24 in 0.93 in 0.93 / 1.24 = 0.75

  10. Trampoline What’s the coefficient of restitution of a person?

  11. Trampolines can increase our coefficient of restitution… …just like a tennis racquet increases a tennis ball’s coefficient of restitution! Note: the bear doesn’t get hurt because he is limp – his collision with the ground takes a long time, and so the force on him is small. This trick works for people too (esp. drunk people)!

  12. Tennis racket Look at how much the strings are bent. Some of the collision energy goes into that spring (which is a better spring than the ball)!

  13. Dropped from 100 inches: Onto concrete, COR=0.75, ball surface bends by 6 mm Onto a racquet, COR=0.84, ball surface bends by 3 mm

  14. Courtesy of CE Composites, via Al Nathan (UIUC physics)

  15. Bouncing fromStationary, Elastic Surfaces • Both ball and surface dent during bounce. • Work is proportional to dent distance. • Surface stores part of collision energy. • Surface returns part of rebound energy. Surface liveliness or deadness is important.

  16. Clicker question Professional tennis players want to hit the ball very hard. How should they have their racquets strung? • stiff • loose • it doesn’t matter

  17. You have to change your point of view when both the surface and the ball are moving…

  18. Separating Speed Approaching Speed Bouncing from Moving Surfaces • Incoming speed becomes approaching speed. • Outgoing speed becomes separating speed. • Coefficient of Restitution becomes: Coefficient of Restitution =

  19. Ball and Bat: Approaching • Ball approaches home plate at 100 km/h. • Bat approaches pitcher at 100 km/h. • Approaching speed is 200 km/h.

  20. Ball and Bat: Separating • Bat approaches pitcher at 100 km/h. • Ball approaches pitcher at 210 km/h. • Separating speed is 110 km/h.

  21. 110 km/hr 200 km/hr = = 0.55 Ball and Bat Separating Speed Approaching Speed Coefficient of Restitution = Separating speed is 110 km/hr Approaching speed is 200 km/hr

  22. Clicker question During a serve, Federer’s racquet moves at about 70 mph. Just before he hits the ball, it is almost at rest. The COR for the tennis ball on the racquet is 0.84. How fast does he serve the ball? A) 70 mph B) 83 mph C) 130 mph D) 140 mph

  23. The physics of baseball bats and tennis racquets Center-of-percussion Vibration

  24. Sweet spot Fundamental Mode: When the ball hits a Node of the Fundamental Mode, the bat doesn’t vibrate much when ball hits it. The “Sweet Spot” is the place where the bat vibrates the least. It is very close to the node of the fundamental mode.

  25. Courtesy of Al Nathan

  26. Al Nathan, UIUC’s “Mr. Baseball” http://webusers.npl.illinois.edu/~a-nathan/pob/

  27. For next class: Read Section 3.3 See you next class!

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