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Bouncing Balls. Introductory Question. If you place a tennis ball on a basketball and drop this stack on the ground, how high will the tennis ball bounce? To approximately its original height Much higher than its original height Much less than its original height.

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Introductory Question

  • If you place a tennis ball on a basketball and drop this stack on the ground, how high will the tennis ball bounce?

  • To approximately its original height

  • Much higher than its original height

  • Much less than its original height


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Observations aboutBouncing Balls

  • Some balls bounce better than others

  • Dropped balls don’t rebound to their full height

  • Balls bounce differently from different surfaces

  • Ball bounce differently from moving objects


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4 Questions about Bouncing Balls

  • Why can’t a ball that’s dropped on a hard floor rebound to its starting height?

  • Why does the floor’s surface affect the bounce?

  • How does a ball bounce when it hits a bat?

  • What happens to the bat when a ball hits it?


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Question 1

  • Why can’t a ball that’s dropped on a hard floor rebound to its starting height?

  • What happens to ball’s energy as it bounces?


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Bouncing from a Rigid Floor

  • As it strikes a rigid floor, a ball’s

    • kinetic energy decreases by the “collision” energy

    • elastic potential energy increases as it dents

  • As it rebounds from that surface, the ball’s

    • elastic potential energy decreases as it undents

    • kinetic energy increases by the “rebound” energy

  • Rebound energy < collision energy

    • A “lively” ball wastes little energy as thermal energy

    • A “dead” ball wastes most of its energy


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Measuring a Ball’s Liveliness

  • Coefficient of Restitution

    • is a measure of a ball’s liveliness

    • is the ratio of outgoing to incoming speeds:

      coefficient of restitution = outgoing speed / incoming speed


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Question 2

  • Why does the floor’s surface affect the bounce?


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Bouncing from an Elastic Floor

  • Both ball and floor dent during a bounce

  • Work is proportional to dent distance

  • Denting floor stores and returns energy

    • A “lively” floor wastes little energy

    • A “dead” floor wastes most of its energy

  • A floor has a coefficient of restitution, too

  • A soft, lively floor can help the ball bounce!


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Question 3

  • How does a ball bounce when it hits a bat?

  • Do both the ball and bat bounce?


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Bouncing from Moving Surfaces

  • Incoming speed → approaching speed

  • Outgoing speed → separating speed

  • Coefficient of Restitution becomes:

    coefficient of restitution = separating speed / approaching speed


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Ball and Bat (Part 1)

  • Ball heads toward home plate at 100 km/h

  • Bat heads toward pitcher at 100 km/h

  • Approaching speed is 200 km/h


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Ball and Bat (Part 2)

  • Approaching speed is 200 km/h

  • Baseball’s coefficient of restitution: 0.55

  • Separating speed is 110 km/h


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Ball and Bat (Part 3)

  • Separating speed is 110 km/h

  • Bat heads toward pitcher at 100 km/h

  • Ball heads toward pitcher at 210 km/h


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Introductory Question (revisited)

  • If you place a tennis ball on a basketball and drop this stack on the ground, how high will the tennis ball bounce?

  • To approximately its original height

  • Much higher than its original height

  • Much less than its original height


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Question 4

  • What happens to the bat when a ball hits it?


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Bouncing’s Effects on Objects

  • A bouncing ball transfers momentum

    • while stopping

    • while rebounding

  • A livelier ball transfers more momentum

  • A bouncing ball can also transfer energy

  • These two transfers together govern bouncing

    • A ball transfers momentum and energy to a bat

    • Identical elastic balls can transfer motion perfectly


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Impact Forces

  • Harder surfaces bounce faster

    • Momentum is transferred more quickly

    • Time is shorter, so force is larger

  • No one likes bouncing off hard surfaces


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The Ball’s Effects on a Bat

  • The ball pushes the bat back and twists it, too

  • When the ball hits the bat’s center of percussion,

    • the bat’s backward and rotational motions balance

    • the bat’s handle doesn’t jerk

  • When the ball hits the bat’s vibrational node,

    • the bat doesn’t vibrate

    • more energy goes into the ball


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Summary about Bouncing Balls

  • Each ball has a coefficient of restitution

  • Energy lost in a bounce becomes thermal

  • The surface can affect a ball’s bounce

  • Surfaces bounce, too


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