Bouncing Balls the tennis ball bounce? To approximately its - - PDF document

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Bouncing Balls 1

Bouncing Balls

Bouncing Balls 2

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?

A.

To approximately its original height

B.

Much higher than its original height

C.

Much less than its original height

Bouncing Balls 3

Observations about Bouncing 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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Bouncing Balls 7

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 =

• utgoing speed / incoming speed

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Question 2

Why does the floor’s surface affect the bounce?

Bouncing Balls 9

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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Bouncing Balls 13

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?

A.

To approximately its original height

B.

Much higher than its original height

C.

Much less than its original height

Bouncing Balls 16

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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Bouncing Balls 19

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