1.2 Falling Balls1.2 Falling Balls

•ball

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Ideas for today:Ideas for today:

• Weight• Acceleration due to gravity• Falling objects• Horizontal and vertical motion

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RecapRecapThe force exerted on an object is equal to the

product of that object’s mass times its acceleration.

The acceleration is in the same direction as the force.

Force = mass x acceleration

F = m a(force and acceleration are vectors)

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a = F / m Mass is a measure of inertia

Recap, continuedRecap, continued

Animation (link):simulation of 1-d forces

Physics Education Technology(Carl Wieman’s project at CU)

Courtesy of:

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Clicker Clicker Question:Question:Suppose that I throw a ball upward into the air. Right after the ball leaves my hand, is there any force pushing the ball upward?

(A) Yes(B) No

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Galileo, age 60, drawn by Ottavio Leoni in 1624.

Galileo was the first to analyze motion in terms of measurements and mathematics.

He described acceleration, which is the rate of change of speed: (should be velocity…)

acceleration = final speed – initial speed time required

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Important!Important!• Galileo did not use vectors• Really:

acceleration = final velocity – initial velocity time required

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•Galileo’s Inclined Plane

Galileo did experiments to convince others that the acceleration caused by gravity would be the same for all freely falling objects if there was no air to retard their motion.

He dropped two heavy metal balls together from the leaning tower. Although one weighed much more than the other, they reached the ground almost at the same time.

1. Experiment repeated MANY times

2. Led by a thought experiment (brick that splits in two)

Important for Scientific Method:

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The nature of science*:

*according to me

• Physics is about predicting the future• There is always a limit to accuracy• Verified by experiment• Experiments must be reproducible• Scientific knowledge is constantly evolving,

and is always a little wrong (but can still predict well enough)

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A tennis ball and a golf ball dropped side-by-side in air. The tennis ball is affected more by the air’s resistance than the golf ball.

The larger the object is, and the faster it is falling, the greater the air’s resistance to its motion, as skydivers all know…

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•Large and Small Balls

When most of the air is removed from a container, feathers and apples fall almost side-by-side, their speeds changing at almost the same rate.

If all the air was removed, they would accelerate downward at exactly the same rate.

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•Coin and Feather

Observations About Falling BallsObservations About Falling Balls

• A dropped ball:– Begins a rest, but soon acquires downward speed– Covers more and more distance each second

• A tossed ball:– Rises to a certain height– Comes briefly to a stop– Begins to descend, much like a dropped ball

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Dropped Ball: Falling Dropped Ball: Falling DownwardDownward

velocity = initial velocity+ acceleration × time

position=initial position +initial velocity × time + ½ acceleration × time2

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•Repeat Galileo’s Inclined Plane

How do position, velocity, and acceleration relate?

Time ( s )

Position ( m )

Velocity ( m/s )

Acceleration ( m/s2 )

0 -4 3 -1

1 -1 2 -1

2 1 1 -1

3 1 0 -1

4 0 -1 -1

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•Acceleration tells Velocity how to change•Velocity tells Position how to change•Time is a marker common to all three

In free fall objects accelerate constantly toward Earth at the rate of g . Objects moving upward slow down until their direction is reversed, and then they accelerate downward.

At the top of their path the upward speed is zero. How long? Only instantaneously. A constant acceleration means the speed is changing all the time, so the speed only passes through the value of zero at the top of the path.

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Tossed Ball:Tossed Ball: Falling Upward

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•Clicker Question

•Is it possible to have an object that has

•a negative position, a positive velocity,

•and a negative acceleration all at the

•same time?

•A) Yes

•B) No

Tossed ball:Tossed ball: Falling Upward, then Downward, with a constant horizontal velocity component

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•Drop and Shoot Sideways Demo

Here two heavy balls begin “free fall” at the same time.

The red one is dropped, so it moves straight downward.

The yellow ball is given some speed in the horizontal direction as it is released.

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The horizontal lines show that they keep pace with each other in the vertical direction.

Why?

They have the same acceleration, g, downward, and they both started with zero speed in the downward direction.

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The yellow ball’s

horizontal speed is not

affected by gravity,

which acts only in the

vertical direction.

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•Repeat Galileo’s Inclined Plane

Cannonballs shot horizontally with different speeds from the ship travel different distances.

But each cannonball drops the same distance in the same amount of time, since the vertical acceleration is the same for each.

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A simulated strobe illustration of a plane flying

horizontally with constant speed dropping a cannonball

package of food and medical supplies, ignoring air

resistance.

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The cannonball package of food and medical supplies

initially has the same horizontal speed of the airplane.

Neglecting air resistance, it keeps that horizontal speed

as it falls, so it stays beneath the airplane.

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Another example of “packages of food and medical supplies” being dropped by a WWII food delivery system

Note the streamlined packages. Allowances are made for air drag. Note also the acceleration.

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•Shoot the Monkey

Weight is a type of forceIt is the earth’s gravitational force on an object

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Weight and Mass• An object’s weight is proportional to its mass

weight = g · mass• On the Earth’s surface, that constant, g, is

9.8 Newtons/kilogram = 9.8 meters/second2

(9.8 is approximately 10) 32 feet/second2

• g is called the acceleration due to gravity

•1 Newton 1 kilogram·meter/second2 •A Newton is a unit of force, like pounds. A Newton is about ¼ pound, about the weight of a medium apple

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Acceleration Due to Acceleration Due to GravityGravity

On Earth’s surface, all falling objects accelerate downward at the acceleration due to gravity, g !

• force = mass x acceleration, or F=ma (Newton’s 2nd law)

• weight = m g = force

m g = m a

g = a

Don’t think that this is quite so simple…28

m g = m a

Why should gravitational and inertial masses be the same?

Einstein’s equivalence principle – still being tested!

U. Washington

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