1.2 Falling Balls

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1.2 Falling Balls

• ball

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Ideas for today

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

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Recap
The force exerted on an object is equal to the
product of that objects 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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Recap, continued
a F / m
Mass is a measure of inertia
Animation (link) simulation of 1-d forces
Courtesy of
Physics Education Technology (Carl Wiemans
project at CU)
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Clicker 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 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)
Galileo, age 60, drawn by Ottavio Leoni in 1624.
final speed initial speed time required
acceleration
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• Galileos Inclined Plane

Important!

• Galileo did not use vectors
• Really

final velocity initial velocity time required
acceleration
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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

• 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)

according to me
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• Large and Small Balls

A tennis ball and a golf ball dropped
side-by-side in air. The tennis ball is affected
more by the airs resistance than the golf
ball. The larger the object is, and the faster
it is falling, the greater the airs resistance
to its motion, as skydivers all know
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• Coin and Feather

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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Observations 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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• Repeat Galileos Inclined Plane

Dropped Ball Falling Downward
velocity initial velocity acceleration
time positioninitial position initial
velocity time ½ acceleration time2
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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

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

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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 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

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• Drop and Shoot Sideways Demo

Tossed ball Falling Upward, then Downward,
with a constant horizontal velocity
component
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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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• Repeat Galileos Inclined Plane

The yellow balls horizontal speed is not
affected by gravity, which acts only in the
vertical direction.
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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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• Shoot the Monkey

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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Weight is a type of force

• It is the earths gravitational force on an object

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Weight and Mass

• An objects weight is proportional to its mass
• weight g mass
• On the Earths 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 kilogrammeter/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 Gravity

• On Earths surface, all falling objects
  accelerate downward at the acceleration due to
  gravity, g !
• force mass x acceleration, or Fma
  (Newtons 2nd law)
• weight m g force

m g m a
g a
Dont think that this is quite so simple
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m g m a
Why should gravitational and inertial masses be
the same?
Einsteins equivalence principle still being
tested!
U. Washington