HOW THINGS MOVE

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CHAPTER 3

• HOW THINGS MOVE

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• 3.1 ARISTOTELIAN PHYSICS
• Everything on Earth made of (mixture of) four
  elements earth, water, air, fire
• Every element has a natural place
• Earth at center of Earth,
• Water above Earth,
• Air above Water,
• Fire above air
• Celestial bodies (stars, planets, Moon) made from
  5th element, ether
• Two kinds of motion on Earth
• Natural motion happens by itself - things tend
  to move towards their natural place (stone falls,
  fires rises).
• Violent motion needs effort (external push or
  pull)

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• 3.2 PROBLEMS WITH ARISTOTELIAN PHYSICS
• Galileo Galilei's used scientific method
• Falling bodies
• According to Aristoteles, heavy bodies (contain
  more earth element) fall faster than lighter
  bodies
• Observation fall equally fast if they have same
  shape and size
• Galilei difference in speed of differently
  shaped falling bodies due to air resistance

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• Pendulum
• Ball suspended on string reaches same height as
  that to which it was lifted to set it in motion
  (not quite - due to friction)
• Height independent of path (pendulum with
  shortened string)

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• Ball rolling on inclined plane
• Ball rolling down inclined plane speeds up
• Ball rolling up slows down rate of slowing down
  depends on steepness of incline less steep ?
  longer distance traveled
• Extrapolation to zero slope of incline ball
  will go on forever

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• Galileo Galilei (1564 - 1642) -- founder of
  modern science
• New methods introduced by Galilei include
• Controlled experiments designed to test specific
  hypotheses
• Idealizations to eliminate any side effects that
  might obscure main effects
• Limiting the scope of enquiry - consider only one
  question at a time
• Quantitative methods - did careful measurements
  of the motion of falling bodies

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• From observations and thought experiments,
  generalizes to two new laws
• LAW OF INERTIA
• Without external influence (force) acting on it,
  a body will not change its speed or direction of
  motion
• It will stay at rest if it was at rest to begin
  with
• inertia property of bodies that makes them obey
  this law, their ability to maintain their speed
  (or stay at rest)
• LAW OF FALLING
• if air resistance is negligible, any two objects
  that are dropped together will fall together
• Speed of falling independent of weight and
  material.

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• 3.4 SPEED AND VELOCITY
• Consider a car moving with a constant, rightward
  () velocity of 10 m/s

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• While on vacation, Lisa Carr traveled a total
  distance of 440 miles. Her trip took 8 hours.
  What was her average speed?
• Avge Speed 440/8 55 miles/hr
• Definitions
• Instantaneous Speed - speed at any given instant
  in time.
• Average Speed - average of all instantaneous
  speeds.

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Average Speed (Distance Traveled)/Time Average
Velocity Displacement / Time
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• Example Seymour Butz views football games from
  under the bleachers. He frequently paces back and
  forth to get the best view. The diagram below
  shows several of Seymour's positions and times.
  At each marked position, Seymour makes a "U-turn"
  and moves in the opposite direction. In other
  words, Seymour moves from position A to B to C to
  D. What is Seymour's average speed and average
  velocity?

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Avge Speed Distance Traveled/Time 95
yds/10 min 9.5 yds/min
Avge Velocity Displacement/Time 55 yds/10
min 5.5 yds/min
See excellent examples at www.physicsclassroom.co
m/class/1DKin/U1L1d.html
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3.5 ACCELERATION

• Observe the animation of the three cars below.
  Which car or cars (red, green, and/or blue) are
  undergoing an acceleration?

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For objects with a constant acceleration, the
distance of travel is directly proportional to
the square of the time of travel.
d ½ a t2
d distance, a acceleration, t time
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• Calculating Acceleration
• The acceleration of any object is calculated
  using the equation

Example
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• The figure above represents a multiple-flash
  photo of two balls moving to the right, and shows
  both balls at several numbered times. In the
  figure,
• (a) neither ball passes the other ball during
  their motion.
• (b) the upper ball, which has a larger
  acceleration, passes the lower ball.
• (c) the lower ball, which has a larger
  acceleration, passes the upper ball.
• (d) the upper ball, which is moving faster,
  passes the lower ball.
• (e) the lower ball, which is moving faster,
  passes the upper ball.

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• FALLLING OBJECTS
• A free-falling object is an object which is
  falling under the sole influence of gravity.
• Free-falling objects do not encounter air
  resistance.
• All free-falling objects (on Earth) accelerate
  downwards at a rate of approximately 10 m/s/s (to
  be exact, 9.8 m/s/s).

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• The acceleration due to gravity is 10 m/sec2. If
  an object falls from rest, its instantaneous
  speed at the end of the fifth second is
• (a) 10 m/sec.
• (b) 50 m/sec.
• (c) 100 m/sec.
• (d) 5 m/sec.
• (e) impossible to determine from the given
  information. NOTE neglect air resistance

v a t 10 x 5 50 m/s
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• A rock is dropped from rest off of a high cliff
  on another planet, planet X. There is no
  atmosphere, and thus no air resistance, on planet
  X. At the end of 1 second, the rock is moving at
  a speed of 6 m/s. At the end of 2 seconds, it is
  moving at 12 m/s. How fast will the rock be
  moving at 4 seconds after being dropped?
• (a) 18 m/s.
• (b) 20 m/s.
• (c) 24 m/s.
• (d) 36 m/s.
• (e) 40 m/s.

v a t 6 x 4 24 m/s
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• On Mars, an object dropped from rest falls a
  distance of 4 m in 1 second. How far will it
  fall in 2 second, neglecting "air" resistance on
  Mars?
• (a) 8 m
• (b) 12 m
• (c)16 m
• (d) 24 m
• (e) 32 m.

d ½ a t2 ? 4 ½ . a . 12 ? a 8 m/s2
d ½ a t2 ? d ½ . 8 . 22 ? d 16 m