Free Fall

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Free Fall

• J. Frank Dobie H.S.

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Free Fall

• Free-falling object falling falls only under the
  influence of gravity.
• Free-falling object is in a state of free fall.
• Two important characteristics
• 1. Free-falling objects do not encounter
• air resistance.
• 2. All free-falling objects on Earth
• accelerate downwards at a rate of
• 9.81 m/s2.

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1. Free falling objects fall only under
the influence of what ?

• Free falling objects fall only under the
  influence of gravity.

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2. What does an acceleration of -9.81 m/s2
really mean?

• Every second the object is increasing its
  velocity 9.81 m/s downward.

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3. What is the direction of the acceleration
during free fall?

• Free fall is acceleration that is directed
  downward.

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4. What is absent when an object is undergoing
free fall?

• Air resistance is absent during free fall.

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5. Is an object thrown upward undergoing free
fall?

• Yes, any object released in the air is undergoing
  free fall.

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6. If an object is thrown downward, is it
undergoing free fall?

• An object thrown downward is undergoing free
  fall.

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• Free-falling objects are accelerating
• downwards at a rate of 9.81m/s2.
• A ticker tape trace of it motion is a
• model that depicts the acceleration.
• The diagram at the right shows the ticker
• tape trace that shows the position every
• 0.1 second.
• The distance the ball travels
• every interval of time is increasing is a
• sign that the ball is speeding up as it
• falls downward.
• The acceleration is
• directed downward in the same direction
• the speed is increasing.

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7. What is the value of the acceleration due to
gravity?

• The acceleration due to gravity is
• -9.81m/s2.

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Acceleration of Gravity

• The acceleration of a free-falling object is so
  important that it is known as the
• acceleration of gravity.
• Physicists have a special symbol to denote it
  --- the symbol g.
• The numerical value for the acceleration of
  gravity is most accurately known as 9.81 m/s2.
• We will use 10m/s2 during conceptual
  understanding of the acceleration.

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8. What is the symbol for the acceleration due
to gravity?

• The symbol for the acceleration due to gravity is
  g.

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9. Does the acceleration due to gravity change at
your location on the earth?

• The acceleration due to gravity does not change
  at a particular location on the earth.

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Velocity and Time Pattern

• A velocity and time table for a free-falling
  object being dropped from rest would look like
  the following
• Time(s) Velocity(m/s), downward
• 0 0
• 1 10
• 2 20
• 3 30
• 4 40
• 5 50
• Remember, the acceleration of 10m/s2 causes the
  velocity to increase 10 m/s per s.

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Speed Pattern during Free Fall

• Assuming that the position of a
• free-falling ball dropped from a
• position of rest is shown every
• 1 second, the speed of the ball
• will be shown to increase as
• depicted in the diagram at the right.
• (This diagram is not drawn to scale.)

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10. If you follow the pattern for the speed
during free fall when an object is released
from rest 10 m/s, 20 m/s, what would be
the next two values for the speed?

• The next two values for the speed would be 30 m/s
  and 40 m/s.

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Representing Free Fall by Graphs

• Position vs. Time Graphs for free-falling objects
• Observe that the line is curved. A curved line on
  a position vs. time graph signifies an
  accelerated motion 10 m/s2

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• A closer look at the position-time graph reveals
  that the object starts with a small velocity
  (slow) and finishes with a large velocity (fast).
• The negative slope of the line indicates a
  negative (downward) velocity.

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11. What does the position vs. time graph for
free fall from rest look like?
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12. What does the negative slope on a position
vs. time graph for an object undergoing free fall
indicate?

• The negative slope on a position vs. time graph
  for an object undergoing free fall indicates the
  object is undergoing a downward velocity.

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Velocity vs. Time Graphs

• The velocity vs. time graph for a free-falling
  object is shown below.
• Observe that the line on the graph is a straight,
  diagonal line which signifies an accelerated
  motion.

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• A closer look at the velocity-time graph reveals
  that the object starts with a zero velocity and
  finishes with a large, negative velocity that
  is, the object is moving in the negative
  direction and speeding up.
• Analysis of the slope is -10 m/s2 or more
  accurately -9.81 m/s2.

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13. What does the velocity vs. time graph look
like for an object released from rest and
undergoes free fall?
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What does the slope of a velocity vs. time
graph for free fall represent?

• The slope of a velocity vs. time graph for free
  fall represents the acceleration of gravity
  (-9.81 m/s2).

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How Fast? and How Far?

• Free-falling objects are in a state of
  acceleration.
• How Fast?
• The speed is dependent upon
• the length of time for which it
• has fallen.
• vf vi gt
• Ex If t 5 s
• vf 10 m/s2 (5 s) 50 m/s

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15. What is the velocity of an object moving
after released from rest for 8 s?

• vf vi at
• 0 -10 m/s2 (8s)
• -80 m/s

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What is the velocity of an object undergoing free
fall from rest for 10 s?

• vf vi at
• Vf 0 -10 m/s2(10s)
• Vf -100 m/s

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How Far?

• The distance a free-falling object falls
  depends upon the time of fall.
• x vi (t) ½ a t2
• Ex vi 0 m/s and t 1 s
• x ½ (10 m/s2 ) (1s)2 5 m
• The diagram shows the results
• of several distance calculations
• For a free-falling object dropped
• from a position of rest.

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17. How far does a stone fall in 3 s from rest?

• x vit ½ at2
• x 0(3s) ½ (-10 m/s2) (3s)2
• x -45 m45 m

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18. What is the displacement for an object that
falls freely for 8.0 s?

• x vit ½ a t2
• X 0 t ½ (-10. m/s2) (8.0s)2
• -320 m

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The Big Misconception

• Doesnt a massive object accelerate at a greater
  rate than a less massive object?
• Nearly everyone has observed the difference in
  rate of fall of a single piece of paper and a
  textbook.

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• The answer to the question Doesnt a massive
  object accelerate at a greater rate than a less
  massive object? is absolutely not!
• That is, absolutely not, if you are considering
  the specific type of falling motion know as
  free-fall.
• Free-falling object do not encounter air
  resistance.
• Massive objects will only fall faster than less
  massive objects if there is an appreciable amount
  of air resistance present.

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The Big Answer

• The explanation of why all objects accelerate at
  the same rate involves the concepts of force and
  mass.
• You will learn that the acceleration of an object
  is directly proportional to the force acting on
  it and inversely proportional to its mass.
• All objects, regardless of their mass, free-fall
  at the same rate of acceleration.

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19. Why does a hammer and feather hit the ground
at the same time on the moon?

• A hammer and feather hit the ground at the same
  time on the moon because there is very little air
  resistance on the moon.

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Does a massive object accelerate at a greater
rate than a less massive object when there is an
absence of air resistance?

• A heavy object will accelerate at the same rate
  as a less massive object when there is an absence
  of air resistance.

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Definition for Free Fall

• Object falling only influence of gravity
• Air Resistance is ignored.
• Under such conditions, all objects will fall with
  the same rate of acceleration, regardless of
  their mass.

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Falling with Air Resistance

• Object falling through air usually encounter some
  degree of air resistance.
• Air resistance results from collisions of the
  objects leading surface with air molecules
• Actual amount of resistance depends on various
  factors--- speed of object and
• cross-sectional area of the object.
• Increased speeds result in increased amount
  of
• air resistance.
• Increased cross-sectional areas result in
• increased amount of air resistance.

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Terminal Velocity

• Objects which encounters air resistance
  eventually reach a terminal velocity.
• As an object falls, it picks up speed, which
  increases air resistance.
• The force of air resistance becomes large enough
  to balance the force of gravity. The object has
  now reached terminal velocity where it no longer
  increases in speed.

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• When there is air resistance, more massive
  objects fall faster than less massive objects.
• Consider the objects below of different masses
• A falling object will continue to accelerate to
  higher speeds until they encounter an amount of
  air resistance equal to their weight.

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• Since the 150-kg skydiver weighs more
  (experiences a greater force of gravity), it will
  accelerate to higher speeds before reaching a
  terminal velocity.
• More massive objects fall faster than less
  massive objects because they are acted upon by a
  larger force of gravity.
• More massive objects accelerate to higher speeds
  until the air resistance force equals the gravity
  force.