LECTURE 3
FALLING
Instructor: Kazumi Tolich
Lecture 3
2
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Reading chapter 2-7
¤ Free
falling
Free fall
3
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Free fall is the motion of an object under the influence of gravity alone.
The magnitude of the acceleration due to gravity near the surface of Earth, g, varies
depending on the location on the surface of Earth and the altitude, but in all
calculations in this course, we will use g = 9.81 m/s2.
For a free falling object, the acceleration is -g defining upward to be the positive
direction.
Quiz: 1
4
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Which of the following object or objects are free-falling? In all cases,
neglect air resistance. Choose all that apply.
A.
B.
C.
D.
A ball moving upward after leaving the hand that threw it up.
A ball moving downward after being thrown up and reaching the
maximum height.
A ball moving downward after leaving the hand that threw it down.
A ball moving downward after being dropped from rest.
Quiz: 3-1 answer
5
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All choices
An object is in free fall from the time it is released until it lands, whether it is
dropped from rest, thrown downward, or thrown upward.
The figures below show the position, velocity, and acceleration of an object thrown
upward.
Position
Velocity
Acceleration
Quiz: 2
6
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A Guinea (metal coin) and a feather are dropped from the same
height at the same time. Assuming there is no air resistance, which hits
the ground first?
A.
B.
C.
Guinea
Feather
Both at the same time
Quiz: 3-2 answer
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Both at the same time.
Without air resistance, objects of different weight fall with the same
downward acceleration, g.
Demo: 1
8
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“Guinea and Feather” Tube
¤ Demonstration
of falling objects without air resistance.
Example: 1
9
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A monkey drops from a tree limb
to grab a piece of fruit on the
ground 1.80 m below. Neglect the
effects of air resistance.
a)
b)
How long does it take the
monkey to reach the ground?
How fast is the monkey moving
just before it reaches the
ground?
Quiz: 3
10
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When a particle thrown upward with an initial velocity, +𝑣, returns to
the initial height, what is its velocity?
Quiz: 3-3 answer
11
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−𝑣
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𝑣 $ = 𝑣&$ + 2𝑎∆𝑥 = 𝑣&$ − 2𝑔∆𝑥 = 𝑣&$ − 2𝑔 0 = 𝑣&$
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𝑣 = ±𝑣& , where +𝑣& is the initial velocity.
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When it comes back, it is falling down with the same speed.
Not a recommended move!
Quiz: 4
12
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Alice and Bill are at the top of a cliff of height 𝐻. Both throw a ball
with initial speed 𝑣& , Alice straight down and Bill straight up. The
speeds of the balls when they hit the ground are 𝑣/ and 𝑣0 . If there is
no air resistance, compare 𝑣/ and 𝑣0 .
A.
B.
C.
D.
𝑣/ > 𝑣0
𝑣/ < 𝑣0
𝑣/ = 𝑣0
It's impossible to compare.
Quiz: 3-4 answer
13
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𝑣3 = 𝑣4
The displacement of both balls is the same with the same
initial speed.
𝑣 $ = 𝑣&$ + 2𝑎∆𝑥 = 𝑣&$ + 2 −𝑔 −𝐻
Example: 2
14
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When startled, a springbok leaps upward several
times in succession, reaching a height of several
meters. (This behavior, called pronking, may inform
predators that the springbok knows of their
presence.) During one such jump, a springbok leaves
the ground at a speed of v0 = 6.00 m/s.
a)
What maximum height above the ground
does the springbok attain?
b)
How long does it take the springbok to
attain this height?
What is the springbok’s velocity when it is
x = 1.25 m above the ground?
At what times is the springbok 1.25 m
above the ground?
c)
d)
Example: 3
15
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A tennis ball is hit straight up at
v0 = 20.0 m/s from the edge of a
sheer cliff. Ignore the effects of air
resistance.
a)
b)
c)
How fast is the ball moving when
the ball passes the original height
from which it was hit?
If the cliff is 30.0 m high, how long
will it take the ball to reach the
ground level?
What total distance did the ball
travel?
Example: 4
16
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Wrongly called for a foul, an
angry basket player throws the
ball straight down to the floor. If
the ball bounces straight up and
returns to the floor 2.8 s after first
striking it, what was the ball’s
greatest height above the floor?
Ignore the effects of air resistance.
Example: 5
17
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A ball is dropped from an upper floor,
some unknown distance above your
apartment. As you look out of your
window, which is 1.50 m tall, you
observe that it takes the ball 0.180 s
to traverse the length of the window.
Determine how high above the top of
your window the ball was dropped.
Ignore the effects of air resistance.