Transcript Objects in Free Fall

Objects in Free Fall 2.7
What is gravity?
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Gravitation is a natural phenomenon by
which objects with mass attract one
another.
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Responsibilities: tides, keeping the moon in
orbit around the earth, keeping the earth and
planets in orbit around the sun
“Gravity" refers specifically to the net
force exerted by the Earth on objects in
its vicinity as well as by other factors,
such as the Earth's rotation
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Objects in free fall undergo
uniformly accelerated motion.
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Assume that air resistance is negligible
The only force acting on it is gravity
downward.
The rate of acceleration due to gravity
(g) is 9.8 m/s/s
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Galileo dropped a
cannonball and a musket
ball simultaneously from
a tower, and observed
that they hit the ground
at nearly the same time.
This contradicted
Aristotle's long-accepted
idea that heavier objects
fell faster.
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Why is it that some objects, like the
coin and the shoe, have similar
motion, but others, like a feather or
a bit of paper, are different?
Galileo speculated that in addition
to the force that always pulls
objects down, there was an upward
force exerted by the air.
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Speed decreases as the object goes up
and increases as the object comes back
down.
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Symmetrical in value
Opposite in direction
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How do the velocity and acceleration
compare? Think about the direction.
What is the speed at the top of the
throw? What is the acceleration?
summary
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Objects in free fall gain speed at a
constant rate.
Objects thrown up lose speed at a
constant rate, stop, then gain speed
at a constant rate coming down.
Acceleration on an object in free fall
is constant, b/c gravity is the force
causing the acceleration and gravity
does not shut off.
use the same equations as before but now
every thing is in the vertical (up down)
direction
v = vo + at
v
2
=vo
2
becomes
v = vyo + gt
+ 2a (x –xo) becomes
v 2 = vyo 2 + 2g (y –yo)
x = xo + vot + ½ at2
becomes
y = yo + vyo t + ½ gt2
hints
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When an object is thrown upwards,
use g = -9.80 m/s2 as your
acceleration because you are going
against gravity (negative means in
the opposite direction)
When an object is dropped,
initial velocity (vyo) = 0 m/s,
acceleration = g = 9.80 m/s2
What is the magnitude of the velocity of an
object after free falling from rest after 3.0
minutes?
Given:
Vyo = 0.0 m/s
(“from rest”)
t = 3.0 min. = 180
sec.
g = 9.8 m/s2
Asked for: Vy
Use:
vy= vyo + gt
Substitute:
Vy= 0+(9.8 m/s2)(180 s)
Solve for vy:
Vy=1764 m/s = 1800 m/s
Assuming negligible air resistance, how long will it
take for a sphere to fall 36.0 meters if thrown
downward at 12.0 m/s
Given:
Vyo = 12.0 m/s
g = 9.8 m/s2
y-yo = 36.0 meters
Asked for: t
Use:
y = yo + vyo t + ½ gt2
36.0 = 12.0t + ½ (9.8)t 2
4.9t2 + 12t -36 = 0
Use quadratic formula to
get t.
t =1.75 sec,
We ignore the negative
answer b/c time can
not be negative.
What is the minimum positive initial velocity
necessary for an object to be launched from ground
level so that it reaches a height of 80 meters?
Given:
Use:
vy 2 = vyo 2 + 2g (y –yo)
yo = 0 meters
Substitute:
(from ground)
0 2 = vyo 2 + 2(-9.8) (80 –0)
g = - 9.8 m/s2
(negative because
going against gravity) Solve for vyo
vyo 2 = 1568
y = 80 meters
vyo = 39.6 m/s = 40 m/s
Vy = 0 m/s
(b/c stops at top)
Asked for: Vyo