Transcript free fall

Gravity
And Free Fall
When gravity is the
only force acting on
an object,it is said to
be in free fall.
The acceleration of an object in free fall is called
the Acceleration due to gravity.
Free fall acceleration is denoted by the symbol g
g = 9.80 m/s²
g is always directed downward toward the
center of the earth
Ignoring air resistance and assuming g doesn’t
vary with altitude over short vertical distances,
free fall is constantly accelerated motion
(384 BC – March 7, 322 BC)
Aristotle
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1564 - 1642
Galileo formulated
the laws that govern
the motion of objects
in free fall
Galileo took an interest in rates of fall when he was
about 26 years old and a math teacher at the
University of Pisa.
It seemed to him that -- with no air resistance -- a
body should fall at a speed proportional to its
density. He decided to test this modified
Aristotelian view by making an experiment.
Galileo was trying to prove
that earth's gravity
exerts the same
acceleration on all masses
regardless of their weight
and size.
His experiment consisted
of dropping a large and a
small canon balls from the
top of the leaning tower
of Pisa and observing that
they reached ground at
the same time.
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Newton studied objects
Falling under the
influence of Gravity and
explained why Galileo’s
ideas had been correct.
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A famous story says that Newton uncovered the laws of
gravity after being hit on the head by a falling apple.
There is no proof that this story is true. However, his
assistant John Conduitt later wrote that Newton had said
he was inspired to think about gravity after seeing an
apple fall in his garden around 1666.
Hammer and Feather Drop
Free Fall – Object being dropped from rest
A. Initial velocity is zero
B. Down is negative
C. Acceleration is g = -9.80
m/s2
Free Fall – Object thrown downward
A. Initial velocity is not zero
B. Down is negative
C. Acceleration is g = -9.80
m/s2
Free Fall – Object thrown upward
A. Initial velocity is upward,
so positive.
B. The instantaneous
velocity at the maximum
height is zero.
C. A = g = -9.80 m/s2
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Let’s try some sample problems!
A stone is dropped off a cliff. What is its velocity 5 seconds
later?
0
-9.8
5
vf = -49 m/s
A ball is tossed straight up at 30 m/s. How long will it take
To land? (It returns to the same height.)
-9.8
-30 - 30
t = 6.122 s
At 400 km above the earth's surface, gravitational
acceleration is reduced from 9.8 m/s/s to
approximately 8.7 m/s/s.
This would cause an astronaut weighing 1000 N to
be reduced in weight to approximately 890 N.
Suppose that an elephant and a
feather are dropped off a very tall
building from the same height at the
same time.
Suppose also that air resistance
could be eliminated such that
neither the elephant nor the feather
would experience any air drag
during the course of their fall.
Which object - the elephant or the
feather - will hit the ground first?
In the animation at the
right, the motion of the
elephant and the
feather in the absence
of air resistance is
shown.
In the absence of air
resistance, the
elephant and the
feather strike the
ground at the same
time. Why is this so?
In the absence of air resistance objects fall at the
same rate regardless of their masses.
Falling objects encountering air resistance, do not fall
at the same rate
So what is
Well, eventually, the force of air resistance becomes large
enough to balance the force of gravity. At this instant in time,
the net force is 0 Newtons — the object stops accelerating.
The object is said to have "reached a terminal velocity."
Fg = FR
a = 0 m/s2
Find the acceleration for A, B, C, and D.
•
a = (Fnet / m) = (1000 N) / (100 kg) = 10 m/s/s
•
a = (Fnet / m) = (600 N) / (100 kg) = 6 m/s/s
•
a = (Fnet / m) = (200 N) / (100 kg) = 2 m/s/s
•
a = (Fnet/m) = (0 N) / (100 kg) = 0 m/s/s.
Which diagram represents terminal velocity?
Free Fall – How Fast
The formula for determining how fast an object is
falling from rest (the instantaneous velocity) after an
elapsed time of t seconds is
v = g * t
where
A. g is the acceleration of gravity.
B. t is the time in seconds
Example calculations for the velocity of a free-falling
object after six and eight seconds are shown below.
v = g * t
At t = 6 s
vf = (9.8 m/s2) * (6 s) = 58.8 m/s
At t = 8 s
vf = (9.8 m/s2) * (8 s) = 78.4 m/s
Free Fall – How Far
The distance which a free-falling object has fallen from a
position of rest is also dependent upon the time of the
fall.
This distance fallen after a time of t seconds is given by
the formula.
x = 0.5 * g * t2
•Derived from the
equation Δx = vit + ½ at2
•Vi = 0 m/s
Or
½ gt2
g = acceleration due to gravity (9.8 m/s2 on Earth).
t = time
x = distance
Jason hits a volleyball so that it moves with an initial velocity
Of 6 m/s straight upward. If the volleyball starts from 2m
Above the floor, how long will it be in the air before it strikes
The floor?
Choose origin to be the initial position of ball
The displacement of the ball is –2m
Or use the quadratic equation:
-b ± √b2 – 4ac
2a