Transcript Acceleration Free Fall

An object in free-fall is
only subject to the force
of gravity (weight)
Fnet = Fg
(Neglect Air Resistance)
In Free-fall:
Fg
Fg
Fg
F = ma
Fg
a = F/m
Fg
so acceleration
must be constant
Fg
Fg
Galileo
Galileo dropped two cannon balls
of different weights from the top of
Leaning Tower of Piza. The two cannon balls reached the
ground at the same time. He proved that when objects of
different weights are dropped at the same height and time,
they take the same amount of time to fall to the ground
(ignoring air resistance).
Using Newton’s second law, we can conclude
that the force of gravity on an object is
proportional to the mass of the object.
Yes, They Rounded!
Since the acceleration of gravity is down,
when in free-fall, ignoring air resistance:
g=a=
- 9.8 m/s2
What observations can you
make about the picture?
Δv = aΔt
If vi and ti are equal to Zero
vf = at
∆y = ½at2
Free-Fall Motion
A 1-kg rock is thrown into the air
at 10 m/s upward. Neglecting air
resistance, what is the net force
acting on the rock?
Answer: In the absence of air resistance,
the only force exerted on the 1 kg rock is
simply the force due to gravity, mg, at
any speed along its trajectory!
Net Force = mg = (9.8m/s2)(1kg)= 9.8N
Remember: g = -10 m/s2
0 m/s
- 10 m/s
Ignoring Air Resistance
10 m/s
- 20 m/s
20 m/s
- 30 m/s
30 m/s
Sign Conventions for Free-Fall
Up “+”
Down “-”
A
B
C
D
Dy
0
+
0
v
+
-
a
-9.8
0
-9.8
-
-9.8
-9.8
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•
•
•
Zero
Reference
Point
•
At point A the change in y is 0, the
velocity is positive.
At point B the change in y is positive,
the velocity is zero.
At point C the change in y is 0, the
velocity is negative.
At point D, the change in y is
negative, the velocity is negative.
The acceleration for all the points is
-9.8 m/s2
Remember Motion Graphs?
Object is slowing down
x
- acceleration
v
t
+ velocity
t
Object is
speeding up
- acceleration
- velocity
a
t
-Which object hits
the ground first?
(ignore air friction)
-Which object hits
the ground first
when we include air
friction?
No Air Resistance
With Air Resistance
Why did air resistance slow down the feather
so much and not the elephant?
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
Skydiving
Observe the motion of the skydiver below. As the skydiver
falls, he encounters the force of air resistance. The
amount of air resistance is dependent upon two variables:
the speed of the skydiver, and
the cross-sectional area of the skydiver.
Draw FBDs at the following points.
Describe the direction of the net
force, acceleration, and velocity.
1) Just released from the helicopter.
2) Falling for a few seconds.
3) Falling for a few seconds more to a
point where the air resistance force
equals the gravitational force.
4) Deployment of a parachute.
5) Repeat of (3) for the parachute.
Now draw velocity and acceleration motion
map showing the motion.
Parachutes
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?
Air Resistance
A sky diver in the spread-eagle position opens the
parachute. (She has reached terminal velocity before
she opens the parachute)
a) Is the diver accelerated?
b) Which direction? Explain your answer.
Yes, she is accelerated in the
upward direction. She is slowing
down, yet still falling.
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As an object falls through air, it usually encounters
some degree of air resistance.
The actual amount of air resistance encountered by an
object depends upon a variety of factors.
The two most common factors which have a direct
effect upon the amount of air resistance present are
the speed of the object and the cross-sectional area of
the object. Increased speeds result in an increased
amount of air resistance. Increased cross-sectional
areas result in an increased amount of air resistance.
Watch This!
In situations in which there is air resistance, massive
objects fall faster than less massive objects. Why?
Massive objects fall faster
than less massive objects
because they are acted upon
by a larger force of gravity;
for this reason, they
accelerate to higher speeds
until the air resistance force
equals their gravity force.
Basically the more massive object accelerates longer
before reaching terminal velocity.
1.Draw Picture
2.List Givens
3.Write Equations
4.Solve For Unknowns
Fun Problems!!!!
1) A penny is dropped from the top of a
rollercoaster. The height of the ride is
110m. (neglect air resistance)
A. Find the speed of the penny when it hits the
ground.
B. Find the time it takes for the penny to fall to
the ground.
C. Would it be different for a quarter?
(how about with air resistance?)
2) A stone is thrown straight upward with a speed
of 20 m/s.
a) How high does it go?
b) How long does it take to rise to its maximum
height?
3) An object is thrown straight upward and falls
back to the thrower after a round trip time of
0.80 s.
How fast was the object thrown?
4)A cell phone is thrown
upward from the edge
of a building with a
velocity of 20 m/s.
Where will the object be
at 3s after it is thrown?
After 5s.?
5) George throws an apple vertically
upward from a height of 1.3 m with an
initial velocity of +24 m/s.
a)Will the apple reach a friend
in a tree 5.3 m above the ground?
b) If the apple is not caught, how
long will the apple be in the air
before it hits the ground?