Physics 5.2
Galilei Galileo
1600’s
Studied how things fell
Didn’t have a good clock
Rolled balls down an inclined
plane
• Found that the speed
increased as it rolled down the
ramp
• 1st person to explain
acceleration of moving objects
and falling bodies.
•
•
•
•
Galileo
t=0
t = 1 second
t = 2 seconds
t = 3 seconds
Galileo
Free Fall Acceleration
Due to the Earth’s Gravity
When dropped, these two
different masses will fall with
the same acceleration!
Free Fall – All objects fall at the same rate
• If you drop a coin and a feather at the same
time you will notice that the coin reaches the
ground way before the feather. Why???
• However, if you were to take the air out of the
container (vacuum) you would find that the
coin and feather fall together and hit the
bottom at the same time!
Acceleration due to gravity, g
• We don’t feel the attraction of most objects because their mass
is small relative to the Earth which has a huge mass.
• The Earth pulls so that objects experience an acceleration of
about 9.81 m/s2. This acceleration is given a special letter, g.
• g = 9.81 m/s2 m or 32 ft/s2. (These numbers are important,
remember it!)
• So during each second an object is in free fall, its velocity
increases by 9.81 m/s. If the object experiences air resistance its
velocity won’t increase as fast because air resistance will slow it
down.
Free Fall
• The constant acceleration of an object
moving only under the force of gravity
is "g".
• The acceleration caused by gravity is
9.81 m/s2
• If there was no air (vacuum), all objects
would fall at the same speed
• Doesn’t depend on mass
• After 1 second falling at 9.81 m/s
• After 2 seconds 19.62 m/s
• 3 seconds 29.43 m/s
Videos
http://www.youtube.com/watch?v=zXDZWKmRxI0&feature=related
http://www.youtube.com/watch?v=KDp1tiUsZw8
http://www.youtube.com/watch?v=_XJcZ-KoL9o
Terminal Velocity
•
You can assume that a = g = 9.81 m/sec2
for speeds up to several meters per
second.
•
The resistance from air friction increases
as a falling object’s speed increases.
•
Eventually, the rate of acceleration is
reduced to zero and the object falls with
constant speed.
•
The maximum speed at which an object
falls when limited by air friction is called
the terminal velocity.
Since acceleration is a vector and vectors must have
magnitude and direction we will always use the following
system in our acceleration problems:
Y-Axis
 Initial Motion is always positive (+) from reference point
 Opposite Direction of Initial Motion is always negative (-) from
reference point
X-Axis
 Direction of movement is positive (+)
GRAVITY
 g = + / - 9.81 m/s2 or + / - 32 ft/s2 (Depending on direction of
reference point)
Acceleration as a Vector
A pebble dropped from a bridge
The vector is
oriented down.
A baseball tossed up in the air, halfway up the path
The vector is
oriented down.
A baseball tossed up in the air, at the top
The vector is
oriented down.
A baseball tossed up in the air,
right before it strikes the ground
The vector is
oriented down.
A football is thrown at a 450 angle,
at the top of its path
The vector is
oriented down.
A cannonball rolling off a table
The vector is
oriented down.
Example #1
A body falls freely from rest. Find:
(a)
(b)
(c)
(d)
(e)
Its acceleration
The distance it falls in 3 s
Its speed after falling 70 m
The time required to reach a speed of 25 m/s
The time taken to fall 300 m.
Example #2
A stone falls from rest from a fourth-floor window that is 14 meters
above ground level. How long does it take to reach the ground?
What is the velocity just before it strikes the ground?
Example #3
A stone is thrown vertically upward with a velocity of 10 m/s from a
fourth-floor window 14 meters above ground level. What is the
velocity just before striking the ground? How long does it take to
reach the ground?
Example #4
A ball dropped from a bridge strikes the water in 5 seconds.
Neglecting air resistance, find:
(a) The speed with which it strikes the water
(b) The height of the bridge
Example #5
A stone is thrown vertically upward with a velocity 40 m/s at the edge
of a cliff having a height of 110 m. Neglecting air resistance, find:
(a) With what velocity does it strike?
(b) The time required to strike the ground at the base of the cliff.
Example #6
A ball is thrown vertically downward from the edge of a high cliff
with an initial velocity of 25 ft/s.
(a) How fast is it moving after 1.5 s?
(b) How far has it moved after 1.5 s?
Values of “g” in different places
There are various different values of “g”. Since “g” is due to the attraction of
the earth, it will decrease as we get farther from the earth’s center.
 Acceleration due to gravity is smaller at higher elevations
 Acceleration due to gravity is larger at a higher latitude
City
Elevation
Latitude
G (m/s2)
Washington DC
8m
38⁰ 54’ N
9.8008
Denver
1,640 m
39⁰ 43’ N
9.7961
London
30 m
51⁰ 30’ N
9.8228
Therefore; 9.81 m/s2 is an average figure. This value includes effects due to
the earth’s rotation and the value excludes effects due to air resistance. So,
we will treat all free falling bodies as undergoing constant acceleration.