Download Gravity and Motion

Gravity and Motion
Aristotle (400B.C.)
• Thought that an objects mass determined
how fast it would fall.
• If you dropped a baseball and a marble at
the same time, he would have predicted
that the baseball would land first.
Galileo (Late 1500’s)
• Young Italian Scientist who questioned
Aristotle’s idea about falling objects.
• Proved that the mass of an object does
NOT affect the rate at which it falls.
• Proved this by dropping two cannonballs
of different masses from the top of the
Leaning Tower of Pisa.
• The crowd witnessed the two cannonballs
landing at the SAME time
• Galileo’s idea changed people’s
understanding of gravity and falling
objects.
All Objects Fall with the SAME
Acceleration!
• Objects fall to the ground at the same rate
because the acceleration due to gravity is the
same for ALL objects.
• The force of gravity is the same between Earth
and an object with a large mass than between
Earth and a less massive object.
• You may think that the acceleration due to
gravity should be greater too, BUT a greater
force must be applied to a large mass than to a
small mass to produce the same acceleration.
• The difference in force is canceled by the
difference in mass.
Accelerating at a
Constant Rate
• All objects accelerate toward Earth at a
rate of 9.8 m/s2
• This means that for every second that an
object falls, the objects downward velocity
increases by 9.8 m/s.
• This acceleration is the same for all
objects regardless of their mass.
Velocity of Falling Objects
• To find the change in velocity (∆v) of a
falling object, multiply the acceleration due
to gravity (g) by the time it takes for the
object to fall in seconds (t):
• FORMULA:
∆v = g x t
Try this one!
• A stone at rest is dropped from a cliff, and
it takes 3 seconds to hit the ground. What
is its downward velocity when it hits the
ground?
• Remember, ∆v = g x t
• ∆v = 9.8 m/s/s x 3 s
• ∆v = 29.4 m/s
And some more!!
1. What is a penny’s velocity after it has
fallen for 2 seconds?
2. A marble at rest is dropped from a tall
building. The marble hits the ground with
a velocity of 98 m/s. How long was the
marble in the air?
3. An acorn at rest falls from an oak tree.
The acorn hits the ground with a velocity
of 14.7 m/s. How long did it take the
acorn to land?
Air Resistance Slows Down
Acceleration
• Drop 2 pieces of paper - one crumpled in a
tight ball and the other kept flat.
• What kept the flat paper from falling at the
same rate as the crumpled paper?
• Fluid friction is also known as air
resistance.
• Air resistance occurs between the surface
of the falling object and the air that
surrounds it.
Air Resistance
• The amount of air resistance acting on an
object depends on the size and shape of
the object.
• Air resistance affects the flat sheet of
paper more slowly than the crumpled one,
causing the flat sheet to fall more slowly
than the crumpled one.
• Any falling object you see is affected by air
resistance.
Represents the force of air resistance
pushing up on the object. This force
is subtracted from the force of gravity
to produce the net force.
Represents the net force on
the object. Because the net
force is not zero, the object
still accelerates downward,
just not as fast as it would
without air resistance.
Represents the force of
gravity on the object. If there
wasn’t air resistance, the
object would accelerate at a
rate of 9.8 m/s/s.
• As long as the net force on a falling object
is not zero, the object accelerates
downward.
• The amount of air resistance on an object
increases as the speed of the object
increases.
• As an object falls, the upward force of air
resistance continues to increase until it
exactly matches the downward force of
gravity.
Terminal Velocity
• When the air resistance (upward force)
matches the downward force of gravity,
the net force is zero, and the object stops
accelerating.
• The object then falls at a constant velocity,
which is called the terminal velocity.
Free Fall
• Sky divers are often described as being in
free fall before they open their parachutes.
• This in an incorrect description, because
air resistance is always acting on the sky
diver.
• An object is in free fall only if gravity is
pulling it down and no other forces are
acting on it.
Free Fall Cont’d
• Because air resistance is a force (fluid
friction), free fall can occur only where
there is no air - in a vacuum (a place in
which there is no matter) or in space.
• Astronauts “float” in orbiting spaceships
because of free fall.
Orbiting
• An object is said to be orbiting when it is
traveling in a circular or nearly circular
path around another object.
• The moon orbits the Earth, Earth and
other planets orbit the sun, and many stars
orbit large masses in the center of the
galaxies.
• Any object in a circular motion is
constantly changing direction.
• Because an unbalanced force is
necessary to change the motion of any
object, there must be an unbalanced force
working on any object in a circular motion.
• The unbalanced force that causes objects
to move in a circular path is called
centripetal force.
Centripetal Force
• Gravity provides the centripetal force that
keeps objects in orbit.
• The word centripetal means “toward the
center”.
Types of Motion due to Gravity
• Projectile Motion - the curved path an
object follows when thrown or propelled
near the surface of the Earth.
 Has 2 components- horizontal and vertical.
When the 2 motions are combined, they form
a curved path.
• Horizontal Motion - motion that is parallel
to the ground (side to side).
• Vertical Motion - motion that is
perpendicular to the ground (up and
down).
• The downward acceleration of a dropped
object versus a thrown object are the
same (if air resistance is ignored).
• They both are being pulled down by
gravity with the acceleration of 9.8 m/s2.
Answer on a Separate Sheet of
Paper!
1. How does air resistance affect the acceleration
of falling objects?
2. How does gravity affect the 2 components of
projectile motion?
3. How is the acceleration of falling objects
affected by gravity?
4. A rock at rest falls off a tall cliff and hits the
valley below after 3.5 s. What is the rock’s
velocity as it hits the ground?