Chapter 9 Gravity

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Chapter 9 Gravity
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Newton and the Moon

• Newton realized that Earths gravity was the
  centripetal force that kept the moon in orbit.
• Also discovered that gravity was weaker at that
  great distance.

Gravity force
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Gravity Distance

• We dont notice that gravity gets weaker as we
  move away from Earth because we rarely go very
  far.

Moon is 30 Earth diameters away
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Universal Law of Gravity

• Force of gravity has magnitude given by
• (Gravity Force) (G) x

( Mass of Object A ) x ( Mass of Object B)
( Distance ) x ( Distance )
DISTANCE
Object A
Object B
Force
Force
Equal and opposite forces (Newtons Third law)
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Universal Gravity Constant, G

• In the formula for gravity force, we have
• G 0.0000000000667 N m2 / kg2
• 6.67 x 1011 N m2 / kg2
• The formula and the constant are called
  universal because, up to now, this theory
  predicts gravity anywhere in the universe.

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Cavendish Experiment

• For non-astronomical objects gravity force is
  very small.
• Need sensitive balance to detect.
• First measured by Cavendish in his home
  laboratory in 1797 at age 67.

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Intelligent Falling
"Things fall not because they are acted upon by
some gravitational force, but because a higher
intelligence, 'God' if you will, is pushing them
down,"
The Onion, August 17, 2005
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Sample Problem

• Here is an example of using the formula
• (Gravity Force) (G) x

( Mass of Object A ) x ( Mass of Object B)
( Distance ) x ( Distance )
Object A (1 kg mass)
Object B (Earth)
Force
DISTANCE Earths Radius
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Sample Problem

• Find gravity force for a 1 kg mass on surface of
  Earth.
• (Force) (6.67 x 1011) x
• Value comes out to 9.8 Newtons (check this with
  your calculator its good practice).

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Sample Problem (cont.)

• Find gravity acceleration on a 1 kg mass.
• Using Newtons Second Law,
• (Acceleration)
• Answer is 9.8 m/s2, which weve been rounding off
  as 10 m/s2.

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Inverse Square Law
1/4 Earth Gravity

• Gravity force weakens with distance as the
  inverse of the square of the distance.
• Geometric property of area and distance.

Earth Gravity
Outer circle is twice Earths radius so it has 4
times the area
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Demo Perspective
These four figures are equally spaced in distance
and, in perspective, you are standing that
distance from the first.
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Demo Perspective Cards

• Hold large card at arms length.
• Close one eye then hold small card at a distance
  such that it is same size as large card.
• That distance will be half way between your eye
  and large card.

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Arms length
Half
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Weightlessness

• In deep space, far away from all stars, planets,
  etc. there is almost no gravity force.
• In orbit near Earth, gravity is still strong
  (only 10 less than on surface).
• Why are Shuttle and Space Station astronauts
• weightless?

Earth is nearby
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Freefall Weightlessness
Freefall is a state of weightlessness, even
though gravity is present.
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Movie Roller Coaster
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Check Yourself

• Sit in a seat on Ferris wheel.
• Where do you feel heaviest?
• Where do you feel lightest?

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Demo Ferris Wheel in Hand
Support Force

• Place a heavy object in your hand, hold your arm
  out and rotate your arm, palm upward, in a small
  circle.
• Object will feel lightest at the top of the
  circle and heaviest at bottom.

Support Force
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Demo Falling Slinky

• Hold a Slinky and its weight stretches it out.
• Now drop it.
• In freefall its in a state of weightlessness so
  Slinky immediately contracts.

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NASAs Vomit Comet

• NASA has a special airplane for training
  astronauts in free-fall weightless conditions.
• The Vomit Comet nickname tells you its quite a
  wild roller-coaster ride.

The plane flies between 20,000 and 30,000 feet,
same as commercial flights.
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Flight of the Vomit Comet
Weightless Freefall
At the top of the arc, the planes trajectory is
projectile motion.
Power Climb
Pull out of Dive
Boeing 707 (modified)