Transcript Inverse Square Law

Gravity
Sucks!
The acceleration due to gravity on the
International space station is 8.7 m/s2. If
an 50 kg astronaut stood on a scale what
would it read?
435 N
B. 5.7 N
[Default]
C.
[MC.17
Any] N
[MC All]
D. 0 N
A.
The “Discovery” of Gravity
We’ve all heard the story…
an apple fell on Newton’s
head and he discovered
gravity.
 Most scholars believe that
Newton did see an apple fall
and it got him wondering
about the rules for falling
objects.
 He wondered if the force that
pulled the apple down also
affected the Moon.

Remember Newton’s 1st Law
He had already explained that straight-line
motion was perfectly natural and moving in a
circle required a force
 Johannes Kepler had shown that planets and
moons moved in an ellipse.
 Newton wanted to understand what made
them move that way.
 His breakthrough was to explain how the
same rules apply to little things like apples
and big things like the moon.

Making sense of one force and two very
different results
We already learned that the apple will accelerate at
about 9.8 m/s2 downward
 Newton also knew that the moon accelerates
toward the Earth at 0.00272 m/s2

Distance is only part of the story
Distance has a large effect on the force of gravity
(we’ll explore this more in a minute)
 Remember, though F = m • a

 The force of gravity is also affected by the mass
 or more correctly, both masses
Gravitational Force





Gravitational Force is the mutual force of
attraction between particles of matter
This force always exists between two masses,
regardless of the medium that separates them
It is not just between large masses, like the
sun and the Earth.
The chair you are sitting on is attracted to the
person next to you.
However, the force of friction between the
chair and the carpet is so great that you don’t
move.
m1m2
Fg  G 2
r



Newton’s Law of Universal Gravitation is an example of an
inverse-square law
This is because the force decreases the further the two
objects get from each other.
The distance is measured from the center of each mass.

Remember, the Force of gravity (Fgrav) that acts
on an object is the same as that object’s weight
(in Newtons)
Inverse Square Law
4
1/4
9
1/9
16
1/16
Inverse Square Law
At 4d
3d
2d
5d apple weighs
1/9
1/25
1/4
1/16NN
If a large meteor hits the moon,
causing it to get closer to the earth. If
the moon’s orbits the earth at half of
its original radius, would its force be?
Double the original force
[Default]
B. Half the original force
[MC Any]
[MC
C. All]
Four times the original force
D. One fourth the original force
A.
Connecting the two formulas
Example #1
Find the force of gravity between a 30 kg girl and her
10 kg cat if they are 2 meters apart.
m1 = 30 kg
m1m m
2 kg
=
10
2
Fg  G
2
G = 6.67
r x 10-11 N·m2/kg2
r = 2m
Fg  6.67 x10
11
30kg  10kg
2
(2m )
9
Fg  5.0025 x10 N
Example #2
Find the distance between a 0.300 kg billiard ball
and a 0.400 kg billiard ball if the magnitude of the
gravitational force is 8.92 x 10-11 N.
m1  m2 m1 = 0.3 kg
Fg  G
m2 = 0.4 kg
r2
-11 N
=
8.92
x
10
r 2  Fg  G Fm

m
g1
2
r
=
?
m

m
2
r2 G 1
Fg
m1  m2
r  G

Fg
6.67 x10 11  0.300  0.400
8.92 x10 11
r  0.2996 m about 30cm
Determine the magnitude of the
gravitational force between a baseball
player with a mass of 100 kg and Earth
(5.98 X 1024 kg), if they are separated by a
distance of 5.38 X 106 m.
[Default]
[MC Any]
[MC All]
[Option 1]
B. [Option 2]
C. [Option 3]
D. [Option 4]
A.
Tides
Newton also used the inverse square
law to explain the tides.
 People had known for centuries that the
moon affects the tides.
 No one until Newton knew how it did
this.

d-R
d
d+R
Which of the two forces:
moon on left mass (m) or
moon on right mass (m)
is stronger and why? Fd-R
Tidal Bulges
Ocean tides are the alternate rising and
falling of the surface of the ocean that
usually occurs in two intervals everyday,
between the hours of 7a.m. to 7p.m.
 It is caused by the gravitational attraction
of the moon occurring unequally on
different parts of the earth.
