Transcript Law of Universal Gravitation - Mr. Nguyen's Website

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Newton’s Law of Universal
Gravitation
Every body in the universe attracts every other body with
a force that is directly proportional to the product of the
masses of the bodies and inversely proportional to the
square of the distance between the bodies.
Newton’s Law of Universal
Gravitation
When 2 masses are separated by a distance (r)
r
Fg
m1
-Fg
m2
m1 m2
11
F  G 2 ; G  6.67  10 (
r
The proportionality constant, G is called the universal gravitational
constant. Its value in the SI system of units is,
G = 6.67  10-11Nm2/kg2.
Cavendish link
The Law of Universal gravitation states that
every object in the universe is attracted to every
other object in the Universe!
Greater the masses = greater the force of attraction
Greater the distance = smaller the force of attraction
The more mass an object has, the greater its force of attraction.
You are extremely attractive.
Sample Problems
Find the gravitational attractive force between two
identical 50 g spheres with centers .8 meters apart?
G = 6.67x10-11 N m2/kg2
So you use the equation
Fg = GMm/r2
Fg = 6.67E-11*.05*.05/.82
Fg = 2.61E-13 N
Weight and Gravitational Attraction.
1. Find the weight of a 75 kg person on the
planet earth.
•W= 75 X 9.8=735 N
2. Find the gravitational force of attraction
between a 75 kg person and the Earth?
mearth = 5.98 x 1024 kg
rearth = 6.37 x 106 m
• Fg = GMm/r2=
• 6.67E-11(5.98E24 )(75) / (6.37E6)2
• Fg = 737.46 N
Acceleration Due to Gravity
Calculate g for planet Earth at sea level.
Example 6
The mass of the Hubble Space Telescope is 11,600 kg.
Determine the weight of the telescope (a) when it was resting
on the earth and (b) as it is in its orbit 598 km above the
earth's surface.
Mearth = 5.98 x 1024 kg
Rearth = 6.37 x 106 m
G
= 6.67 x 10-11 N m2/kg2
Answer: 114, 027 N
95,295 N
INNER SPACE
Down in a cave below the surface of the earth there is:
a) More gravity than at the earth’s surface
b) Less gravity than at the earth’s surface
c) The same gravity as at the surface
Newton’s Law of Universal
Gravitation:
• Conceptual Questions
1. The moon and the Earth are attracted to each other
by gravitational force. Does the more massive
earth attract the moon with a greater force than the
moon attracts Earth? Explain.
2. What happens to the gravitational force between
two masses when the distance between the masses
is doubled?
3. If the Earth were twice as massive but remained
the same size, what would happen to the value of
G? g?
4. Jupiter has about 300 times the mass of Earth and
about 10 times earth’s radius. Estimate the size of
g on the surface of Jupiter.
Cannonball
• A cannonball is fired horizontally from a tall
mountain to the ground below. Because of gravity, it
strikes the ground with increased speed. A second
cannonball is fired fast enough to go into circular
orbit but gravity does not increase its speed. Why
Refer to #19 & #23 in conceptual physics
Speed of a Satellite:
2
mv
M
m
e
Fg = G _________
= ____
r²
r
Speed of a Satellite:
v=
√
GMe
r
v = velocity (m/s)
G = gravitational constant
Me = mass of Earth (kg)
r = distance to center of
the Earth (m)
Satellites
• What is the minimum velocity needed for a
satellite to stay in orbit at 1500 km above
the earth’s surface.
• Given
• Mearth = 5.98 x 1024 kg
• Rearth = 6.37 x 106 m
And the answer is….
7913.047866 m/s