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Isaac Newton and the Universal Law of Gravitation
Discovered:
three laws of motion,
one law of universal gravitation.
Isaac Newton (1643-1727): English
= a push or pull acting on an object.
Examples:
gravity = pull
electrostatic attraction = pull
electrostatic repulsion = push
Force
Newton’s Second Law of Motion:
The acceleration of an object is directly proportional to the force acting on it,
and inversely proportional to its mass.
In mathematical form:
Or alternatively: amF m
Fa
Example of Newton’s Second Law:
A package of cookies has mass m = 0.454 kilograms,
And experiences gravitational acceleration g = 9.8 meters/second2
How large is the force acting on the cookies?
pound) 1 Newtons (4.4
Newtons 4.4m/sec kg 4.4
)m/sec kg)(9.8 454.0(2
2
F
F
amF
Newton’s Third Law of Motion:For every action, there is
an equal and opposite reaction.
Whenever A exerts a force on B, B exerts a force on A that’s equal in size and opposite in direction.
All forces come in pairs.
Example of Newton’s Third Law:
Cookies push on hand: F = 1 pound, downward.
Hand pushes on cookies: F = 1 pound, upward.
Remove hand!
Earth pulls on cookies: F = 1 pound, downward.
Cookies pull on earth: F = 1 pound, upward.
THIRD Law states: force on Earth = force on cookies
SECOND Law states: acceleration = force divided by mass
Mass of Earth = 1025 x mass of cookies
Therefore, acceleration of cookies = 1025 x acceleration of Earth.
(Cookies reach a high speed while the Earth hardly budges.)
But…why do the cookies and the Earth exert a force on each other?
Newton’s Law of Gravity states that gravity is an attractive force acting between ALL pairs of massive objects.
Gravity depends on:
(1) MASSES of the two objects,
(2) DISTANCES between the objects.
Newton’s question: can GRAVITY be the force keeping the Moon in its orbit?
Newton’s approximation: Moon is on a circular orbit.
Even if its orbit were perfectly circular, the Moon would still be accelerated.
The Moon’s orbital speed:
radius of orbit: r = 3.8 x 108 m
circumference of orbit: 2r = 2.4 x 109 m
orbital period: P = 27.3 days = 2.4 x 106 sec
orbital speed:
v = (2r)/P = 103 m/sec = 1 km/sec!
Acceleration required to keep Moon on a circular orbit
28
232
8
3
2
m/sec 00272.0m 103.8
m) 10(
m 108.3
m/sec 10
:Moon For the
radius orbitalr speed, orbitalv
:ison accelerati required The
r
va
r
v
r
va
Ratio of Accelerations to Distances
????? m/sec 00272.0
m/sec 8.9
)m/sec 00272.0(aMoon theoforbit At the
m/sec 8.9
Earth) of radius(Earth theof surface At the
2
2
2
2
a
r
Bottom Line
If gravity goes as one over the square of the distance,
Then it provides the right acceleration to keep the Moon on its orbit (“to keep it falling”).
Triumph for Newton!!
Fig. 5-1, p.80
Fig. 5-2, p.81
Fig. 5-3, p.82
p.83
(4) Newton’s Law of Gravity:
The gravitational force between two objects
F = gravitational force
M = mass of one object
m = mass of the second object
r = distance between centers of objects
G = “universal constant of gravitation”
2r
MmGF
Example: What is gravitational force between Earth and
cookies?
:in numbers theplug sLet'
2211
6
24
2
kg/m Newtons 107.6
m 106.4Earth of radius
kg 454.0 cookies of mass
kg100.6 Earth of mass
G
r
m
M
r
MmGF
Example: What is gravitational force between Earth and
cookies?
pound 1 Newtons 4.4F
kg/m Newtons 107.6
m 106.4Earth of radius
kg 454.0 cookies of mass
kg100.6 Earth of mass
:in numbers theplug sLet'
2211
6
24
2
G
r
m
M
r
MmGF
Table p.85
p.85
p.89
p.90
Fig. Q5-3, p.92
Fig. Q5-19, p.93
Fig. Q5-25, p.93