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1 Gravitation I Mikaela Irene Fudolig Physics 71 Lecture
7/27/2019 Gravitation I
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1
Gravitation I
Mikaela Irene Fudolig
Physics 71 Lecture
7/27/2019 Gravitation I
http://slidepdf.com/reader/full/gravitation-i 2/24
Newton’s Law of Gravity
There is a force of attraction
(GRAVITATIONAL FORCE) between each
pair of objects in the universe that is
proportional to the masses of the objects
inversely proportional to the square of the
distance between them
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7/27/2019 Gravitation I
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Newton’s Law of Gravity
For two masses m1 and m2:
3
m1 m
2
Fon 1, due to2 Fon 2, due to 1
SAME MAGNITUDE,OPPOSITE DIRECTIONS!
7/27/2019 Gravitation I
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Newton’s Law of Gravity
The magnitude of the gravitational forceexerted by m2 on m1 is:
4
1 2
2 g Gm m F
r
11 2 26.673 10 /G N m kg
•The direction of the force is alwaystowards the other particle – the force isATTRACTIVE!
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Newton’s Law of Gravity
m1 (or m2), F
r, F
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Let’s look at Angelina and Brad…
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mB=72kg m A=54kg
r=2m
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Angelina and Brad
What is the gravitational force exerted by:
Brad on Angelina?
Angelina on Brad?
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Angelina and Brad
We know that (by Newton’s 3rd Law), the
MAGNITUDE of these forces are the
SAME, but OPPOSITE in DIRECTION.
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F A on B FB on A
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Angelina and Brad
The magnitude is given by
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2
11 2 2
2
(6.673 10 / )(72 )(54 )
(2 )
A B g
Gm m F r
N m kg kg kg
m
86.486 10 N
EXTREMELYSMALL!
7/27/2019 Gravitation I
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Gravitational Force
For large masses, r is taken to be the
center-to-center distance.
That is, we treat them like PARTICLES
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The Earth and the Moon
What is the magnitude of the gravitational
force exerted by the Earth on the Moon?
(mmoon=7.36 x 1022kg, mEarth=5.98 x
1024kg, center-to-center distance fromEarth to moon = 3.84 x 108m)
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2
Earth to Moon
Earth Moon g
Gm m F
r
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The Earth and the Moon
13
2
11 2 2 24 22
8 2
(6.673 10 / )(5.98 10 )(7.36 10 )
(3.84 10 )
Earth Moon g
Gm m F
r
N m kg kg kg
m
201.99 10 N LARGE!
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Weight on Earth
Your weight is just the force exerted by
the earth on you.
What is the weight of an object with mass
m on the sur face of the Earth?
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2
center of the Earth to You
Earth g
Gm m F
r 2
Earth
E
Gm m
R
6380 E
R km
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Weight on Earth
But we know that your weight is just equal
to
so
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g F mg
2
Earth
E
Gm m
mg R
6380 E R km
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Weight a distance d from the surface
of the Earth
What is the weight of an object far from
the surface of the Earth?
the weight is NOT equal to mg!
why?
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Weight a distance d from the surface
of the Earth
A mass m is a distance d away from the
surface of the earth.
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center of Earth to mass m E r R d
So the weight of mass m
(=gravitational force exerted by earth onmass m) is
2
( )
Earth
E
Gm m
R d
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Weight a distance d from the surface
of the Earth
So the weight of mass m (=gravitational
force exerted by earth on mass m) is
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2
( )
Earth
E
Gm m
R d
SMALLERTHAN THE
WEIGHT ON
THESURFACE OFTHE EARTH!
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Weight a distance d from the surface
of the Earth
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m
Weight varies inversely with the
square of the distance from the
earth’s center
2r
mG g E
r= R E
W(N)
700
500
300
0
200
100
400
600m
W= mg o
r > R E
r (x 106 m)
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Weight a distance d from the surface
of the Earth
Problem: At what distance above the
surface of the earth is the acceleration due
to gravity 0.981 m/s2 if the acceleration
due to gravity at the surface has amagnitude of 9.81 m/s2?
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Ans. ( 10 1) 14,000 E d R km
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Example: Weight Elsewhere
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The mass of Venus is 81.5% that of earth,
and its radius 94.9% that of earth.
(a) What is the acceleration due to gravity
on the surface of Venus?
(b) What is the weight of a 5.00 kg rock
on the surface of Venus?
, on Venus2Ans. 8.88 , 44.4Venus s
m g w N
s
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Example: Multiple Objects
Angelina (54kg), Brad (72kg), and Jen (50kg)
are at rest in outer space, as shown in the
configuration below.
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A
J B4.0m
2.0m
To whom will Brad bemore attracted? Why?
What is the magnitude
and direction of the net
force on Brad?
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Example: Multiple Objects
1.501 x 10-8 N – Jennifer on Brad
6.486 x 10-8 N – Angelina on Brad
6.657 x 10
-8
N – net force on Braddirected 77 above the horizontal.
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Summary
To apply Newton’s Law of Gravity:
What are the masses involved?
What is the distance between them?
(remember, we need the CENTER-TO-CENTER distance)
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1 2
2 g
Gm m F
r EVERYTHING’S
HERE!
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Summary
The acceleration due to gravity near the
surface of the Earth
30
2
Earth
E
Gm mmg R
