Download AP Physics – Applying Forces

Chapter 5
AP Physics – Gravity
Every particle in the universe attracts every other particle
with a force that is proportional to the product of their
masses and inversely proportional to the square of the
distance between them. This force acts along the line
joining the two particles.
F G
m1m2
r
G  6.67 x 10
2
11
N m
kg 2
2
G  constant of universal gravitation
Same everywhere
Inverse-square Law
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Newton’s Law of Universal Gravitation
1. Gravitational force is a field force between two
particles -- in all mediums.
2. Force varies as the inverse square of the distance
3. Force is proportional to mass of objects,
Gravity force acts from the center of object.
4. Gravity is always an attractive force.
 A Girl, Brandy (42.5 kg), sits 1.50 m from boy
(63.0 kg) George, she feels a force of attraction
(it’s not chemical). What is force of gravity
between them?
F G
m1m2
r2
2

  42.5 kg  63.0 kg 
11 N  m
F   6.67 x 10
2 
2

kg
1.50 m 


F  7940 x 1011 N
F  7.94 x 108 N
2
What is the mass of Earth?
Find mass of earth. re = 6.38 x 106 m. 10.0 kg mass,
other mass is earth’s mass.
m1mEarth
F G
r2
mEarth
98.0 N  6.38 x 10 m 
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mEarth 
Fr 2

Gm1
2
2


N

m
11
6.67
x
10

 10.0 kg 
2
kg


mEarth  59.8 x 1023 kg
mEarth  5.98 x 1024 kg
 You weigh 567 N on earth. How much would you
weigh on mars? mm = 6.42 x 10 23kg, rm = 3.37 x
10 6 m
W  mg
W
m
g

kg  m  1
m  567

2
s  9.8 m

s2







3
m1m2
F G 2
r
m  57.86 kg
23
2
6.42
x
10
kg   57.86 kg 



N

m
11
F   6.67 x 10
2 
2

6
kg


3.37 x 10 m 
F  218 N
 What is the acceleration of gravity on Venus?
mv = 4.88 x 10 24 kg and rv = 6.06 x 10 6 m
F  ma
m2 a  G
and
F G
m1m2
r2
m1 m2
r2
24
2
4.88
x
10
kg 


kg

m

m

11
a   6.67 x 10

2
2
2
6
s

kg

  6.06 x 10 m 
a = 8.86 m/s2
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Keplers III Laws of Planetary motion:
1. The orbit of every planet is an ellipse with the Sun at
one of the two foci.
2. A line joining a planet and the Sun sweeps out equal
areas during equal intervals of time.
3. The square of the orbital period of a planet is directly
proportional to the cube of the semi-major axis of its
orbit.
Concept Practice) Two satellites orbit the Earth in circular
orbits of the same radius. One satellite is twice as
massive as the other. Which of the following statements
is true about the speed of these satellites?
a) The heavier satellite moves twice as fast as the lighter
one.
b) The two satellites have the same speed.
c) The lighter satellite moves twice as fast as the heavier
one.
d) The heavier satellite moves four times as fast as the
lighter one.
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1. The following are true/false questions.
a. There is no gravity in outer space - like on board the
space shuttle.
b. Newton discovered gravity.
c. The earth’s gravity does not extend out to the outer
planets, and certainly not to the next nearest star.
d. The force of the earth’s gravity on objects in orbit is
near zero.
e. The crescent shape of the moon is caused by the
earth’s shadow.
f. The pull of the moon’s gravity causes the tides. The
pull of the sun does not cause any significant tides.
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1. Neptune is an average distance of 4.5 10 9 km from
the Sun. Estimate the length of the Neptunian year
given that the Earth is 1.50 108 km from the Sun on
the average.
2. Mars’ period was noted by Kepler to be about 687
“Earth” days, which is1.88 yrs. Determine the
distance of Mars from the Sun using the Earth as
a reference. re = 1.5 x 10 11 m.
3. Use Kepler’s laws and the period of the Moon
(27.4 d) to determine the period of an artificial
satellite orbiting very near the Earth’s surface.
rmoon = 3.84 x 10 8 m, rNear Earth = 6.38 x 10 6 m.
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AP Question:
1. (I5 points)
The Sojourner rover vehicle shown in the sketch above was used to explore the
surface of Mars as part of the Pathfinder mission in 1997. Use the data in the
tables below to answer the questions that follow.
Sojourner Data
Mass of Sojourner vehicle:
Wheel diameter:
Stored energy available:
Power required for driving
under average conditions:
Land speed:
11.5kg
0.13 m
5.4 x l05 J
10 W
6.7 x 10-3 m/s
The Sojourner rover vehicle shown in the sketch above was used to explore the surface of Mars
as part of the Pathfinder mission in 1997. Use the data in the tables below to answer the
questions that follow.
Mars Data
Radius:
Mass:
0.53 x Earth's radius
0.11 x Earth's mass
(a) Determine the acceleration due to gravity at the surface of Mars in terms of g, the acceleration due to
gravity at the surface of Earth.
(b)
Calculate Sojourner's weight on the surface of Mars.
(c)
Assume that when leaving the Pathfinder spacecraft Sojourner rolls down a ramp inclined at 200 to
the horizontal. The ramp must be lightweight but strong enough to support Sojourner. Calculate
the minimum normal force that must be supplied by the ramp.
(d)
What is the net force on Sojourner as it travels across the Martian surface at constant velocity?
Justify your answer.
(e)
Determine the maximum distance that Sojourner can travel on a horizontal Martian surface using
its stored energy.
Suppose that 0.010% of the power for driving is expended against atmospheric drag as Sojourner
travels on the Martian surface. Calculate the magnitude of the drag force.
(f)
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