2. Newton’s Law of Universal Gravitation:
Two objects of mass m1 and m2 separated by
a center-to-center distance r ___________ each
other with a gravitational force:
attract r m1 m2 Fg Fg
Fg =
…where G = ____________________________
is called the _______________ gravitational constant.

3. PhysRT,
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4. Newton’s Law of Universal Gravitation:
Two objects of mass m1 and m2 separated by
a center-to-center distance r ___________ each
other with a gravitational force:
attract r m1 Fg m2 Fg
G m1 m2 r2
Fg =
…where G = ____________________________
is called the _______________ gravitational constant.

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6. Newton’s Law of Universal Gravitation:
Two objects of mass m1 and m2 separated by
a center-to-center distance r ___________ each
other with a gravitational force:
attract r m1 Fg m2 Fg
G m1 m2 r2
Fg =
6.67 x N·m2/kg2
…where G = ____________________________
is called the _______________ gravitational constant.
universal

7. Notes:
Fg is an _________ range, _______________ force.
Fg is stronger when the objects are__________ .
3. The constant G is very __________  Fg is the
________________ of the fundamental forces.
4. Fg is always ___________________.
5. Both masses pull each other with ____________
magnitude forces, but in _____________ directions.
6. Equation is only true for ____________ masses.
 for spheres, you must assume mass is
concentrated at __________________
 for complicated shapes, _____________ is needed,
but equation works ________________ anyway.
infinite
"at a distance"
closer
small
weakest
attractive
equal
opposite
point
its center.
calculus
approximately

8. Ex. A mass of 1.8 x 103 kg (F-150) is 0.50 meter
from a mass of 6.0 x 101 kg (student). Find the
magnitude of the force of gravitational attraction
between the two masses. Show all work.
G m1 m2 r2
Fg =
(6.67 x Nm2/kg2)
(1.8 x 103 kg)
(6.0 x 101 kg)
Fg =
(0.50 m)2
(7.2 x 10-6 Nm2)
Fg =
(0.25 m2) /
Fg =
2.9 x 10-5 N
≈ 3/1000 of one dollar bill
neither
Which mass pulls with a greater force?

9. G m1 m2 r2
Fg =
inverse
squared Fg m1 Fg m2 Fg r
direct
direct
Double m1  Fg ________________
Triple m2  Fg ________________
Double both m1 and m2  Fg ________________
Triple m1 and double m2 Fg ________________
Double r  Fg ________________
Halve r  Fg ________________
Triple r  Fg ________________
Double m1 and r  Fg ________________
Double m1, m2 and r  Fg ________________
2x greater
3x greater
4x greater
6x greater
4x weaker
4x greater
9x weaker
2x weaker
same

10. Ex: If the Fg is between an object of mass m and a planet, then Fg is called the _________: Fg = ___
weight w
Ex: Earth m
Fg = Gm1m2 r2
r =
1 Re
GMem
Fg =
Re2 Me m
GMe
Fg =
Re2
w = m g
1 Earth radius
Re = ________________
Me = ________________
mass of Earth
g =
GMe/Re2 =
9.81 m/s2

11. Earth ms Ex: Are you weightless in the space shuttle (mass = ms)?
The space shuttle orbits
at ≈ _______ = __________
above Earth's surface.
Its __________ distance
from Earth's center is
r = _____ + _____ Mm
= _______ Mm.
= ________ Re
So the ___________ (Fg)
of the shuttle and all its
contents in orbit,
compared to its weight
on land, is:
Earth
Re = ___________
≈ ___________ ms
GMems
GMems =
Fg = = 

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13. Earth ms Ex: Are you weightless in the space shuttle (mass = ms)?
The space shuttle orbits
at ≈ _______ = __________
above Earth's surface.
Its __________ distance
from Earth's center is
r = _____ + _____ Mm
= _______ Mm.
= ________ Re
So the ___________ (Fg)
of the shuttle and all its
contents in orbit,
compared to its weight
on land, is:
300 km
0.3 Mm
total
Earth
6.4
0.3
6.7
1.05
6.37 x106 m
weight
Re = ___________
≈ ___________
6.4 Mm ms
GMems
GMems
0.91
GMems =
Fg = =
91% 
(1.05Re)2
(1.05)2
Re2
Re2

14. The Vomit Comet:
The airplane produces about 25 s of apparent weightless-ness by following a parabolic vertical flight path. A parabolic flight path is the same path that would be taken by an object in free fall, such as a cannonball fired into the air.

15. Ex: r is the ____________________ distance center-to-center
r = __ Re 4 C
__ Re above
surface 3
r = __ Re 3 B
__ Re above
surface 2
r = __ Re 2 A
__ Re above
surface 1
r = 1 Re
Earth
If Fg at surface = 200 N,
what is the weight (Fg) at A?
200/22
= 200/4
= 50 N
= 22 N
At B?
200/32
At C?
200/42
= 12.5 N

16. Ex: A 20-N box on a table is lifted from 1 m to 2 m
above the floor. Since the height was doubled,
the new weight should be w = 20/22 = 5 N ??????
5 N ?
This _________
______________
because these
heights are
from ________
_____________ .
does not
happen
not measured
20 N
2 m
Earth's
table
center
1 m

17. Ex: A 600-N volleyball player
jumps in the air. What is the
force of gravity acting on her…
1/ …while in the air?
2/ …as she is landing?
3/ …when she is again
at rest on the ground?
4/ What is her weight in
all three cases above?
600-N
600-N
600-N
600-N

18. Ex: A rock in Same rock at rest freefall: on a table: Fg = 1.33 N
a/ What is the weight of the rock in each case?
1.33 N
b/ What is the net force acting on the rock in each case?
free fall: Fnet = ______
on table: Fnet = ______
-1.33 N
c/ What is the acceleration of the rock in each case?
free fall: a = ______
on table: a = ______
-9.81 m/s2
d/ What is the reaction force to the weight of the rock in
each case?
The rock pulls up on Earth with a 1.33 N
gravitational force.

19. Ex: Cavendish "Weighing the Earth" Experiment:
When a ____ sphere
(m2) was brought
close to the barbells,
the _______________
attraction
caused the
thin wire
to _________ . Pb
thin wire
From the wire's
properties, the
______________
needed to make
the wire twist
that much could
be _____________
gravitational
force, Fg r m2 m1
Pb barbells
twist
estimated
Then Fg, r, m2 and m1 were substituted into:
G m1 m2 r2
Fg =
and this was solved to find ______ . G G
Once _____ was known, an object of
known mass m and weight w were used
to find ___________ unknown mass Me using
G m
Re2 Me
w =
Earth's

20. One last note:
In PhysRT:
g =
Fg/m
Solve this for:
Fg = mg
same
________
equation
Not in PhysRT: w = mg
acceleration
____________
due to gravity
Even though g appears in the equation for w,
an object does NOT have to be ________________
to use this equation. Think of g as simply a
________________________ between ____ and ____ .
In fact, g can have ___________________ in different
locations, which is why ____________ may change
even though _________ remains the same.
accelerating
conversion factor m w
different values
weight
mass