The Universal
Law of
Gravitation
Mr.Rockensies
Regents Physics
• A remote force of mutual attraction between any two
masses
• Magnitude of the force depends on the distance between
the masses and their size
m1
m2
r
Distance between the centers
Gravity
Fg = Gm1m2/r2
Works everywhere for all masses
Fg = The force due to gravity
m1 and m2 = The masses
r = the distance between the center of the two masses
G = The Universal gravitation constant = 6.67x10-11N·m2/kg2
G can be found on the front of the reference table
Newton’s Law of Universal
Gravitation
• The forces due to gravity are small for ordinary
objects. In order to see a large noticeable force,
there needs to be large scale masses – planets,
moons, stars, etc.
• G was measured in a Cavendish Experiment a
century after Newton
• Newton’s Universal Law of Gravitation
F
F
r2
Inverse Relationship
Relationships
r
Inverse Square Relationship
100 kg box
Fg = (GmEmbox)/rE2
mE = 5.98 x 1024 kg
rE = 6.37x106 m
both on reference table
rE
Earth
Fg = (6.67 x 10-11N•m2/kg2)(5.98 x 1024 kg)(100 kg)
(6.37x106 m)2
Fg = 983 N – same as Fg = mg = 100(9.81) = 981 N
Weight Revisited
Gravity is an inverse-square law
Fg α 1
r2
Earth
Weight off of Earth
A question asks you what will happen to the Force of
Gravity when the radius between two objects is doubled.
How do you find out what will happen?
If we multiply r by…
We multiply Fg by…
2
1/22 = ¼
3
1/32 = 1/9
10
1/102 = 1/100
½
1/(½)2 = 1/¼ = 4
So in the example from the previous slide, a 100 kg box 2rE from
Earth’s center weighs 981/22 = 245N
What do we do when a
question asks…
Newton’s (what we will use)
Space around a mass is
altered to be a gravitational
field. The field exerts a force
on a second mass.
M
Fg
Einstein
Space is warped by
mass. Traveling in a
straight line is
impossible. Objects
orbit by the
following curves in
space.
Modern
Masses exchange
particles (called
Bosons) which
bind them
together.
m1
m
The Explanations of Gravity
m2
Apparent Weight on an Elevator
How does our weight
change when we ride in
an elevator?
Apparent Weight
Free-Body Diagram
Elevator
FN = Fscale
m
scale
Fg
Scales will read normal
force, which is the
“apparent weight”
4 cases:
1) Standing still; v = 0, a = 0,
FNET = 0
FN = Fg
2) Moving at a constant speed (up or down) a = 0
FNET = 0
FN = Fg
3) Accelerating up, FNET is up therefore FN > Fg
scale reads above true weight – you feel heavier
4) Accelerating down, FNET is down therefore Fg>FN
scale reads below true weight – you feel lighter
If the elevator is in free fall, FN = 0!
Apparent Weight on Incline
FN
F||
F|
θ
Fg
Scale reads:
FN = F |
FN = Fgcosθ
always less than Fg