Gravitation
Universal Law of Gravitation
• Every mass attracts every mass in universe - Fg.
• Fg directly proportional to mass.
– Doubling the mass of one object doubles the force of
gravity between the two objects.
• Fg decreases with the square of the distance between their
centers.
– Doubling distance between two objects weakens force of
gravity by a factor of 22 (or 4).
NEWTON’S UNIVERSAL
LAW OF GRAVITATION
Fg =
GM1m2
r2
• G universal constant = 6.67 x 10-11 N m2.
kg2.
• M1 m2 are mass of objects - kg.
• r is distance between ctrs m.
• When standing on planet surface, r = planet radius.
Make a sketch graph of Fg (Y axis) vs. distance
(X axis). As 2 objects get further apart, what
happens to Fg?
Fg
D between objects
• For any two particular masses, the gravitational
force between them depends on their separation
as:
magnitude
of the
gravitational
force
between 2
fixed
masses
as the separation between the
masses is increased, the
gravitational force of attraction
between them decreases quickly.
distance between the masses increasing
Gravity and Weight
• The weight of an object is a measure of
the gravitational force the object feels in
the presence of another mass.
• If one mass is large we s/t call it M and
the small mass m.
Ex 1: Write the equation we use to
calculate weight on Earth.
• Fg = mg.
Calculate the weight of 1-kg object on
Earth.
Calculate gravitational attraction between
the Earth & the same 1-kg object. Use
your tables to find Earth’s mass & radius.
Solution
• Fg = GMm/r2.
• Fg = (6.67 x 10-11)(5.98x1024kg)(1kg)
(6.37 x 106m)2.
• 9.8 N
• THE SAME VALUE!
2. Use the Universal Law of Gravity to find the
weight of a 50-kg person in Newtons on Earth?
3. What would be the weight of the 50-kg
person on a planet whose radius is 3 x 106 m.
and whose mass is 6 x 1022 kg?
4. What is g, the accl of gravity on that planet?
For a 50 kg person:
W= Fg = mg
(50 kg) (~10 m/s2) = 500 N.
For a 50 kg person on the new planet:
W = mg = GMm.
r2.
(6.67x10-11)(6 x 1022 kg)(50kg).
(3 x 106 m)2
W = 22.2 N
4. Find the distance between a
0.3 kg ball and a 0.4 kg ball if the
gravitational force between them is
8.92 x 10-11 N.
• 0.3 m
Trick for finding F if a variable is doubled, halved etc.
• Write the equation out.
• Replace any variable that is not changing with the number 1 (as a
place holder).
• Replace any variable that is doubled with the number 2, any that
is halved with the number ½, etc.
• Solve the equation with the replacements.
• Your answer is the factor by which to multiply F.
• Ex: if your answer is 3, then F is tripled, if it is ¼ then it is
quartered…etc.
5. What happens to Fg between 2 masses A & B if:
• Mass A is tripled?
• Mass A is doubled and mass B is
halved?
• The distance between their centers is
doubled?
• Mass A is tripled and the distance
between their centers is tripled?
Hwk textbook:
Read 263 – 265
do pg 265: prac prb’s 2,3
Film Clips
• Mech Universe apple and moon
• .http://www.youtube.com/watch?v=JCh9uXy8
PHI Isaac Newton 15 min.
Concept Check 1: How does a person’s weight
differ at 100 km above the Earth’s surface
compared with at the surface?
• 1. The weight is always less than their weight at
the surface.
• 2. Their weight is more than their weight at the
surface.
• 3. Their weight is the same as at the surface.
Gravitational Field: A region of space where
mass feels Fg toward center of planet or star.
Each point has a certain degree of pull.
Gravitational Field Vectors
Gravitational Field
• A region of space where mass feels gravitational force.
• g the gravitational field measured in N/kg.
• It is how hard (N) gravity pulls on each kg of mass
affected by it.
•
•
•
•
Gravitational field strength (g)
Same as accl of grav.
g = GM/r2.
g = Fg/m
Ex 1. What is the gravitational field strength at
a point where a 10-kg mass has a weight of 25N?
• Field strength is the same as accl grav!
• g = Fg
m.
• 25-N/10-kg
• g = 2.5 N/kg.
2. Calculate the gravitational field strength at
a point 9,000 km above the Earth’s surface.
•
•
•
•
•
•
Find r.
6.37 x 106 m + 9000 x 103 m
1.537 x 107 m
g = GM/r2.
(6.67 x 10-11)(5.98x1024) / (1.537 x 107 m)2.
1.69 N/kg.
3. An 50-kg object weighs 22.2 N at a point
above the Earth. What is the gravitational
field strength at that point?
Fg = mg
=
g = Fg/m
22.2 N =
50 kg
0.44 N/kg.
Ex 4. A 60-kg student has a weight of 50-N on
planet X. What is the gravitational field strength
on planet X?
• g = Fnet
m
• g = 50-N
60-kg
• g = 0.83 N/kg.
HWK Rb pg 105 #32-38
Grav Einstein
• http://www.youtube.com/watch?v
=4yyb_RNJWUM