Transcript Gravitation - Red Hook Central School District

Gravity
Newton’s Universal Law of Gravitation
Newton’s conceptual leap in
understanding
gravity was his realization
that the same force governs
the motion of a falling object
on Earth & the motion of the
Moon in its orbit around
the Earth.
Universal Law of Gravitation
• Every mass attracts every other mass
through gravity.
• The force of attraction between any 2
objects is directly proportional to the
product of their masses.
• Doubling the mass of 1object doubles Fg
between the 2 objects.
Inverse Square
• Doubling distance between two objects
weakens force of gravity by a factor of
22 (or 4).
• Fg drops off by ¼.
NEWTON’S UNIVERSAL
LAW OF GRAVITATION
Fg =
GMm
2
r
G is universal gravitation
constant.
G = 6.67 x
-11
10
2
m .
N
kg2.
m1 m2 are mass of objects in kg.
r is distance between ctrs m.
Gravity and Weight
• Definition: The weight of an object is a measure
of the Fg one object feels in the presence of
another.
• Weight Fg = mg. Where g is known.
Mass can be measured in 2 ways
• Inertial mass - the mass of a body as determined by its
momentum, as opposed to gravitational mass. How it
accelerates
• m = Fnet/a
• Gravitational mass -the mass of a body determined by its
response to the force of gravity.
1. Prove that the acceleration of gravity
g = GM/r2, where M is the mass of a
planet or star r is its radius.
Fg = m2g = GM1m2.
r 2.
g = GM1 is accl due to gravity
r 2.
Mass of the object cancels out.
Acceleration depends only on the mass of the
planet (or star).
Questions: Raise Hands.
• Is heavier body attracted to the Earth
with more force than a light body.
•Does the heavier object free fall faster?
•Explain.
Newton’s Universal Law of
Gravitation
• Fg = GMm.
R2.
Describes Force btw point masses.
What is a point mass?
Gravitational Field deals with
space around the mass.
Gravitational Field Strength/Intensity Force per unit mass experienced by a
small “test mass” in space.
Gravitational Field Lines
drawn in direction of acceleration of small
mass.
Gravitational Field = g.
The value for acceleration, g, is also called the
gravitational field. Set the weight equal the Fg.
The units of the gravitational field are N/kg.
Since mg = GMm.
r2.
Grav Field
The small mass m cancels
g = GM
r2.
units N/kg.
Use to find acceleration or gravitational field.
2. What is the gravitational field
strength due to Earth at a point
450 km above the surface?
• g = GM
r2.
• (6.67 x 10-11)(6 x 1024kg)
(6.4 x 106m + 450 x 103m)2.
• 4 x 1014.
(6 850 000)2.
• 4 x 1014.
4.7 x 1013.
8.5 N/kg
Fields are vectors. Forces resulting
from more than 1 field is the sum of
the field strengths.
Ex 3. Two spheres lie along a straight line.
The sphere on the left has m = 1000-kg, and
the right on the right has m = 100-kg. The
distance between their centers is 5-m.
Point A lies between the spheres at 2.5-m
from the center of each.
Calculate the field strength at point A.
9.63 x 10
–9
N/kg left
Rd Hamper 127 – 129 do pg 129 - 131.
Purple boxes #1 – 5.
Show all work.
Einstein vs. Newton
9.5 min
• http://www.youtube.com/watch?v=4yyb
_RNJWUM
Orbits Maintained By Gravity
4. Derive an equation to
express the minimum
velocity a satellite must have
to stay in orbit.
Fg keeps the satellite in orbit.
Set Fc equal to gravitational force.
Fg
=
GMem
r2
v=
Fc
=
mv2.
r
(GMe)1/2.
(r) 1/2.
5. What is the velocity needed
for a satellite to stay in orbit 200
km above the Earth’s surface?
First find the total distance
between their centers.
2.0 x 105 m.
6.37 x 106 m.
6.57 x 106m total r.
v=
1/2
) .
(GMe
(r) 1/2.
(6.67x10-11)(5.98x1024 kg)1/2
(6.57 x 106m )1/2.
7790 m/s.
Cavendish Torsion Balance
measurement of G.
Einstein vs. Newton
9.5 min
• http://www.youtube.com/watch?v=4yyb_R
NJWUM
http://www.phy.ntnu.edu.tw/java/pro
jectileOrbit/projectileOrbit.html
• Newton’s Cannon Launch Satellite
• Apparent weightlessness. Satellites are in
freefall around the Earth! That is why
astronauts appear weightless. They are
constantly falling toward Earth. Their rate
of fall is balanced by their tangential
momentum.
The universe season 2
Gravity, Roller Coasters,
Space Travel & PEg.
https://www.youtube.com/watch?v=Eilj
zeDL0co 45 minutes