Transcript New Phenomena: Recent Results and Prospects from the Fermilab

Physics 218
Lecture 10
Dr. David Toback
Physics 218, Lecture X
1
Physics 218, Lecture X
2
Overview
• Newton’s gravitational law
• Dynamics and Gravity
• Example problems
• Connection with Uniform
Circular Motion
• Kepler’s Laws
Physics 218, Lecture X
3
Gravitation
Newton’s law of Universal
Gravitation
“Every particle in the
universe attracts every
other particle”
Physics 218, Lecture X
4
Large number of scales
Kinda amazing!
• Gravity covers the attraction between
–
–
–
–
–
–
–
–
An apple near the earth
The earth and the moon
The earth and the sun
The sun and our galaxy
Our galaxy and the universe
Every particle in the universe and an apple
The Earth and you
Bevo and Reveille
Physics 218, Lecture X
5
Newton’s Law
“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 particles”
• Gravity has a magnitude and direction
 Gravity is a force
Physics 218, Lecture X
6
The Magnitude of the Force of Gravity
m1m 2
Force  G 2
r
Distance between
the masses
G  6.67 10
11
N  m /kg
2
2
Physics 218, Lecture X
7
Vector Form
Force ON particle 2 due to particle 1

m1m 2
F21  G 2 rˆ12
r21
Physics 218, Lecture X
8
More on Vector Form
r̂21  r̂12
By Newtons Laws :


F21  F12
Physics 218, Lecture X
9
Bevo and Reveille
Bevo and Reveille have masses m1 and m2 and
are standing R meters apart.
Despite what you might like to believe, what is
the attraction between them?
Hint: Assume a spherical cow
Perhaps this explains why we’ve never
observed any attraction…
Physics 218, Lecture X
10
A “Spherical” Earth
It takes some fancy integration, but
one can show that we can “model”
the Earth as if all the mass were
concentrated at its center
• One can model a sphere as a point
• This is why we like to model things
as spheres in the first place.
• “spherical cow” = “point-like
cow”
Physics 218, Lecture X
11
Calculate the Magnitude of g
• Calculate the magnitude of g
• Use
24
–ME = 5.97*10 kg
-11
2
–G = 6.67*10 N*M/kg
–R = REarth = 6.38*106 m
Physics 218, Lecture X
12
Space craft in Orbit
A space craft, with mass m, is
circling the earth at radius R =
2rEarth. What is the force on the
space craft in terms of g and m?
Model the Earth
and space craft as
single points at
their center
Physics 218, Lecture X
13
Forces and Circular Motion
Tying this stuff together
• Use the force of gravity along with
other forces in force diagrams
• Circular motion is the motion
pointed towards the center of a
circle
• The Earth is a good “center”
acceleration
Physics 218, Lecture X
14
Satellites/Orbiting Problems
A satellite problem is a good example of the
substantive problems we need to be able to
solve. Predict the outcome of the experiment
Physics 218, Lecture X
15
How to solve these types of problems
• Some thoughts
– What keeps a satellite up? Its speed
– Accel = v2/r
– Force = ma = mv2/r
• The trick is going to be to ask the question
– What are the forces?
Is it in uniform circular motion? If so, we
can use Newton’s law:
FGravity = FUniform Circular Motion
Physics 218, Lecture X
16
Geosynchronous Satellite
A satellite is in orbit around the earth and its
speed is such that it always stays above the
same point on the earth throughout the day.
Assuming a spherical Earth with mass ME:
• What is the period of the satellite?
• Determine the height of the satellite in
terms of the period, ME and G
• Determine its speed
• Compare this speed to the speed at a height
twice as far from the center of the earth
Physics 218, Lecture X
17
This Week
• Next Lecture:
–Kepler’s Laws
–Examples
• HW due Monday
Physics 218, Lecture X
18
Weightlessness
• What is the weight of
the person in the
figure?
• What is the difference
between being in “free
fall” and being “out of
the reach of large
gravitational forces?”
Physics 218, Lecture X
19
Throwing a Baseball
A person throws a baseball at 100 km/hr, but
it is attracted back towards him because of
gravity.
• Estimate the force 1 Meter away?
• Assuming constant acceleration (Bad
assumption), how long does it take to turn
around?
Physics 218, Lecture X
20