Do Now (on a new sheet please):

What net force must act on a 5 kg mass that is moving at a constant speed of 4 m/s around a circle with a radius of 2 m?

Objective/Homework


Objective:
Homework:
◦ Circular Motion – due Tuesday 12/14
◦ Quiz: Circular Motion – Tuesday 12/14
◦ Lab: Circular Motion – Friday 12/17
◦ Kepler’s Laws Worksheet: Monday 12/20
◦ Test: 2-D Motion – Tuesday December 12/21



Keplar’s Laws and Universal
Gravitation
12/13/10

Do Now (12/19):
1.
2.
3.
What are the three views of the universe that changed over time?
Who are the men who developed each?
Which is our current view?

History of Views of the Universe
Aristotle: Geocentric (everything rotates around the Earth in perfect circles)


Patterns of stars in the sky never change
Planets drift with respect to background stars

History of Views of the Universe
Nicolas Copernicus: Heliocentric
(everything rotates around the sun in perfect circles)


Accurately predicts the rising and setting
Sun, moon, and stars
Accounts for retrograde motion of Mars,
Jupiter, and Saturn

History of Views of the Universe
Johannes Keplar: Heliocentric


Used the accurate recorded observations of Tyco Brahe to develop a new planetary model and three laws
Planets rotate around the sun in ellipses with the sun at one focus

Keplar’s Laws

First law: The path of each planet about the sun is an ellipse with the sun at one focus

Keplar’s Laws


Second Law: Each planet moves so that the planet sweeps out equal areas in equal periods of time http://www.physicsclassroom.com/mmedi a/circmot/ksl.cfm

Keplar’s Laws

Third Law: The ratio of the squares of the periods (time of rotation: T) of any two planets revolving around the sun is equal to the ratio of the cubes of their radius R from the sun
T
1
2 r
1
3

T
2
2 r
2
3 or
K

T
2 r
3

Variables and constants:






T=period of orbit
R or r= radius of orbit
G=universal gravitational ; G= 6.67x10
-11
Nm 2 /kg 2 m=mass
F= force
K=Kepler’s constant





Newton’s Law of Universal
Gravitation
Fg = force of gravity
G = 6.67x10
-11 Nm 2 /kg 2 r = distance between two objects m = mass 1 or 2
F g

Gm
1 m
2 r
2

Equations:
F g

Gm
1 m
2 r
2 v

Gm r

Practice/Review:

Please use the rest of class to work on “Kepler’s Laws and Universal
Gravitation.” Make sure your test trial results are in by the end of the day!!!

Example:

A 3 kg mass and a 2 kg mass are placed with their centers 5 m apart. What is the force of attraction between them?

Do Now:


A 5 kg mass and a 6 kg mass are placed with their centers 0.5 m apart. What is the force of attraction between them?
Turn in your Circular Motion worksheet and your Do Now’s from last week
(starting with 12/6)

Quiz:

Clear your desks except for a piece of paper and a writing utensil

Quiz:

A 9800 N car is driven on a circular track with a diameter of 600 m at 30 m/s.
Calculate the car’s centripetal acceleration & its centripetal force.

Do Now (12/20):

A 5 kg mass and a 6 kg mass are placed with their centers 0.5 m apart.
What is the force of gravitational attraction between them?

Law of Universal Gravitation:
The gravitational force between two objects
F g

Gm
1 m
2 r
2

Period of a planet orbiting the sun
• m s
: the mass of the sun (constant)
• r: radius of orbit
T

2
 r
3
Gm s

Speed of a satellite orbiting earth

 m e
= mass of the earth r=radius of orbit v

Gm e r

Period of a satellite orbiting the earth
 r=radius of orbit
T

2
 r
3
Gm e

Practice/Review:

Please use the rest of class to work on “2-D Forces
Review.” Make sure your test trial results are in!!!
Once you finish, you may work on your notecard for tomorrow’s test.

Do Now:

What is the speed of the planet Jupiter around the sun?
◦ hint – look on page 178 of your classroom textbooks
◦ Hint – look for the radius of the ORBIT not the radius of the planet

Do Now:

What is the period of the planet Neptune around the sun?
◦ hint – look on page 178 of your classroom textbooks