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/HomeworkObjective: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

What are some things you know about the universe?

Keplar’s Laws and Universal Gravitation12/13/10

Do Now (12/19):1.What are the three

views of the universe that changed over time?

2.Who are the men who developed each?

3.Which is our current view?

History of Views of the UniverseAristotle: 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 UniverseNicolas 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 UniverseJohannes 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 LawsFirst law: The path of each planet

about the sun is an ellipse with the sun at one focus

Keplar’s LawsSecond Law: Each planet moves

so that the planet sweeps out equal areas in equal periods of time

http://www.physicsclassroom.com/mmedia/circmot/ksl.cfm

Keplar’s LawsThird 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

orr

T

r

T32

22

31

21

3

2

r

TK

Variables and constants: T=period of orbitR or r= radius of orbitG=universal gravitational ; G=

6.67x10-11 Nm2/kg2

m=massF= forceK=Kepler’s constant

Newton’s Law of Universal Gravitation

Fg = force of gravityG = 6.67x10-11 Nm2/kg2

r = distance between two objectsm = mass 1 or 2

221

r

mGmFg

Equations:

221

r

mGmFg

r

Gmv

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

221

r

mGmFg

Period of a planet orbiting the sun

sGm

rT

3

2

•ms: the mass of the sun (constant) •r: radius of orbit

Speed of a satellite orbiting earthme= mass of the earthr=radius of orbit

r

Gmv e

Period of a satellite orbiting the earth

r=radius of orbit

eGm

rT

3

2

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