circular motion and gravitational force introduction section 0 lecture 1 slide 1 lecture 12 slide 1...

Circular Motion and Gravitational Force

Introduction Section 0 Lecture 1 Slide 1

Lecture 12 Slide 1

INTRODUCTION TO Modern Physics PHYX 2710

Fall 2004

Physics of Technology—PHYS 1800

Spring 2009

Physics of Technology

PHYS 1800

Lecture 12




Lecture 12 Slide 2


Fall 2004


Spring 2009

PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet

*Homework Handout

Date Day Lecture Chapter Homework Due Jan 5 6 7 9

M T W F*

Class Admin: Intro.Physics Phenomena Problem solving and math Units, Scalars, Vectors, Speed and Velocity

1 App. B, C 1 2

-

Jan 12 14 16

M W F*

Acceleration Free Falling Objects Projectile Motion

2 3 3

1

Jan 19 21 23

M W F*

Martin Luther King Newton’s Laws Mass and Weight

No Class 4 4

2

Jan 26 28 29 30

M W Th F

Motion with Friction Review Test 1 Circular Motion

4 1-4 1-4 5

3

Feb 2 4 6

M W F*

Planetary Motion and Gravity Energy Harmonic Motion

5 6 6

4

Feb 9 11 13

M W F*

Momentum Impulse and Collisions Rotational Motion

7 7 8

5

Feb 16 17 18 19 20

M Tu W H F*

Presidents Day Angular Momentum (Virtual Monday) Review Test 2 Static Fluids, Pressure

No Class 8 5-8 5-8 9

-

Feb 23 25 27

M W F*

Flotation Fluids in Motion Temperature and Heat

9 9 10

6

Mar 2 4 6

M W F*

First Law of Thermodynamics Heat flow and Greenhouse Effect Climate Change

10 10 -

7

Mar 9-13 M-F Spring Break No Classes Mar 16 18 20

M W F*

Heat Engines Power and Refrigeration Electric Charge

11 11 12

8

Mar 23 25 26 27

M W H F*

Electric Fields and Electric Potential Review Test 3 Electric Circuits

12 13 9-12 13

-

Mar 30 Apr 1 3

M W F

Magnetic Force Review Electromagnets Motors and Generators

14 9-12 14

9

Apr 6 8 10

M W F*

Making Waves Sound Waves E-M Waves, Light and Color

15 15 16

10

Apr 13 15 17

M W F*

Mirrors and Reflections Refraction and Lenses Telescopes and Microscopes

17 17 17

11

Apr 20 22 24

M W F

Review Seeing Atoms The really BIG & the really small

1-17 18 (not on test) 21 (not on test)

No test week 12

May 1 F Final Exam: 09:30-11:20am



Lecture 12 Slide 3


Fall 2004


Spring 2009


PHYS 1800

Lecture 11


Introduction and Review



Lecture 12 Slide 4


Fall 2004


Spring 2009

... have anything in

common with circular motion

on Earth?

Does the circular motion of the moon around the Earth ...



Lecture 12 Slide 5


Fall 2004


Spring 2009

Describing Motion and Interactions

Position—where you are in space (L or meter)

Velocity—how fast position is changing with time (LT-1 or m/s)

Acceleration—how fast velocity is changing with time (LT-2 or m/s2)

Force— what is required to change to motion of a body (MLT-2 or kg-m/s2)

We will focus on a special kind of force, termed a central forces that results from change in direction of velocity.

Now look at a specific central force, the force due to gravity.



Lecture 12 Slide 6


Fall 2004


Spring 2009

Newton’s Laws in Review

• 1st Law —a special case of the 2nd Law for statics, with a=0 or Fnet=0 • An objects velocity remains unchanged, unless

a force acts on the object.

• 2nd Law (and 1st Law)—How motion of a object is effected by a force.– The acceleration of an object is directly

proportional to the magnitude of the imposed force and inversely proportional to the mass of the object. The acceleration is the same direction as that of the imposed force.

• 3rd Law —Forces come from interactions with other objects.• For every action (force), there is an equal but

opposite reaction (force).

F ma

units : 1 newton = 1 N = 1 kgm s2



Lecture 12 Slide 7


Fall 2004


Spring 2009

The Math Approach

• We are going to explore a different kind of central force that is no longer constant, but is proportional to 1/r2.

20

0

2

1

222attvt

vvt

vvd

t

vvaoratvv

ga

ofoo

off

k/r2

We will take a pragmatic approach (hindsight is 20-20!)

We simply replace the force of the “string” with the force of gravity

2rkT gravitystring F



Lecture 12 Slide 8


Fall 2004


Spring 2009


PHYS 1800

Lecture 11


Historical Perspectives



Lecture 12 Slide 9


Fall 2004


Spring 2009

Historical Perspective on Gravity

Hart’s list of most influential people in the history of the world:Newton (2)* Einstein (10)Galileo Galilei (12)*Aristotle (13)***Copernicus (19) *Kepler (75) *

*(even though they got the wrong answer on the test)

Simmon’s list of most influential scientists in the history of the world Newton (1) * (and 2 and 6 and 40)Einstein (2)Galileo Galilei (7) *Copernicus (9) *Kepler (10) *Tyco Brahe (22) *Aristotle (an honorable mentioned) ***

Explore a trail of science from the early Greeks through work today at USU to improve our understanding and scientific models for the interaction of two masses through gravity.



Lecture 12 Slide 10


Fall 2004


Spring 2009


Aristotle

Circular orbitsGeocentric

This works pretty well for the orbits of the Sun, Moon and stars, but not so well for planets.



Lecture 12 Slide 11


Fall 2004


Spring 2009


Ptolemy

Epicycle orbitsGeocentric

This works pretty well for the orbits of the Sun, Moon and stars, and a little better for planets.



Lecture 12 Slide 12


Fall 2004


Spring 2009

Planetary Motion

• Retrograde motion occurs in a planet’s orbit when the planet appears to move against the background of stars



Lecture 12 Slide 13


Fall 2004


Spring 2009


Copernicus and Galelio

Circular or Epicycle orbitsHeliocentric

This works pretty well for the orbits of the Sun, Moon and stars, and a better for planets. Cleans up the retrograde motion (mostly)



Lecture 12 Slide 14


Fall 2004


Spring 2009


Tyco Barhe

Enter the “last great naked-eye astronomer.

A phenomenal set of data showed slight inconsistencies in our descriptions of astronomical orbits.

So who is right?

Team Geo: Aristotle/PtolemyTeam Helio: Copernicus/Galileo



Lecture 12 Slide 15


Fall 2004


Spring 2009


Kepler

Tycho’s assistant painstakingly analyzed all that careful data.

This works pretty well for the orbits of the Sun, Moon and stars, and a little better for planets.



Lecture 12 Slide 16


Fall 2004


Spring 2009

Kepler’s First Law of Planetary Motion

Kepler was able to show that the orbits of the planets around the sun are ellipses, with the sun at one focus.



Lecture 12 Slide 17


Fall 2004


Spring 2009

Kepler’s Second Law of Planetary Motion

• Because planets move faster when nearer to the sun, the radius line for each planet sweeps out equal areas in equal times.

• The two blue sections each cover the same span of time and have equal area.



Lecture 12 Slide 18


Fall 2004


Spring 2009

Kepler’s Third Law of Planetary Motion

• The period (T) of an orbit is the time it takes for one complete cycle around the sun.

• The cube of the average radius (r) about the sun is proportional to the square of the period of the orbit.

T 2 r3



Lecture 12 Slide 19


Fall 2004


Spring 2009


Newton

Enter Newton to tie it all up in a neat bundle

Found the form of the force that fit into Newton’s Laws that fully explained all the planetary observations (except very detailed orbital motion and precessions).



Lecture 12 Slide 20


Fall 2004


Spring 2009


Newton

To get Kepler’s Laws of Planetary Motion to match with Newton’s Laws of (general) Motion

Newton set the centripetal force to a central force proportional to 1/r2.

gravitylcentripeta rk

rv FF 2

2



Lecture 12 Slide 21


Fall 2004


Spring 2009


PHYS 1800

Lecture 11


Newton’s Universal Law of Gravitation



Lecture 12 Slide 22


Fall 2004


Spring 2009

Newton’s Law of Universal Gravitation

• Newton recognized the similarity between the motion of a projectile on Earth and the orbit of the moon.

• If a projectile is fired with enough velocity, it could fall towards Earth but never reach the surface.

• The projectile would be in orbit.

• Newton’s law of universal gravitation says the gravitational force between two objects is proportional to the mass of each object, and inversely proportional to the square of the distance between the two objects.

• G is the Universal gravitational constant G.

221

r

mGmFgravity



Lecture 12 Slide 23


Fall 2004


Spring 2009


Cavendish

Developed a clever way to measure the weak gravitational force between small masses.

Confirmed Newton’s Law of Universal Gravitation (and in essence measured the mass of the Earth in comparison to the kg mass standard).

The effect the 320 kg balls of the 1.5 kg balls was about that of a grain of sand!

That’s 20 parts per billion precision!!!

Wikeapedia has a nice description of the experiment.

2r

GmM earthgravity F



Lecture 12 Slide 24


Fall 2004


Spring 2009


Cavendish

Measured the mass of the Earth in comparison to the kg mass standard.

Set weight equal to gravitational attraction, then solved for (little) g.

2

2

earth

earth

earth

earthgravity

r

GMg

so

Wmgr

GmM

F



Lecture 12 Slide 25


Fall 2004


Spring 2009


PHYS 1800

Lecture 11


Extensions to Newton’s Law of Gravitation



Lecture 12 Slide 26


Fall 2004


Spring 2009

Three equal masses are located as shown. What is the direction of the total force acting

on m2?

a) To the left.b) To the right.c) The forces cancel such that the total force is zero.d) It is impossible to determine from the figure.

There will be a net force acting on m2 toward m1. The third mass exerts a force of attraction to the right, but since it is farther away that force is less than the force exerted by m1 to the left.



Lecture 12 Slide 27


Fall 2004


Spring 2009

Extensions to Newton’s Theory of Gravity

Complex Motion Problems

Consider the Sun, Earth, Moon system (the three body problem).

Approximating the complex forces using Newton’s Laws leads to very accurate solutions to the problem.

2r

GmM earthgravity F



Lecture 12 Slide 28


Fall 2004


Spring 2009

The Moon and Other Satellites

Phases of the moon result from the changes in the positions of the moon, Earth, and sun.



Lecture 12 Slide 29


Fall 2004


Spring 2009

An artist depicts a portion of the night sky as shown.

Is this view possible?

a) Yesb) No

No. There are no stars between the Earth and the moon. (Maybe blinking lights of a passing jet?)



Lecture 12 Slide 30


Fall 2004


Spring 2009


Complex Motion Problems

NASA predicts elaborate orbits for spacecraft like the Solar Probe Mission to the Sun or the Cassini-Huygens Mission to Saturn and its moons.



Lecture 12 Slide 31


Fall 2004


Spring 2009


But…Using retroreflectors left by the Apollo astronauts, we measure the moon's distance with staggering precision: better than a few cm out of 385,000 km (about 20 parts per trillion!!!)

Results of this long-term experiment are:

• The moon is spiralling away from Earth at a rate of 38 mm/yr. • The moon probably has a liquid core of about 20% of the Moon's radius. • The universal force of gravity is very stable. The experiments have put an upper limit on the change in G of less than 1 part in 1011 since 1969.

• Results strongly supporting the validity of the Strong Equivalence Principle.

• Einstein’s General Theory of Relativity predicts the moon's orbit to within the accuracy of the laser ranging measurements.



Lecture 12 Slide 32


Fall 2004


Spring 2009

Extensions to Newton’s Theory of Gravity Einstein’s Special Theory of Relativity

Based on how E&M works, Einstein postulated:• The laws of physics are the same for all observers in uniform motion relative to one another (Galileo’s principle of relativity), • The speed of light in a vacuum, c, is the same for all observers, regardless of their relative motion or of the motion of the source of the light.

Some surprising results these are:

Relativity of simultaneity: Two events, simultaneous for some observer, may not be simultaneous for another observer if the observers are in relative motion. Time dilation: Moving clocks are measured to tick more slowly than an observer's "stationary" clock. Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to the observer. Mass-energy equivalence: E = mc2.



Lecture 12 Slide 33


Fall 2004


Spring 2009


General Theory of Relativity

Einstein’s theory special relativity and Newton's law of universal gravitation.

Equivalence Principle: Inertial mass in Newton's second law, F = ma, mysteriously equals the gravitational mass in Newton's law of universal gravitation

Classical tests predicted by Einstein (and subsequently verified)

• Perihelion precession of Mercury • Deflection of light by the Sun • Gravitational redshift of light

Tc

GgRgR

r

GmM earthgravity

421

2

8

F



Lecture 12 Slide 34


Fall 2004


Spring 2009


Current Problems in Gravity

Is Einstein’s General Theory of Relativity the final word? (Maybe not)

Do gravitational waves exist? (Yes, maybe)

Are G and Λ truly constants? (Controversial evidence say NO!)

What happens when black holes (or galaxies) collide?

Can General Relativity be merged with Quantum Mechanics? (QM has been tested to 17 decimal places- ~10 parts per quintillion, even though we don’t really understand how to interpret the theory.)

Is there a 5th force in nature?



Lecture 12 Slide 35


Fall 2004


Spring 2009

USU Perspective on Gravity

Hart’s list of most influential people in the history of the world:Newton (2)* Einstein (10)Galileo Galilei (12)*Aristole (13)***Copernicus (19) *Kepler (75) *

*(even though they got the wrong answer on the test)

Simmon’s list of most influential scientists in the history of the world Newton (1) * (and 2 and 6 and 40)Einstein (2)Galileo Galilei (7) *Copernicus (9) *Kepler (10) *Tyco Brahe (22) *Aristole (an honorable mentioned) ***

Work today at USULarsen, Torre and Wheeler



Lecture 12 Slide 36


Fall 2004


Spring 2009


PHYS 1800

Lecture 11


Comments on the Nature of Scientific Theories



Lecture 12 Slide 37


Fall 2004


Spring 2009

Lessons from the Theory of Gravity

Scientific Theories Are NOT Static

Aristotle was extended by Ptolemy, who was corrected by Copernicus, who was generalized by Galileo, who was supplemented by Brahe, who provided Kepler with data, who was merged with laws of motion by Newton, who was quantified by Cavendish, who was supplanted by Einstein, who was expanded by Einstein himself, who was tested by 20th century scientists and challenged by QM and cosmology…

But they can describe a lot of what goes on in the world around us.



Lecture 12 Slide 38


Fall 2004


Spring 2009

Lessons from the Theory of Gravity

Scientific Theories are descriptions of nature, based ultimately on our observations…

But they do not attempt to state what their origins are or why they exist.

Scientific theories address where, when and how, but not why



Lecture 12 Slide 39


Fall 2004


Spring 2009


Next Lab/Demo: Circular Motion & GravityEnergy & OscillationsThursday 1:30-2:45

ESLC 53 Ch 5

Next Class: Wednesday 10:30-11:20BUS 318 roomRead Ch 5

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