Loading...

PPT – Physics of Technology PHYS 1800 PowerPoint presentation | free to download - id: 71a3a7-ODgyZ

The Adobe Flash plugin is needed to view this content

Physics of Technology PHYS 1800

- Lecture 12
- Circular Motion and Gravitational Force

PHYSICS OF TECHNOLOGY Spring 2009 Assignment

Sheet

Homework Handout

Physics of Technology PHYS 1800

- Lecture 11
- Circular Motion and Gravitational Force

Introduction and Review

Does the circular motion of the moon around the

Earth ...

... have anything in common with circular motion

on Earth?

Describing Motion and Interactions

- Positionwhere you are in space (L or meter)
- Velocityhow fast position is changing with time

(LT-1 or m/s) - Accelerationhow 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.

Newtons Laws in Review

- 1st Law a special case of the 2nd Law for

statics, with a0 or Fnet0 - 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).

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.

? 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

Physics of Technology PHYS 1800

- Lecture 11
- Circular Motion and Gravitational Force

Historical Perspectives

Historical Perspective on Gravity

Harts 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)

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.

Simmons 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)

Historical Perspective on Gravity

Aristotle Circular orbits Geocentric This

works pretty well for the orbits of the Sun, Moon

and stars, but not so well for planets.

Historical Perspective on Gravity

Ptolemy Epicycle orbits Geocentric This works

pretty well for the orbits of the Sun, Moon and

stars, and a little better for planets.

Planetary Motion

- Retrograde motion occurs in a planets orbit when

the planet appears to move against the background

of stars

Historical Perspective on Gravity

Copernicus and Galelio Circular or Epicycle

orbits Heliocentric This works pretty well for

the orbits of the Sun, Moon and stars, and a

better for planets. Cleans up the retrograde

motion (mostly)

Historical Perspective on Gravity

So who is right? Team Geo Aristotle/Ptolemy Team

Helio Copernicus/Galileo

Tyco Barhe Enter the last great naked-eye

astronomer. A phenomenal set of data showed

slight inconsistencies in our descriptions of

astronomical orbits.

Historical Perspective on Gravity

Kepler Tychos 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.

Keplers 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.

Keplers 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.

Keplers 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.

Historical Perspective on Gravity

Newton Enter Newton to tie it all up in a neat

bundle Found the form of the force that fit into

Newtons Laws that fully explained all the

planetary observations (except very detailed

orbital motion and precessions).

Historical Perspective on Gravity

Newton To get Keplers Laws of Planetary

Motion to match with Newtons Laws of (general)

Motion Newton set the centripetal force to a

central force proportional to 1/r2.

Physics of Technology PHYS 1800

- Lecture 11
- Circular Motion and Gravitational Force

Newtons Universal Law of Gravitation

Newtons 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.
- Newtons 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.

Historical Perspective on Gravity

Cavendish Developed a clever way to measure the

weak gravitational force between small

masses. Confirmed Newtons 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!

Thats 20 parts per billion precision!!! Wikeap

edia has a nice description of the experiment.

Historical Perspective on Gravity

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.

Physics of Technology PHYS 1800

- Lecture 11
- Circular Motion and Gravitational Force

Extensions to Newtons Law of Gravitation

Three equal masses are located as shown. What is

the direction of the total force acting on m2?

- To the left.
- To the right.
- The forces cancel such that the total force is

zero. - 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.

Extensions to Newtons Theory of Gravity

Complex Motion Problems Consider the Sun,

Earth, Moon system (the three body

problem). Approximating the complex forces using

Newtons Laws leads to very accurate solutions to

the problem.

The Moon and Other Satellites

- Phases of the moon result from the changes in

the positions of the moon, Earth, and sun.

An artist depicts a portion of the night sky as

shown. Is this view possible?

- Yes
- No

No. There are no stars between the Earth and the

moon. (Maybe blinking lights of a passing jet?)

Extensions to Newtons Theory of Gravity

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.

Extensions to Newtons Theory of Gravity

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. - Einsteins General Theory of Relativity

predicts the moon's orbit to within the accuracy

of the laser ranging measurements.

Extensions to Newtons Theory of Gravity

- Einsteins Special Theory of Relativity
- Based on how EM works, Einstein postulated
- The laws of physics are the same for all

observers in uniform motion relative to one

another (Galileos 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.

Extensions to Newtons Theory of Gravity

- General Theory of Relativity
- Einsteins 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

Extensions to Newtons Theory of Gravity

Current Problems in Gravity Is Einsteins

General Theory of Relativity the final word?

(Maybe not) Do gravitational waves exist? (Yes,

maybe) Are G and ? 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

dont really understand how to interpret the

theory.) Is there a 5th force in nature?

USU Perspective on Gravity

Work today at USU Larsen, Torre and Wheeler

Harts 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)

Simmons 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)

Physics of Technology PHYS 1800

- Lecture 11
- Circular Motion and Gravitational Force

Comments on the Nature of Scientific Theories

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.

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

Physics of Technology

- Next Lab/Demo Circular Motion Gravity
- Energy Oscillations
- Thursday 130-245
- ESLC 53
- Ch 5
- Next Class Wednesday 1030-1120
- BUS 318 room
- Read Ch 5