-www.mrjoncollins.spaces.live.com videos Galileo Gravity my explanation of material.

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14 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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These notes are to supplement the reading of Chapter two pages 38
-
69 in the Holt Text Physics Text Book by
Serway and Faughn.


Additionally the following are helpful.

-


The moving man demo at
http://phet.colorado.edu/simulations/sims.php?sim=The_Moving_Man




-


The kinematics web demos at
http://www.mrwaynesclass.com/teacher/index.html#kinematics




-


Graph that motion at
http://www.physicsclassroom.com/shwave/graphthat.cfm

use in conjunction
with the worksheet at
http://www.physicsclassroom.com/shwave/gtmintro.cfm




-


Good description of most topics here
http://www.physicsclassroom.com/Class/1DKin
/




-

Click on 1
-
D kinematics for helpful flash videos
http://www.physicsclassroom.com/mmedia/



-

You tube on special Relativity
http://www.youtube.com/watch?v=Ux
-
YD8Ky1hs


http://www.youtube.com/watch?v=6rl3Z9yCTn8


http://www.youtube.com/watch?v=WgsKlSnUO0k


http://www.youtube.com/watch?v=W6o_
-
yTa168



-


Vel and accel explained
http://www.youtube.com/watch?v=ZrRSc3aKABk


Note they are using “s” for
displacement, this is not done much anymore, most people use” d” or “x”


-


www.mrjoncollins.spaces.live.com

videos Galileo Gravity my explanation of material.


VA SOL’s covered:

PH.2

The student will
investigate and understand how to analyze and interpret data. Key concepts include

a)

a description of a physical problem is translated into a mathematical statement in order to find a
solution;

b)

relationships between physical quantities are determined using t
he shape of a curve passing through
experimentally obtained data;

c)

the slope of a linear relationship is calculated and includes appropriate units;

d)

interpolated, extrapolated, and analyzed trends are used to make predictions; and

e)

analysis of systems employs

vector quantities utilizing trigonometric and graphical methods.

PH.3

The student will investigate and understand how to demonstrate scientific reasoning and logic. Key
concepts include

a)

analysis of scientific sources to develop and refine research hypothe
ses;

b)

analysis of how science explains and predicts relationships;

c)

evaluation of evidence for scientific theories;

d)

examination of how new discoveries result in modification of existing theories or establishment of
new paradigms; and

e)

construction and defense

of a scientific viewpoint (the nature of science).


PH.4

The student will investigate and understand how applications of physics affect the world. Key concepts
include

a)

examples from the real world; and


PH.5

The student will investigate and understand the

interrelationships among mass, distance, force, and time
through mathematical and experimental processes. Key concepts include

a)


linear motion;

PH.14

The student will investigate and understand that extremely large and extremely small quantities are not
necessarily described by the same laws as those studied in Newtonian physics. Key concepts include

e)


relativity;

1

D
imensional Motion


Displacement

( please note the text book uses an “x” for displacement, I will use a “d”)

-


Displaceme
nt is the net distance
travelled along with the direction, calculated
by subtracting the final position from the initial.



d=x
f
-
x
i

-

Because it has both magnitude and direction it is called a vector.

-


Often this is the same as the distance traveled
, but it does not have to be.

-


E
xamples (Imagine a car driving on a number line.)

o

A car starts at position 0m, then travels to position 100m. In this case
both the distance and displacement are 100m.

o

A car starts at position 100m and travels to position 0m. In this case the
distance is

100m but the displacement is
-
100m because the final
position (0m)


initial position (100m) =
-
100m

o

A car starts at 0m travels to 100m and then back to 0m. In this case the
distance is 200m but the displacement is 0m
-

0m= 0m


Velocity

-

velocity is a s
peed w/ a direction.

-

c
alled a vector (+ forward/up,
-

backward/down)

-

v=d/t velocity= displacement/ time

-

SI unit: m/s

-

v = (v
f

+v
i
)/2

-

both are avg. vel., shown w/ bar


Acceleration

-


Is a change in velocity

-

a=

v/

t



a= (v
f

-
v
i
)/t

-



is the Greek letter “delta,” we use it to mean “a change in”

-

SI unit is the m/s
2


-

when your speedometer moves

you are accelerating

-

Also is a vector


Steps to solving a problem

-

Step 1 Read the entire question word for word without writing.

-

Step 2 Sketch

the diagram of what is happening.

-

Step 3 Make a list of all the given information include symbols and units.

-

Step 4 Identify what you are looking for and list it with a “?”

-

Step 5 Write down any equation that applies.

-

Step 6 Use the list to put numb
ers into the equation and solve.

-

Step 7 Write down your answer w/ units and circle it.

-

Step 8 Check to see if you answer is reasonable.


Example Problem

-

If a car is going 20m/s for 10s, how far will it travel?


V=20m/s





t=10s

d=?




-

Two types of graphs.



Position (Displacement) vs. time



The slope (rise/run) equals the velocity



Velocity vs. time



The slope (rise/run) equals the acceleration



Position VS. Time graphs
































Who is not moving? Who is moving

at a constant
velocity?

Who has the fastest instantaneous velocity?

Describe Carol’s motion.

What is Norman’s average velocity from 2
-
20s?





Velocity vs. time graphs


A horizontal line

on a velocity vs. time graph indicates
constant velocity, (or
moving at a constant speed.) The
higher the line is the faster the movment is. Here blue
is going faster than red. Both have a positve velocity
because they are above the x
-
axis. Green however is
below the x
-
axis, this means that the velocity is
negati
ve, or in other words the green movment is in the
oposite direction of the red and blue.










A slanted line on a velocity vs. time graph

indicates
constant acceleration.
The slope is the acceleration.
Therefore, the red line has a negative acceleration,
while the green and blue lines both have a positive
acceleration. When the red line crosses the x
-
axis it is
stopped and changing directions. The red line could be
the
graph of a ball that is rolled up a ramp, then rolls
back down.


















Which
people
stop
and when?

Who is most likely on a moving sidewalk?

Who is speeding up the whole time?

Describe Mike’s motion.

How fast is Holly going at 2s? . . . 15s?

What is Mary’s average acceleration from 2 seconds to 20 seconds?




Aristotle to Galileo notes.


Greek Culture was the most influential

-

other cultures had discoveries, but didn’t spread EX, China and
Mayans

-

good

roads, common language, good sail boats and trade routes lead to the
spreading of ideas from Greece.



Socrates
-

argued against Greek Gods in control.

-

was called “Gad fly”

-

influenced mostly kids

-

was put on trial for corruption of minors

put to death (p
oison)

-

Plato his best student was at the execution and wrote about it.


Plato


w/o Gods in control he looked for other ways things worked

-

truth was found in meditation and thinking

-

Allegory of the cave

-

Most of work was in philosophy, ethics, government, a
nd music but he did
come up with 4 elements.

-

Thought outer space was perfect unchangeable

all things orbit the earth.

-

Started academy lasted 200 years.


Aristotle
-

Plato’s students adopted his ideas, but added observation to thinking.

-

Very good in biology
-

first to dissect

dad was a doctor

-

Explained inductive (probable inferences
-

interpolation & extrapolation) and
deductive reasoning ( if this is true
-

what are consequences.
Einstein next
person to significantly use in science


-

Said 4 elements earth,
fire, water air,
-

were made of hot/cold, wet/dry. Had to
balance chem. Vol. Represented by a
3
, b
3
, a
2
b,ba
2

-

Everything had a natural place

-

When earth fell it returned to its natural place
at rest on the ground.

-

Things fell with constant velocity

-

Heavy
thing fell faster

-

Violent motion was any motion that was not natural
-

required a force.

-

Speed is proportional to the force for violent motion.

-

Made a fifth element, aether, (outer space) circular motion was natural

-

Outer space was believe to be perfect and

unchangeable.

-

school was lyceum

-

Taught Al the Great

For the next 2000 years Aristotle and the
Church where

the authority

Then came Galileo Galilei around 1600


Galileo
-

called father of science

-

started to do experimentation

-

father wanted to be a doctor


went to college and discovered math

-

figured out the pendulum by watching chandeliers in Church

-

greatly improved telescope (
although

he did not invent it) first to use it to look
at sky.

-

First to see mountains on moon, sun spots, phases of Venus, and moons
of
Jupiter
-

called Galleon moons

-

Published in book (Latin)
Starry

Messenger

lead to problems

-

Moons of
Jupiter

showed that all does not orbit earth

-

Phases of
Venus

show it orbits the Sun

-

Sun spots


outer space is change able

-

Mountains on moon


not pe
rfect sphere

-

Wrote a second book in Italian “Discourse on two Chief World Systems”
-

simplicito, sogredo, and this book made church and Aristotle look foolish

-

Was called in to be inquisition and threaten with torture.

-

Forced to recant his beliefs
and placed on house arrest for the rest of his life
(9yrs)

-

Altho didn’t agree with church view still believed in God
-

two daughters were
nuns.

-

Wrote third book while on house arrest 2 new sciences (continued to work in
house,) came up with formulas

-

Ramp wi
th even spaced marks, ball rolls odd number same
amount of time, used water clock to measure time.

-

Total distance to then is time squared

-

d=v
I
t+½ at
2

v
f

=v
I

+ at v
f
2
=v
i
2

+2ad




-

assumes no wind friction

-

Thumb is preserved in Museum of the

History of Science

-

Pope John Paul II apologized for mistake in 1990


-

If gravity is constant acell what is the number. Galileo used increasing slopes
to predict 90


(which he could not measure)

-

g =
-
9.8m/s
2

on earth (32ft/s
2
)

-

slightly higher in death val
ley, slightly less on mountains.




Because the acceleration due to gravity is constant, the velocity that an object is
tossed up with will be the same velocity that the object has when it falls back to the
same height that it was tossed up from, only with t
he opposite sign of course.



v (up) =
-
v(down) therefore bullets shot up !!! bad!!!



Example problem


A football quarterback intentionally grounds the ball by throwing it straight
downward with a velocity of
-
12m/s. What velocity will the football have
just before it
hits the ground 1.8m below?




List



V
i
=
-
12m/s


d=
-
1.8m


a=
-
9.8 m/s
2

v
f
=?





Formula



v
f
2
=v
i
2

+ 2ad


v
f
2
= (
-
12m/s)
2

+ 2 (
-
9.8m/s
2
) (
-
1.8m)





v
f

=

(

)



(




)
(




)


v
f
=

-
13.4m/s



Note: The
displacement is negative because the ball moved in the negative direction. The software
would not allow me to put the units under the radical (square root) properly, so I left them off. Finally,
Mathematically when you take a square root, you get two ans
wers (one positive and one negative) it is
up the person to choose the proper one. Here we chose negative because the ball would be going
down.


Special Relativity



-


In 1905 Albert Einstein wrote three papers, two of which earned him Nobel Prizes (one
for
Brownian motion, the other for the photoelectric effect.) It was
,

however the other paper
(the one on special relativity) that is best remembered and the focus of this section.

-

In Einstein’s Special Relativity paper he borrowed from Lorentz, Michelson

and Morley,
Maxwell

and others. He put together the work they had done and explained it in a simple
way that encompassed many theories and experiments of others.

-

Instead of performing experiments as evidence for his theory, he instead used deductive
rea
soning, where he stated things he felt were true and then explains what the consequences
are if they are true. The statements he started with are called postulates.

-

1
st

Postulate (Collins Paraphrased)


The Laws of Physics’ are the same and work
for every
body, no matter where you happen to be standing or how fast you are
moving.

-

2
nd

Postulate (Collins Paraphrased)


The speed of light is the same for everybody
,
no matter where you happen to be standing or how fast you are moving.


-


Thought experiment:
Ein
stein

said imagine a person on train that is moving at a constant
velocity. If were to bounce a beam of light from the floor to the ceiling and back to the
floor of the train. The light from his perspective would have travelled twice the height of
the tr
ain. However, for a person who is stationary watching this from the side of the train
they would see the light move at a diagonal, therefore travelling a greater distance. Since
the speed of light is the same for both people, the
length

of object in mot
ion must be shorter
than at rest. Furthermore, since d=vt and the speed of light is constant, if the length is
different the time it takes must also be different.


-

Deductions
: For slow speeds, the difference is too small to notice, but as speeds approa
ch
the speed of light the difference get larger.















-

Time Dilation


Time advances slower for an object in motion relative to objects at rest.
For, example (twin paradox) two brothers, who are twins are the same age. One brother
boards a ship
and travels at speeds close to the speed of light, relative to the brother that
stayed home. When the travelling brother returns, he has aged much less than the twin
who did not travel.





-

Where

-

t is the time measured by the stationary observer

-

t’ is the time measured while in motion

-


is the relative velocity between the observer and the moving object,

-


is the speed of light,




-

Length Contraction

-

The length of objects gets shorter relative to their stationary
length.



-


W
here

-

L is the
proper length (the length of the object in its rest frame),

-

L' is the length observed by an observer in relative motion with respect to the object,

-


is the relative velocity between the observer and the moving object,

-


is the speed of light,