Todaybogner/isp209s2010/lectures/l2.pdf · ISP209s10 Lecture 2 -1-Today •Announcements: –HW#1...

ISP209s10 Lecture 2 -1-

Today

• Announcements:– HW#1 is due Wednesday by 8:00 am– The first LONCAPA extra credit is due 1/27 by 8:00

am.– Register your clickers in LON-CAPA

• Review from last time (time dilation, etc.)• Units• Scalars, Vectors and Tensors• Motion and Newton’s Law of Inertia


Overrides and Add-Drops• Override period expired on Friday 1/15

– The final overrides I granted were on Thursday. I could notgive anymore since we are technically over the room capacity.

– Now the only option is to get an add/drop slip from the ISPoffice and ask me to sign it.

– HOWEVER, I cannot sign this until the enrollment goes downbelow the room capacity. Check back with me before class onThursday.

– If you are eventually able to get me to sign your add slip, it isyour responsibility to do extra credits etc. to compensate for

the missed HW #1.– If you want to DROP the course, you can still do this online.


Physics Help Room Hours

• TA = Steven Barthelemy

Monday: 1pm - 3pmTuesday: 4pm - 6pmFriday: 1pm-2pm


Review: Einstein’s Postulates

1) Principle of Relativity: Laws of Nature are the samein all non-accelerated (aka “inertial”) reference frames.

2) Principle of the constancy of the Speed of Light:The speed of light in empty space is the same for allnon-accelerated (aka “inertial”) reference frames:

c = 300,000 km/s

From these 2 postulates and nothing more, Einstein’s Special Theoryof Relativity follows


Review: Relative Motion with Mort and Velma

• Velma rides a train that is going 50 m/s relative to Mort• Velma throws a baseball at a speed 20 m/s (relative to

herself ) towards the front of the train

From Mort’s perspective, how fastis the baseball going?

Ans: 50 + 20 = 70 m/s

This is common sense. The velocitiesof the train and ball add. We call it“Galilean” or “Newtonian” relativity.


Review: Constancy of Lightspeed “c”

You might expect Mort measures the speed of Velma’s light beam to be c + .25c = 1.25c. This is NOT the case. They both get c= 300,000 km/s.

c = 300,000 km/s !!!


Review: Relativity of Time

• Einstein’s simple thought experiment with “light clocks”implied some mind-blowing consequences about Time:– Moving clocks run slow (I.e., Time slows down)– Time is relative according to your reference frame

2

2

201

1

1

1

!""

#=

$$

%

&

''

(

)#

==

c

v

tt

time that elapseson your watch time that elapses

on the moving watch

“Time-Dilation”


Review: Confirmation of Time Dilation

• Airplane experiment: A high-precision clock is takenon a long jet ride that circles the Earth several times. Anidentical clock stays on the ground. When the 2 are comparedafter the trip, the one that was on the jet is behind (I.e., slower)than the one on the ground.

• Lifetime of muons: Muons “live” for a characteristic time(aka lifetime) before they decay into something else (electron +neutrino). This lifetime is longer if the muons are moving in afast-moving beam than if they are just sitting around next toyou.

+ many other experiments. Time REALLY does slow down.


Time Travel• Moving at high speed is a way to travel into the future. (E.g.,

the mom who returns younger than her son after taking a long,fast rocket trip while he stayed on Earth.)

• We can look into the past because, although the speed of lightis fast, distances in space are large.– We see the Sun as it was 8 minutes ago– We see nearby stars as they were 4-10 years ago– The distance light travels in one year is called a light-year.– We see nearby galaxies as they were 1 million years ago– Looking out at the stars is like looking back in time.

• We can move forward in time. Can we move backward intime?


Units

• Physical quantities always have a unit attached;for example, the length of the table is NOT 2, it is2 meters.

• Some quantities are a combination of units; forexample 1 liter = 1000 cm3 (LONCAPA 1000cm^3 or 1.0E3 cm^3 or 1.0E-3 m^3)

• How many liters are in a gallon?

1 US gallon = 3.7854118 liters


LONCAPA Units• We will use the System International (SI) system of units.

Link• Common units

– Kilogram (mass) kg– Meter (length) m– Second (time) s– Newton (force) N – same as kg*m/s^2– Joule (energy) J – same as N*m– Moles (Amount of substance) - mol

• The LONCAPA system has help


An example of unit conversion

231012.1

2

100

00.12.112.11

00.1100

22 m

cm

mcmcm

mcm

!"="=

=

####

$

%

&&&&

'

(

This means there are:cm 100.

m 1.00

L

L

• Area of a square = L2

• you measure L = 11.2 cm• you want the the area in m2 instead of cm2

Suppose…


Prefixes

109

106

103

110-1

10-2

10-3

10-6

10-9

value

gigaGMegaMkilok

decidcenticmillimmicroµ

nanonnameprefix

Example:

GyMyMyGyMy

yMy

3

6

100.20.21000

10.2

100.20.2

!"="=

"=


Scalars, Vectors, Tensors

• Physical quantities can have characteristics.• Scalars – a quantity without direction

– such as the mass of a object– the magnitude of a vector

• Vectors – a quantity that has a length anddirection

• Tensors – generalized versions of vectors inmultiple directions– The number of dimension in a tensor is called the rank– Rank 0 tensor is a scalar– Rank 1 tensor is a vector


Examples of Scalars

• mass, electric charge• speed (magnitude of velocity)• amount of money in my wallet• the volume of a container (gallons or liters)


Examples of Vectors

• Position – 2 miles East of Spartan Stadium• Velocity – 60 mph toward Detroit• Acceleration – 9.8 m/s2 down• Note: velocity and acceleration can have

opposite directions. Example: a ball movingupward.


Vectors

Representation Addition

1 meter EastA+B

A is the same vectorno matter where itsits.

(Click here for a demo)


Motion

• Position – location relative to the center of acoordinate system (0,0). 2 miles NE

• Velocity – rate of change of position. This meanschanging direction as well.

• Acceleration – rate of change of velocity. If eitherthe magnitude of the velocity or its direction arechanging, the object is accelerating.


Velocity – Rate of change of position

4.00.5

3.01.0

2.01.0

1.00.0

0.0-1.0

Time (s)Position(m)

in time change

positionin change=v

r

Velocity is the rate of changeof position

Speed is the magnitude of thevelocity

sm

ss

mm

s

0.10.10.2

0.00.1

tt

xx2s) and 1(between

initialfinal

initialfinal

=!

!

!

!=


Back to Motion

Example: Motion of a car as a function of time.

Velocity is the rate of change of position: 12

12

tt

xxv

!

!=

rrr


Calculation of Motion

What is the average speed at 2.5 min?

h

miles

h

milesmilesmiles

tt

xxv

if

if6.33

min60

min56.0

min8.1min7.2

25.075.0=!=

"

"=

"

"=

We get 0.60 miles/min = 33.6 mph from the velocity graph.


Tensors (tensor fields)

• Example: Curvature of space-time:Riemann curvature tensor

One number is not sufficient todescribe each point in space.

!µR

Tensors are objects that have more than one value at eachpoint in space.

In this example, there are 16 numbers at each point in space!


Example 2: Stress Tensor

• Stress is defined asthe force per unitarea.

• In a solid object eachpoint has three valuesof stress (up-down,left-right, forward-backward)

• The stress tensordescribes the stress atall points in an object http://en.wikipedia.org/wiki/Image:Stress_tensor.png


• Aristotle distinguished three kinds of motion

• Natural motion: falling objects and liquids, risingair and flames

• Violent motion: needing a constant push or pull tocontinue

• Celestial motion: motion of the moon, planets, sun,and stars

Aristotle’s “Common Sense” Theory of Motion

We saw last lecture that our “common sense” or intuition canbe totally wrong…


Now, throw a ball across the room. Once it leaves yourhand, what keeps it moving? Aristotle says there mustbe a constant force to keep it in motion.

Problems with Aristotle’s Theory


Galileo’s thought experiment: Let a ball roll down an incline; itwill speed up. Let it roll up the incline; it will slow down. Inbetween, on a perfectly flat surface with no friction, the ball willkeep rolling at a constant speed forever.

Galileo’s Thought Experiment


Galileo’s method:• Experimentation, to test a specific hypothesis

-E.g., Aristotle’s theory of falling objects

• Idealization, to eliminate side effects that may mislead-E.g., air resistance and friction

• Consider only one question at a time- E.g. speed of falling objects of different masses

• Quantitative methods: precise measurement- E.g., timing the fall of different objects from a tower

Galileo and the Scientific Method


• Imagine we could turn off air resistance, friction, andgravity. How would things move?

• Descartes had the answer (which Newton took as his firstprinciple of motion):

The Law of Inertia: A body that is subject to no externalinfluences (also called external forces) will stay at rest ifit was at rest to begin with and will keep moving if it wasmoving to begin with; in the latter case, its motion will bein a straight line at an unchanging speed. In other words,all bodies have inertia.

The Law of Inertia


• For example, if you are driving a car on an icyroad – a VERY icy road – and try to stop or turn,you will find that your car continues to go in astraight line, as there is little friction.

• You can also watch videos of astronauts – thingswill float around until somebody grabs them, orthey run into the wall.

The Law of Inertia


• The law of inertia tells us that an undisturbedobject will keep moving with a constant velocity.

• If an object’s velocity is changing, it isaccelerating. Acceleration is the rate of change ofvelocity:

acceleration = (change in velocity)/time

Acceleration and the Law of Inertia


• Falling objects accelerate as they fall.

• How do we know this? Hold your book abovethe floor and let it drop.

• What is its speed right when you let it go?(Don’t throw it!) What is its speed when it hitsthe floor?

Falling


• This diagram shows an objectfalling.

•Note that both its distance and itsvelocity are increasing.

•From one second to the next, thedistance traveled increases, but thechange in velocity is the same.

Falling


• We see that the speed is proportional to the time –10 m/s at 1 s, 20 m/s at 2 s, and so forth.• What about the distance? Clearly it is notproportional to the time.

• However, if we look at the pattern of how thedistance changes from second to second, we can seethat the distance is proportional to the square of thetime.

Falling


• The object in the diagram is changing its speedat a rate of 10 m/s per second. Therefore, itsacceleration is 10 m/s2.

• This is (approximately) the acceleration due togravity anywhere on the Earth.

• It does NOT depend on the mass, size, or shapeof the object. Aristotle was wrong.

Falling

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