Today: Brownian motion, energy, kinds of energy, conservation of energy

http://www.flickr.com/photos/davewilliams/ “Wind farm”

Quizzes

Quiz #1 posted tonight, due before class Thursday.

You can take the quizzes more than once One recommended strategy:

1. Do all assignments / readings / problems related to quiz.

2. Take the quiz…note which ones were tricky3. Study those topics, go to office hours, surf the web, re-

read book, etc.4. Re-take quiz after studying5. Before exam – You can take all the quizzes again as

review

Answer to Question 12, Chapter 11

"Why is Brownian motion apparent only for microscopic particles?“

Melody: “…as the size of the particles increases, the speed at which the particles move decreases because they have a larger mass. This was clearly demonstrated in both experiments we did in class. When we added larger plastic balls to the container, they moved slower than the smaller balls. "

Astara: Atoms are always bouncing around, and pushing the tiny particles that surround them. Any momentum that is gained by one of these particles, however, is quickly reversed as it gets bumped back in the opposite direction - Giving the particle a net displacement very near to zero. To our eyes, the particles appear to not be moving because their movement is so little (at a life size view).

There were MANY excellent student answers! I will collect these and post them on WebCT

Answer to Question 12, Chapter 11

"Why is Brownian motion apparent only for microscopic particles?“

Author’s answer (confusing):Brownian motion is apparent only for microscopic particles because of their small mass. Against a large particle, the random bumps exert nearly steady forces on each side that average to zero, but for a small particle there are moments when appreciably more hits occur on one side than the other, producing motion visible in a microscope.

I say: A decent answer, but incomplete

A) The larger radius particles will undergo more Brownian motion

B) The smaller radius particles will undergo more Brownian motion

C)The amount of Brownian motion is unaffected by the radius

Clicker QuestionSay we have a mixture of

two tiny plastic microspheres in watermade of the same materialone kind has a larger radius than the other.

Which is true?

Answer to Question 12, Chapter 11

Author’s answer (confusing):Brownian motion is apparent only for microscopic particles because of their small mass. Against a large particle, the random bumps exert nearly steady forces on each side that average to zero, but for a small particle there are moments when appreciably more hits occur on one side than the other, producing motion visible in a microscope.

My answer (probably confusing also):A larger particle has more mass and requires more force to accelerate.

At the same time, a larger particle gets many more collisions with water molecules.

Inertia r3 (volume) Force r2 (surface area)

(note: because opposite sides almost cancel, it’s even less than this)

“Inertia is proportional to cube of radius”

“Force is proportional to square of radius”

As things get bigger, the volume beats the surface area

Play around with the Brownian

motion applet!

The “math” of Brownian motion

Amount of Brownian Motion Temperature

Particle radius Avogadro’s Number viscosity

(“is proportional to”)

Einstein’s formula in 1905:(Too complicated for us!)

Avogadro’s number

Amount of movement

Time interval

Gas constant

Temperature

viscosity

Particle radius

ArN

RT

t

x

3

2

This is the take home message for us:

A) As you increase the temperature, particles will undergo more Brownian motion

B) As you increase the temperature, particles will undergo less Brownian motion

C) Brownian motion only depends on the particle size, not temperature!!!

Clicker QuestionSay we are looking at Brownian motion of tiny plastic microspheres. First at room temperature, then we increase the temperature. Which is true?

A) As you increase the temperature, particles will undergo more Brownian motion

B) As you increase the temperature, particles will undergo less Brownian motion

C) Brownian motion only depends on the particle size, not temperature!!!

Clicker QuestionSay we are looking at Brownian motion of tiny plastic microspheres. First at room temperature, then we increase the temperature. Which is true?

Brownian motion simulation on the web

Tim’s: http://www.physics.uq.edu.au/people/mcintyre/applets/brownian/brownian.html

Scientists create simplified models that they can simulate on computersThis is a powerful way of gaining understanding of nature

http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/applet.html

Let’s try some experiments with this one: “Tim’s Brownian Motion Applet”

Take home messages for Brownian motion

Amount of Brownian Motion Temperature

Particle radius Avogadro’s Number viscosity

(“is proportional to”)

At room temperature, atoms have a lot of kinetic energy!What

?

Remember the (failed) molecular motion demo last week? What is transferred between the ball bearings when they

collide?

What is energy???

Let’s brainstorm on different kinds of energy

RadiationPotential energy

Solar energyHeat

KineticGravitational\

Convection energyElastic

ElectricalMechanical

NuclearThermal

Mass, chemical, dark

There is no in-a-nutshell definition of “energy”…But that’s not a big problem!

Simple definitions are very misleading:“Energy is the capacity to do work”True: some form of energy is required to do work

But some energy cannot be used for work (crackpots)

This is like saying:“A vegetable is a potato”

(http://home.pacifier.com/~ppenn/whatswrong.html)

We can know recognize something without being able to succinctly define it:

What is economic value? “Value is money?”

What is love? “Love is affection?”

“Nature gives us shapeless shapes: clouds and waves and

flame. But human expectation is that

love remains the same.”--Anyone know the source?

Clicker Question – Total Energy

Consider two baseballs (of identical material and mass) traveling in straight lines, with the same spin, at the same height above the ground.

One is traveling at 98 mph, the other at 101 mph.

Which one has more total energy?

a) Baseball @ 98 mphb) Baseball @ 101 mphc) Same…it only depends on the heightd) Impossible to determine

i.e., there is no difference except their speeds

Clicker Question – Total Energy

Consider two baseballs (of identical material and mass) traveling in straight lines, with the same spin, at the same height above the ground.

One is traveling at 98 mph, the other at 101 mph.

Which one has more total energy?

a) Baseball @ 98 mphb) Baseball @ 101 mphc) Same…it only depends on the heightd) Impossible to determine

What kind of energy does the 101 mph baseball have more

of?

Clicker Question – Total Energy 2

A one kilogram chunk of ordinary steel (iron alloy) is sitting next to a kilogram chunk of enriched uranium. Both are stationary. Which has more total energy?

a) kilogram of steelb) kilogram of enriched uraniumc) Same, they are both at rest and at the same

height.d) Impossible to determine.

Clicker Question – Total Energy 2

A one kilogram chunk of ordinary steel (iron alloy) is sitting next to a kilogram chunk of enriched uranium. Both are stationary. Which has more total energy?

a) kilogram of steelb) kilogram of enriched uraniumc) Same, they are both at rest and at the same

height.d) Impossible to determine.

What kind of energy does the uranium have more of?

This was supposed to be though-provoking

Exam questions will not be this ambiguous or tricky (hopefully!)

Kinetic and Potential Energy

KINETIC ENERGY

“Energy of Motion”

Potential Energy

“Energy of position”

Objects moving in straight line

Objects spinning

Random motion of molecules

Position of object in gravitational field

Chemical

Nuclear

Elastic

Dennis’ little blocks – Energy is in the bookkeeping (mathematics)

We know how to write down the equations for the many forms of energy…but unlike with Dennis, we have no blocks to look at

ALL calculations of energy have the same “units”:Joules (J)Calories (calories or Calories (kilocalories))kilowatt-hourskg m2 / s2 ; Newton-meters; N-m

Work (transfer of “macroscopic” mechanical energy) and Heat (transfer of “internal energy”) have units of energy

For now, don’t worry about all the different formulas for energy.

But, notice that many are not too complicated!

K.E. = ½ mv2

P.E = mgh

Kinetic energy of object = ½ mass * speed squared

Gravitational potential energy = mass * gravitational acceleration * height

E = mc2 Mass Energy = mass * speed of light squared

P.E = ½ k x2 Energy in a spring = ½ spring constant * stretch squared

E = h f Photon (light) energy = constant * frequency

Nose basher

Conservation of Energy

“Energy can flow from one form to another, but cannot be created or destroyed”

For example:

Macroscopic Kinetic Energy Potential Energy

Microscopic K.E. Heat flow

This concept is more amazing the

more you think about it

What about conservation of

energy related to body weight / weight

loss?

Rattleback—Flow of energy from one form to another

The behavior can be complicated and fun!

ENERGY – Take home messages

Energy is hard to define!

Energy flows from one form to anotherAlways has the same mathematical “units”

Potential Energy & Kinetic Energy—important for waves

And…Energy is absolutely

conserved!