Mechanics Semester Review

Here is a list of topics for our final, the second week back from winter break:

Basics:
Vector algebra - vector addition, multiplication (dot and cross products)
Derivatives - finding them; what does it mean graphically; instantaneous values
Define v = dx/dt; a = dv/dt
Antiderivatives - finding them; what does it mean graphically
Motion graphs

Kinematics:
Constant acceleration equations, how to use them in a variety of problems
Free fall
Relative motion (e.g. boat going across a river)
Projectiles

Newton's laws:
Know them by number; conceptually what do they mean? Examples.
Finding resultant forces (vector addition)
Equilibrium, balancing forces in multiple dimensions
Applications of Fnet = ma, all types
Tension, friction, on inclines (gravity triangle), springs
Systems problems, such as multiple blocks tied together
Circular motion, how to set up mv^2/R in problems; horizontal vs vertical problems
NON-constant forces and accelerations
Air friction, f = -kv; derivation of v(t); chain rule
Gravity - Newton's law of universal gravitation; Einstein's thoughts on warped space-time
Orbital motion - orbital speed, Kepler's laws; Binary orbits

Energy:
Conservation law
Different types, conversions of energy
Work redefined as an integral; work is the amount of energy transferred between objects
Using work and conservation to solve a variety of problems, especially with speeds and non-constant forces
Potential energies (gravity, springs)
How to do gravity the right way with energy, U = -GMm/r; what does - sign mean?
Potential wells - U-x graph vs F-x graph; positive force vs negative force
Gradient, F = - dU/dx; what this means
Escape velocity; Schwarzschild radius
Power
Special relativity implications, Einstein's energy equation

Resources:
Videos on most of the topics above. For practice multiple choice, the SAT II site has notes, sample questions, and explanations on all these topics. There is a Learn AP Physics C site, with practice questions. We have our AP Exams folder (but you must be logged in only on your eths202.org account).  Note there is a multiple choice folder, with hundreds of practice questions. There are review sets in each of our unit folders. Read up on any topic and check out dozens of worked examples in Chapter 1-7, which is what we have covered so far. You have your old quizzams and solutions, homework sets, and labs.

EM Semester Review

The main topics are listed below. Keep in mind this is covered in chapters 21-26. There are numerous worked examples and odd problems we can try, along with chapter review pages. There are videos on just about every topic. There are AP Free Response Problems and Solutions  (including a multiple choice folder); be sure to be logged in with your eths202 account for access. There are review sets in each topic folder on the school web site. There are practice problems and notes on the SAT II website. There is practice materials at the Learn AP Physics C site. Get into a study group. Come in for AM Support or lunch periods. Review old quizzams, HW sets. Review the essential questions you've received for each unit, and the objectives file. Review the equation sheet. Lab questions and concepts are fair game. 

Topics

Electrostatics

• Properties of charge
• How do you charge objects? Induction vs conduction

• E-field and Potential for point charges

• F = qE and U = qV
• Work done when charges move around

• Energy conservation to find speeds
• Projectile example

• Equipotentials

• Non-gauss examples, integrals
• Sticks, rings, partial rings

Gauss's Law

• What does it define?

• Why does only 'charge inside' matter?

• Why only the three shapes that we use?

• Thin shells
• Materials: what are physical differences that make them have different properties? Band theory. 

• Conductors

• Nonconductors, uniform density

• Nonconudctors, NON-uniform density

• Combinations of materials in layers

• Finding electric potential for layers

Circuits

• Conceptually how do we setup currents in wires?

• What is resistance? What does it depend on?

• What is current? How would you find charge?

• What is power? How would you find heat energy from resistors?

• Series vs parallel
• Resistance
• Capacitance
• Conceptually what is same, different
• How to find current in each resistor

• Ohm's law, Kirchhoff's 2 rules

• Multi-loop

• Capacitor only circuits
• How to find charge on each

• RC circuits, series
• Conceptually what is happening?
• Can you derive q(t), i(t)?
• Charging
• Discharging

Videos for Dec. 14

Periods 1-2, 5-6, 8-9:

Check out a video on dielectric materials in capacitors. This will outline how to do the homework set for today. Then, check out the analysis/derivation of a RC circuit when the capacitor is charging. After these, the classes can check the solutions to the last test (in our Basic Circuits folder). You can then try to complete the HW set on dielectrics before leaving.


Period 3:

Check out a video on the conservation of momentum, and take detailed notes on this example. You'll need it to try a couple initial problems.
After the video, please get your energy quiz, as well as the solutions. You and 1-2 partners can go over these. Where relevant, do corrections on your quiz, and keep track of anything that does not make sense to you. When you get through the quiz, take a look at the momentum packet, and try questions #1, 4, and 5 on pages 2 and 3. Use your notes from videos, as well as the front page notes, and talk through these with partners. I will collect and check these tomorrow.

Try the Moody's December Math Challenge: Resistor circuits

Moody's, the huge financial firm in NYC, also sponsors the Mega Math Challenge for math modeling. In addition, they put out math challenges each month. The December challenge is one any one of the seniors should be able to do, fairly easily, since they are series and parallel resistor circuits! If you want to spend a few minutes and do these resistor circuits, you can get your solutions to DocV before winter break, and I can send them in. If you have correct solutions, you are eligible for a name drawing for $25 Visa gift cards.

For New Units

Seniors, periods 1-2, 5-6, 8-9:

We will be starting capacitors and how these behave in circuits. Turns out plain capacitor circuits will hopefully look a lot like resistor circuits, as far as how we analyze them. We will still have Kirchhoff's rules. Ohm's law for capacitors will be Q = CV, since this is what capacitors do - they store charge in circuits.

Watch and take detailed notes on two videos.
Take a look at a video for finding total capacitance in series and parallel. The new unit that measures capacitance is called a farad, F, after Michael Faraday.
Then, check out a video on how to find stored charge on capacitors (this is like finding currents flowing through resistors). Note that capacitors in series have the same charge, and in parallel the same voltage.


Period 3:
We are starting momentum. This is a word you have all heard, but now we will be defining it and using it to help us understand collisions of all types.

Watch and take notes on two videos. One is an introduction to momentum.  The second is defining what impulse, or a change in momentum, is for objects when there is a collision.

Relativity and Energy: How E = mc^2 leads to numerous other features of Nature!

In my classes, when we are going through the usual classical physics portions of energy and work, I also throw in a couple days of modern theories of energy, including special relativity and some basic quantum mechanical ideas. After we see one way of deriving E = mc^2, and Einstein's energy equation in special relativity, I want to make a point that this is a truly large breakthrough in our thinking of the physical world. I like to use E = mc^2 as a stepping stone to better understand the following:

The discovery of E = mc2 basically sets up the discovery of quantum  mechanics, and the weirdness we see with particles.

            Energy = matter, is effectively what this tells us.

These are two forms of the same stuff, like steam (energy) and ice (matter)  are two forms of the same H2O molecule.

     Whatever properties energy (waves) can have, then matter (particles)  has those properties.

     Whatever properties matter (particles) can have, then energy (waves)  has those properties.

Examples:

If waves have wavelengths, then so must particles

If particles have momentum, then so must waves (light/photons)

If matter is affected by gravity, then so must waves (light/photons)

This equation also re-defines conservation of mass and conservation of energy. In nuclear reactions, conservation of mass is violated, since products weigh less than reactants.

         Conservation of mass-energy is now more correct!

• This equation changed the course of history, as we entered the age of nuclear power and weapons.

• It allows us to understand how stars form and 'burn,' and their life cycles

• It allows us to understand how heavier elements are formed through thermonuclear fusion (nucleosynthesis; we are made of star dust!!)

• It allows us to understand how the universe can form from a burst of pure energy (Big Bang), as we have phase transitions from energy to matter or vice versa.

• The unification of space and time allows us to understand what causes gravity (warps in space-time)

• It allows us to understand how to make particle accelerators and explore the basic question, "What are we made of?"
• It led to the prediction of antimatter 

• It allows us to think in terms of multiple dimensions, giving rise to things like string theories

• It allows us to begin to understand radioactive processes, and nuclear physics

• The theory of photons allowed Einstein to understand photoelectricity (solar energy), for which he won the Nobel Prize

• This also helped lead to his discovery of 'stimulated emission,' the process that makes lasers possible

• It predicts 'matter waves' or the wave-particle duality, which is the heart and soul of quantum mechanics

Links to energy videos

Here are some quick links for our energy unit.

Energy conservation and finding speeds
Gravitational energy 'the right' way
Potential wells
Finding tension for a pendulum (need energy to do so)
Springs and energy 
Special relativity: one way to get the E = mc^2 result
Special relativity: energy equation to particle-wave duality

And if interested, how a nuclear power plant works. This video does a good job of showing the gist of the different parts of the plant facility.