NOTES FROM PffP MID-TERM REVIEW SESSION 2/21/09

Chapter 1

1. There are many ways to store energy for future consumption

l batteries

l Explosives (TNT)

l chocolate chip cookies, butter (food)

l fossil fuels (coal < gasoline < natural gas)

l hydrogen

l moving objects (depends how fast/ how heavy - smart rocks/brilliant pebbles)

l uranium

* Energy = the ability to do work = force applied over a distance

2. There are many forms that energy can take, but all are measured in the same units (Joules, Calories, Kilowatt hours)

l kinetic (motion)

l gravitational potential (height)

l mechanical (work)

l electrical (lightbulb, circuit)

l thermal (heat)

l chemical (bonds between molecules)

l Nuclear (bonds between atomic nucleii)

Formula for Kinetic Energy: E = ½ mv²

3. Different storage methods have different amounts of energy per gram ("energy density"). It is also important to remember that not all methods for storing energy cost the same.

A. list from I. is roughly in order by energy density

B. COST: coal < natural gas < gasoline < electricity < car battery < computer battery << AAA battery.

4. Energy is conserved when being transformed from one form to another – it is never created or used up. Think of the bowling ball demo. What other examples can you come up with?

5. Power is the rate at which energy is used and is measured in mainly in Watts. Power = Energy/time

- light bulb brightness depends on power, but isn't the same thing

- home lighting = 1 horse(power) = 1kW

- humans can generate 1hp briefly, 1/7 hp sustained

- 1 can of coke = 1/2 hr of vigorous exercise

6. Pros/Cons of gasoline, hybrid, hydrogen fuel cell, solar powered cars

	Gasoline	Hybrid	Hydrogen Fuel cell	Solar Power
Pros	high energy density, convenient to transport & store, no residue from burning, was relatively cheap	allows gas engine to operate more efficiently, uses energy from braking	even more energy density than gasoline (3x more energy /gram) waste = water	renewable source
Cons	expensive compared to coal, contributes to atmospheric CO2	batteries are expensive to replace ($100 / lb)	dangerous to store, difficult to transport (3x less energy per gallon) takes up lots of space, "made" not mined.	not enough space on car rooftop to generate 50-400 hp, only available during day, solar cells are expensive.
best use	cars (then)	cars (now)	bus, trucks, airplanes	boats, planes? power plants*

*Other forms of generating electricity: WIND, COAL, NATURAL GAS

Chapter 2

I. Heat is the average kinetic energy of atoms or molecules in a substance

A. Heat energy = random motion of atoms.

B. Brownian motion was the first proof of the atom's existence.

C. The speed of molecules in air = speed of sound ~ 1000 ft/s

Remember: speed of light = 1ft/computer cycle (ns)

D. Hiss/snow on radio/TV is random electron movement

E. When energy of non-random motion is turned into heat, the energy of the molecules is going from ordered to disordered (Columbia Space shuttle) (Mach rule: T = 300M^2)

II. Temperature is a way of measuring the random KE of molecules

A. Remember: Lighter molecules move faster than heavier ones as the same temp.

B. 3 different scales of temperature - Celsius, Fahrenheit, Kelvin.

Remember: 1 deg. C ~ 2 deg. F

III. 0th Law of Thermodynamics

A. Objects in thermal contact will eventually come to the same temperature (ex. hydrogen, cold death of the universe)

IV. Thermal expansion happens differently in different materials

A. Cooling contracts, heating expands, Water (at freezing) is the only exception

Remember: 1C rise in temp makes things expand between 1/1000 and 1/100,000

B. Examples: thermometer, levees, tight lids, shattering glass, rise in sea level

Remember: predicted sea level rise 6in - 3ft

V. Thermal expansion in air gives us air pressure, air is a poor conductor

A. P = constant x Temperature

B. examples: hot air balloons, hurricanes, airbags, leidenfrost.

VI. Heat can be used as a source of energy (in order to do useful things)

A. Engines/ explosions

1. All engines are inefficient (Gas 25%, Coal 33%, Electricity 90-100%)

2. Greater temperature difference yields greater efficiency (VW Bug).

B. Refrigerators / Heat pumps

1. They're the reverse of an engine - they use mechanical energy to create a temperature difference. (They expand & cool a gas, which can then cool other things, or take heat from cool air and pump it elsewhere).

2. Running a heat pump is more effective (NOT efficient) than burning fuel.

VII. Heat flows by conduction, convection, and radiation

A. Different materials conduct heat at different rates - conductors vs. insulators

VIII. The Three Laws of Thermodynamics:

0) Objects in contact reach the same temperature

1) Energy is Conserved

2) You can't extract heat energy without a temperature difference / entropy will always increase

3) Nothing can reach absolute zero (where entropy = 0)

Chapter 3

Ben Geller

February, 2009

U.C. Berkeley – Physics C10

Chapter 3 Review Notes: Force, Space and Gravity

The role of forces in classical (pre-20th century) physics is determined entirely by 3 very simple laws developed by Isaac Newton (this is what makes physics what it is: huge numbers of phenomena are explained with a small set of simple laws). Newton’s 1st Law states that objects will move in a straight line at a constant speed unless acted on by an external force. We live in a world with lots of friction, so this first law is less obvious than it would otherwise be. If you push a book across your desk, it doesn’t keep moving at a constant speed. It stops! It stops not because Isaac Newton is wrong, but because it was indeed acted on by an external force: friction. Push that same book in outer space, where there is neither friction nor air resistance, and it will indeed continue in a straight line at constant speed forever.

What does this first law say about objects moving in a circle at a constant speed? This is a pretty important question, since satellites and the moon and the earth itself seem to be doing just that. By Newton’s 1st Law, there must be a force on the object that is moving it in a circle (otherwise it would just travel in a straight line, not in a circular path). It turns out that the force that causes an object to travel in a circle at constant speed must be directed toward the center of the circle (this can be proved with a combination of geometry and Newton’s 2nd Law, but let’s not bother proving it – it’s true).

Newton’s 2nd Law states that the force applied to an object causes the object to accelerate at a rate this is determined by the equation F = ma, where a is the acceleration that results from the force F, and m is the ratio between the force applied and the acceleration that results. We call that ratio the object’s mass. If an equal force is applied to two objects of differing mass, the more massive object will accelerate at a slower rate than the more massive one. That’s Newton’s famous 2nd Law. (In the 20th century it was shown that Newton 2nd Law is only right if the objects under consideration are moving much slower than the speed of light, but that is a discussion that we’ll put off for a couple of months!)

If an object is not accelerating (that is, if it’s moving in a straight line at constant speed, or not moving at all), then Newton’s 2nd Law tells us that there must be no NET force on the object. This does not necessarily mean that there are no forces at all acting on the object, just that whatever forces are acting balance each other out exactly. Consider a boat floating on the ocean or a person floating on the surface of a swimming pool: in both case, the object’s downward weight (the pull of gravity) is exactly balanced by an upward force (called buoyancy) that keeps you or the boat from sinking. The buoyant force, it turns out, is always equal to the weight of the fluid that you or the boat displaced. If the weight of the fluid displaced by an object is more than the weight of the object itself (as in the case of, say, a helium balloon), then the object rises until the weight of the outside fluid matches its own weight (the “fluid” in this case would be the air outside of the balloon, which gets less and less dense at higher altitudes). If the object is heavier than the fluid it displaces, the object sinks (like a rock in a swimming pool or a human in foamy water).

In the case of the object that is moving in a circle at constant speed, the acceleration, like the force, must be directed toward the center of the circle. By geometry, one can show (come see me if you’re curious!) that the value of this acceleration is given by v^2/r, where v is the object’s speed and r is the radius of the circle in which it travels. The object is always accelerating toward the center of the circle at this v^2/r rate, but it never gets closer to the center because of its tangential motion. The force that causes this acceleration toward the center must, according to Newton’s 2nd Law, be given by F = ma = mv^2/r. But what force is it that is causing the object to travel in a circle? What force is causing this v^2/r acceleration?

It could be any number of things. Perhaps the object is attached to a rope that is being swung around – in that case it is the tension in the rope that is providing the force. Perhaps the object is you, and you are on the “rotor,” a famous (and, I can attest, nauseating) amusement park ride in which one places their back against a wall and is spun in a circle so fast that the ground can fall away beneath one’s feet – in that case it is the wall of the ride pushing on your back that is causing you to accelerate toward the center at v^2/r.

Anyone who has worked in a biology lab knows that one of the most ubiquitous and useful instruments in biology is the centrifuge. Test tubes are placed in the centrifuge and spun around at very high circular velocities. Because the force on each component of the sample in the tube is given by F = mv^2/r, components of the sample having more mass feel more force than those having less mass. This results in a spatial separation between the heavier and lighter components in the sample, a very useful result when working with cells. (This technology is also important for the separation of uranium isotopes, as we’ll see in a couple of weeks when discussing nuclear technology.)

Another force that can cause circular motion is gravity. The force of gravity between any two objects having mass is proportional to the product of the two masses and inversely proportional to the square of the distance between them: F = GMm/r^2. Here, M and m are the two masses and r is the distance between them. G is just a constant that makes the units easy to manipulate – it’s not important for our purposes. If m is an object near the surface of the earth, and M is the earth itself, then r is the radius of the earth and the force felt by object m is F = ma = m(GMearth/rearth2). The numbers in parentheses comprise the object m’s acceleration near the surface of the earth, and are easy to look up online – try it and you will find that the ratio GMearth/rearth2 is equal to 10 meters per second per second, or, equivalently, 22 miles per hour per second. This is why objects dropped near the surface of the earth fall toward the earth at 22 miles per second per second. After 1 second of freefall you are going at 22 mph, after 2 you are going at 44 mph, etc. That magic number of 10 meters per second per second that you may have heard about in high school is just a special case of the more general gravitational law, useful when you are near the surface of the earth (as we often are!) but by no means a general law of gravity anywhere else. You would fall much more slowly than 10 meters per second per second near the moon, and much more quickly near Jupiter.

Each mass in this gravitational force equation feels the same force. This is due to Newton’s 3rd and final Law, which states that if object A exerts a force on object B, then object B exerts the same force (though in the opposite direction) on object A. So when two masses interact, they pull on each other equally hard, i.e., they both feel the same amount of gravitational pull.

Newton’s 3rd Law says that the earth pulls on the sun just as hard as the sun pulls on the earth. Why then does the earth go around the sun as opposed to the sun going around the earth? When you drop your pencil, the pencil pulls on the earth just as hard as the earth pulls on the pencil. Why then does the pencil fall to the earth as opposed to the earth rising to meet the pencil? The answer in both cases is that, although the forces are equal, the accelerations are not. Remember, if an equal force is applied to two objects that differ in mass, the less massive object accelerates more than does the more massive one. The sun is much more massive than the earth, and the earth is much more massive than the pencil! The 3rd Law also explains plane travel (the plane pushes down on the air around it, but the air pushes back just as hard, and in the upward direction) and rocket propulsion (the rocket pushes the fuel out its rear, and the fuel pushes the rocket up into space). These processes are sometimes described in your textbook in terms of momentum conservation, but you can also think of them in terms of Newton’s 3rd Law – you should understand both ways of thinking about it!

We now know enough to do a couple of interesting and practical calculations. First let’s figure out how fast Low Earth Orbit satellites need to be going if they are to remain in orbit just above the earth’s surface. These satellites are going in a circular path, so they are accelerating toward the center of that circle at a rate of a = v^2/r. The force that is causing that acceleration is gravity, which we now know is given by F = GMm/r^2. Putting these two facts together with Newton’s 2nd Law (F = ma), we arrive at the following equation for objects that are orbiting the earth:

(GMm/r^2) = m(v^2/r).

This may look complicated, but remember that this is just F = ma, where a = v^2/r and F is the gravitational force! Remember that M is the mass of the earth and, for satellites that are just a hundred or so miles above the earth, r is roughly equal to the radius of the earth. Putting these values in and solving for v, we find that the LEO satellites must travel at about 5 miles per second. This is where that rather arbitrary number discussed in lecture comes from… at 5 miles per second, the LEO satellites accelerates toward the center of the earth at a rate of v^2/r but never gets closer to the center!

For geosynchronous orbit, one would have to repeat this calculation with the constraint that the satellite’s orbit must take precisely 24 hours. If one does that, one finds that the r value which satisfied the above equation is about 26,000 miles, or 22,000 miles above the earth’s surface. That is the height at which a satellite’s orbit is geosynchronous.

Finally, let’s figure out why there is lots of oxygen and nitrogen in the earth’s atmosphere, but very little hydrogen. This is a very nice calculation to end with, since it combines ideas from each of the first three chapters of the course. To do this, we need to consider a concept called ‘escape velocity’. If instead of just sending a satellite into orbit, we wanted to actually send it far into outer space (i.e., if we wanted the satellite to escape the earth’s pull entirely), then we would need to provide it with more velocity than is required by the 5 mile per second orbit speed rule. For reasons that I won’t go into here (but am happy to go into elsewhere if you are interested!), we would actually need to provide such a satellite with exactly twice the speed that it would need just to be in orbit. We need to give objects a speed of about 10 miles per second if they are to escape the earth’s gravitational pull and drift off into space – this is the ‘escape velocity’.

What on earth does this have to do with the lack of hydrogen in the earth’s atmosphere? Well, you should recall from the previous chapters that at the temperature of the earth’s atmosphere, all the molecules are moving around with the same kinetic energy (things at the same temperature have the same kinetic energy). This does not mean, however, that all molecules have the same speed. Since kinetic energy is given by KE = ½ m v^2, lighter molecules (smaller m) will have larger speeds (bigger v) and heavier molecules (bigger m) will have smaller speeds (smaller v). At the temperature of the earth’s atmosphere, hydrogen, nitrogen and oxygen molecules all have the same kinetic energy, but they have very different speeds. Oxygen and nitrogen molecules, being much heavier than hydrogen molecules, are moving around relatively slowly. Hydrogen molecules are moving around very fast, so fast in fact that they often exceed 10 miles per second! What happens when an object’s speed exceeds this 10 miles per second escape velocity? The object flies off into space, never to return. Most of the hydrogen has escaped the earth in this manner, leaving the slower moving nitrogen and oxygen molecules behind. Conversely, there is a LOT of hydrogen at the sun, since it is unable to escape the sun’s much stronger gravitational pull.

Chapters 4 & 5

Radiation Poisoning	Cancer
Radiation damages cells, disrupts bodily processes	Radiation damages DNA such that cells stop regulating their own growth
Symptoms include nausea, listlessness, loss of hair, death	Symptoms include cancer
Effects at 100 rem, LD50 at 300 rem	2500 rem = 1 cancer

Linear hypothesis – draw graph for linear effect

Linear Hypothesis	Threshold hypothesis
Says that the linear effect is true even at very low doses of radiation	Says that below a certain level of radiation, there is no additional risk of cancer
Better safe than sorry!	The body can repair a little bit of damage no problem.
It’s difficult to test these hypotheses since about 20% of people will get cancer anyway. Human testing is frowned upon.

Radioactive dating

Radiocarbon dating	Potassium-argon dating
C-14 is made in the atomosphere, plants breathe it in, animals eat plants, so all living things have a certain level of C-14 while they’re alive.	K-40 is leftover from the formation of the solar system, and is found in rocks (and people)
When an organism dies, C-14 decays, but isn’t replaced, so the amount of C-14 decreases over time. The longer its been dead, the less C-14	K-40 in rocks decays, turns into argon gas which is trapped in the solid rock. The longer the rock has been solid, the more argon gas it will have trapped.
Only works on things that died within the last 60,000 years.	Most useful for rocks at least 100,000 years old

	Uranium bombs	Plutonium bombs	Hydrogen bombs
Fuel	U-235	Pu-239	Pu-239, H2, U-238
Design	Gun-type	Implosion	Thermonuclear
Advantages	Easy to build	Easy to get plutonium	Really friggin’ powerful
Disadvantages	Hard to purify U-235 (from 0.7% to 80%)	Hard to build implosion mechanism	You still need a fission bomb (uranium or plutonium)
Historical role	Hiroshima (“Little Boy”)	Nagasaki (“Fat Man”)	Most of our current arsenal of ~12,500 nuclear weapons

How is nuclear power different?

· Lower power – boil water, turn turbine, generate electricity

· Sustained chain reaction – no doubling

o On average, only 1 of 2 neutrons hits another U-235

· Requires only 3% U-235, not 80%

· Uses a moderator (water, heavy water, graphite)

o slows down neutrons (thermal neutrons)

o thermal neutrons more easily absorbed by U-235

o Also keeps reactor cool

· Produces Pu-239 when other neutron hits U-238

o Breeder reactor – use Pu-239 as fuel, extra neutrons hit U-238

§ doubles amount of Pu-239 in 10 years

· Won’t blow up like a nuclear weapon

o Slow neutrons means slower chain reaction

· Can have a “meltdown” if moderator disappears

o chain reaction stops

o temperature increases, material melts

Three Mile Island vs. Chernobyl

Three Mile Island	Chernobyl
Pennsylvania	Ukraine (USSR)
Meltdown	Reactivity accident
Moderator pumps fail 1/3 of core melts, but not through floor	Chain reaction increases out of control Water coolant boiled rapidly - explosion Carbon moderator set on fire Radioactive material escapes in form of smoke
Nobody hurt	~30 deaths from radiation illness ~4,000 cancer deaths expected