Physics 10 Section 1 Handout 1/18/07
I. Logistics
A. Welcome to Zack’s Section.
1. Each week, I will put together a Section Handout and post it on my webpage, http://captainjack74737.fastmail.fm/Physics10/.To savepaper, I will not be making copies of this handout, but it will be helpful for you if you can print it out and bring it to section with you.I will try to email a reminder when I post each new handout.
B. Section Format
1. Generally I find it useful to have a combination of answering your questions, prompting you with questions, and “lecturing” on the material, as there are no problem sets in this class. Sometimes I will also have demos or a “game show” to practice the concepts. I am open to suggestions on the format, as section is to serve you.
C. Expectations for homework
1. Subject header format: Last Name, First Name, PffP:HW, Date HW is due.
2. This is different than the format for the other GSIs, as there is the addition of the text “PffP:HW”, exactly as written there. This is because I don’t have a separate homework email but receive homeworks at my regular email, and I need some kind of text to cue my email filter.
3. If you don’t use this format, not only will you annoy me, but your homework might get lost in my email and then you wouldn’t get any credit.
D. Contact info, office hours, etc.
1. Email:
2. Phone (please use sparingly): 510-847-7618
II. Math Review
A. Exponents
1. When two numbers multiply, their exponents add: .
2. When two numbers divide, their exponents subtract: .
3. When a number with an existing exponent is raised to an additional power, the exponents multiply: .
4. Taking the square root of a number is the same as raising it to the ½ power: .
B. Scientific notation
1. Shorthand notation using exponents; for instance, 1,500,000 becomes 1.5 x 106. You can think of the exponent on the 10 as the number of zeroes after the one; in this case, 6 zeroes yields one million.
2. When adding numbers in scientific notation, you first have to make sure that the exponents are the same: 1 x 106 + 1 x 104 = 100 x 104 + 1 x 104 = 101 x 104 = 1.01 x 106.
3. When multiplying numbers, multiply the coefficients (the first numbers) separately, and then add the exponents: 2 x 108 * 2 x 10-5 = (2*2) x 108-5 = 4 x 103.
4. When taking a square root, take the square root of the coefficient first, and then halve the exponent. If you end up with a .5, then you can remove a factor of . Your calculator will do all this for you. .
III. Units
A. Prefixes: (Don’t worry too much about the ones for very big or very small numbers, but you may come across them in the media.)
1. Pico = 10-12 (trillionth). “p”
2. Nano = 10-9 (billionth). “n”
3. Micro = 10-6 (millionth). “µ”
4. Milli = 10-3 (thousandth). “m”
5. Centi = 10-2 (hundredth). “c”
6. Kilo = 103 (thousand). “k”
7. Mega = 106 (million). “M”
8. Giga = 109 (billion). “G”
9. Tera = 1012 (trillion). “T”
B. In order to have meaning, a physical quantity must have units attached to it. A number by itself, with no units attached, has no physical content.
C. Physicists like to build up units from other units. There are three very fundamental units in physics: the meter (m), the kilogram (kg), & the second (s).
1. For instance, the precise definition of one joule (J) is the amount of energy required to accelerate one kilogram (kg) at a rate of 1 m/s/s (about 2 mph/s), through a distance of 1 m. Thus, . And, of course, W = J/s = . (Remember the difference between energy and power?)
D. Dimensional Analysis
1. When you think about physics or do problems, it is important to be consistent about the units. In an equation, both sides must have the same units. This is very useful for problem solving and leads to a trick called “dimensional analysis.” We won’t be teaching much problem solving in this class, but you can apply this technique to manipulate quantities you encounter in class, in everyday life, or in the news.
2. Example: when I drink an American pint of beer, how many mL (milliliters) have I consumed? Is this larger or smaller than the half liter I would be served at a bar in Germany? (Don’t worry about remembering the conversions: I’m more interested in demonstrating the process.)
E. Be careful when converting between units that are squared or cubed.
1. There are 100 centimeters in a meter, but there are 1002 or 10,000 square centimeters in a square meter.
IV. Forms of Energy
A. Types of energy, and an example of that type corresponding to about 1 kJ.
1. “Kinetic energy”: a 150-lb man riding a bicycle at 12 mph.
2. “Potential energy” (due to gravity): the energy gained by a 100 kg mass as it falls a meter.
3. “Chemical energy”: the energy in 1/20 of a gram of sugar.
4. “Light energy”: the energy deposited by bright sunlight into your skin over a few seconds.
5. “Sound energy”: the energy emitted by powerful concert-style speakers at full blast in 15 minutes. (Notice that there is generally much less energy in everyday sound than in light.)
6. “Nuclear energy”: the energy that can be obtained from 1.2 x 10-8 g of uranium.
7. “Heat energy”: the energy required to make a spoonful of hot tea.
B. Energy is conserved, but it can change quality.
1. Some conversions are easier than others: it’s a lot easier to burn gasoline and convert its chemical energy to heat than it is to collect the heat and the waste products and turn it back to gasoline!
C. More examples of quantities of energy:
1. An electron moving in an atom: 10-19 J.
2. A running mouse: 0.1 J.
3. A car on the highway: 6 x 105 J.
4. The kinetic energy of the earth in its orbit: 3 x 1033 J.
5. The energy of a supernova: 1043 J.
D. Energy in Food
1. How much mass in chocolate chip cookies would you have to eat each day (a CCC is 5 Cal / g) to get your basic caloric needs? (I’m not recommending you try to meet your nutritional needs this way!) What about if you just ate butter – or spoonfulls of sugar in water – instead?
2. In general, 1g of “carbs” (carbohydrates) or protein is 4 Calories; 1g of fat is 9 Calories. Thus, a pound of fat is about 4,000 Cal.
3. Where did the energy in the CCC come from? Where does it go?
V. Problems: “Order of Magnitude Calculations”
(Again, we won’t be stressing this type of problem solving in this class: you won’t be tested on it and there won’t be problem sets. Think of this as merely a warmup exercise to get you thinking like a physicist, and about energy.)
1. How much energy is consumed by US automobiles in a year? Given: there are 42 kJ of energy in a g of gasoline, and gasoline is just a bit less dense than water (which is set as the standard: 1 g / cm3 or 1 kg / L).
2. How many grains of sand could fit in the earth?
3. How much energy is required to heat an Olympic-sized swimming pool from an outdoor temperature of 10 deg. C to a more balmy 25 deg. C? With a standard household 1,000 watt heater, how long would that take? (Hint: Remember the definition of a “Calorie”: the amount of heat it takes to heat one kg of water by 1 C, or about 4,000 J.) If we let the sun do it instead, how long would that take?
4. The New York Times recently ran an article about the weaponization of space. One idea was “rods from God,” in which a 100 kg rod is dropped from low-earth orbit (a few hundred miles) onto its target. The article claimed that it would have the same energy as a small nuclear blast. Is this credible? Hint: we haven’t done gravity yet, but you can assume that a kg gains 10 J for each meter it falls. (A “small” nuclear blast would be about 10 kilotons, equivalent to 10,000 tons of TNT; TNT has an energy of 2700 J / g.)
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