PHL 101 Lecture : The City

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azurewolf864

27 Mar 2011

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Only knowing that can we figure out whether morality really is better. S begins by imagining a kind of social contract : individuals come together to form a community because they aren"t self-sufficient. People become involved with various other people to fulfill various needs, and we have lots of needs, so we gather lots of people together and then we call this living together a community (p. 59). This seems to be a rhetorical question, but maybe we can think of other reasons. S introduces a principle of specialization: different people are inherently suitable for different activities , ii. People will do their work better when they specialize in only one job. (p. 60) It provides for people"s needs, but there are few luxuries. S concedes that luxuries can be introduced, but he describes this as a change from a healthy community to one that is bloated and distended (p. 64) one that will require more doctors.

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You know that certain musical notes sound good together -harmonious - whereas others do not. This harmony is related to the various harmonics of the notes played. The musical notes C (262 Hz) and G (392 Hz) make a pleasant sound when played together; we call this consonance. As the Figure shows, the harmonics of the two notes are either far from each other or very close to each other (within a few Hz). This is the key to consonance: harmonics that are spaced either far apart of very close. The close harmonics have a beat frequency of a few Hz that is perceived as pleasant. If the harmonics of two notes are close, but not too close, the rather high beat frequency between the two is quite unpleasant. This is what we hear as dissonance. Exactly how much a difference is maximally dissonant is a matter of opinion, but harmonic separations of 30 - 40 Hz seem to be quite unpleasant for most people.

What is the beat frequency between the second harmonic of G and the third harmonic of C?

maroonworm543

The Sun is powered by nuclear fusion. In each chain reaction, four hydrogen nuclei fuse together to become a single helium nucleus. The total combined mass of the individual hydrogen nuclei before the reaction is greater than the mass of the helium nucleus. The mass lost as a result of this chain reaction is turned into energy according to Einstein’s famous equation, E = mc² (Chapter 39). Consider the first part of the chain reaction in which two hydrogen nuclei (each a single proton) fuse. Figure P8.56A shows the potential energy curve of a two-proton system. The energy in this graph is given in keV, where “eV” is the abbreviation for the unit electron-volt and 1 eV = 1.6 × 10−19 J. When the protons are more than about 2 fm (2 × 10−15 m) apart, the potential energy is positive. When the protons are close together, the potential energy is negative, and the protons are fused. Figure P8.56B shows a close-up of the potential energy curve when the protons are far apart.

a. What is the minimum mechanical energy required for the two protons to fuse? Give your answer in keV.
b. The mechanical energy of an average two-proton system in the Sun is around 2 keV. What is the minimum distance between the protons in such a system?
c. Explain why it seems impossible for fusion to take place in the Sun. Note: Of course, fusion must take place in the Sun. Although it seems impossible according to classical mechanics, quantum mechanics (Part VI) makes fusion possible. According to quantum mechanics, the seemingly impossible is merely improbable, and even events with a low probability of occurrence may still happen. Because there are so many protons in the Sun, there is a good chance that at any moment many of them will fuse.

erinherring569

PHL 101 Lecture : The City

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