Week 3

Read: Pendular motion and harmony (Chap. 5) and The law of the lever (Chap. 6). Chapter 6 is a bit dense. Don't worry if you don't quite follow some of Galileo's geometrical proofs; we'll talk about this in class.

dissonance (5.1), suspended weight (5.2), violin strings (5.3), harmony essay (5.5), seesaw equilibrium (6.1), achilles tendon (6.2), aligning a support rafter (6.4), transverse fracture (6.5), PHY 201: natural frequency and dimensional analysis (5.4). Just pick one or two easier ones to see if you can do dimensional analysis. Also, if you'd like to try a challenging dimensional analysis problem, check out the atomic bomb problem at the bottom of this page…

Harmony (Ex. 5.6)

Chapter 5 (4 videos):

Check out these two fun and fascinating videos:

Lectures on Dimensional Analysis (2 videos for phy 201 folks):

Chapter 6 (6 videos):

Trinity Atomic Bomb energy yield problem (optional dimensional analysis problem for PHY 201 students)

On July 16, 1945, the United States Government tested the first atomic weapon in what is now the White Sands Missile Range in New Mexico. The energy released during the explosion was kept secret, but several photographs of the explosion were published in Life magazine. Some of these are shown below. Notice that the length scale and the time elapsed is indicated on each photograph.

trinity-16ms trinity-62ms trinity-100ms

By analyzing photos like these, British physicist G.I.Taylor was able to correctly determine the energy released by this atomic explosion. How did he do it? By (i) observing how the blast radius increases as time elapses and (ii) using the technique of dimensional analysis.

Put the problem this way: the radius of the blast depends on the total energy released, E, the surrounding air density, d, and the time elapsed, t. That is: r = r (E, d, t). So what combination of E, d, and t will have the dimension of length? See if you can work it out. Now, by plotting the blast radius versus time, one can determine the blast energy, E, by finding a power-law fit to the curve r(t).

By the way, here is some of the radius versus time data, in case you are interested in plotting it:

t(msec), r (meters)
######, ########
0.10, 11.1
0.24, 19.9
0.38, 25.4
0.52, 28.8
0.66, 31.9
0.80, 34.2
0.94, 36.3
1.08, 38.9
1.22, 41.0
1.36, 42.8
1.50, 44.4
1.65, 46.0
1.79, 46.9
1.93, 48.7
3.26, 59.0
3.53, 61.1
3.80, 62.9
4.07, 64.3
4.34, 65.6
4.61, 67.3
15.0, 106.5
25.0, 130.0
34.0, 145.0
53.0, 175.0
62.0, 185.0

Physics 1