advertisement

Dimensional Analysis Homework 2 due Nov. 20 (3 sig figs for all where appropriate – Show Work!) each problem is worth 2 points 1. The first explosion of an atomic bomb was near Alamogordo, NM on July 16, 1945. To the left is a picture of the approximately spherical shockwave after 25 msec (the tick marks indicating 100 m are about 18.5 mm apart). Use dimensional analysis to find an expression (i. e. what are the exponents) for the radius of the shockwave, R, (the governed parameter) as a function of the density ρ of the medium (the air) through which the shock wave travels, the energy of the explosion, E, and the time, t, elapsed since the explosion, where ρ, E, and t are the governing parameters. 2. Sir Geoffrey Taylor used a theory to calculate that the proportionality constant in R = const. ρaEbtc was approximately 1. Using the density, ρ, of air as 1.2 kg/m3, using mks units for t (sec) and E (Joules), a value for R at t=0.025 s estimated from the picture above, and the conversion that the explosion of 1 metric ton (1000 kg) of TNT releases 4 x 109 J, what was the approximate energy of this explosion expressed as tons of TNT equivalent? (Taylor, using movies of the explosion declassified in 1947, did this same calculation at a time when the energy release was still classified.) (Show work – give your estimate for R, etc.)