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.)