32 Natural relativistic units were introduced on p. 406, and
examples 1 and 2 on pp. 407 and 407 gave examples of how to
convert an equation from natural units to SI units. In example 4 on
p. 408, we derived the approximationγ≈1 +v^2
2
for values ofvthat are small compared to 1 (i.e., small compared
to the speed of light in natural units). As in the other examples,
convert this equation to SI units. .Solution, p. 1043
33 We want to throw a ball of diameterbthrough a hole of
diameterhin a thin wall. Clearly this is possible ifb < h, but
consider the case whereb > h. If the motion is relativistic, then
is it unambiguous whether the ball fits through the hole, or is this
frame-dependent, as in example 7 on p. 410? If the former, then is
there some velocityvthat is required, expressible in terms ofband
h?
34 (a) LetLbe the diameter of our galaxy. Suppose that a
person in a spaceship of massmwants to travel across the galaxy
at constant speed, taking proper timeτ. Find the kinetic energy of
the spaceship. (b) Your friend is impatient, and wants to make the
voyage in an hour. ForL= 10^5 light years, estimate the energy in
units of megatons of TNT (1 megaton=4× 109 J).Key to symbols:
√easy typical challenging difficult very difficult
An answer check is available at http://www.lightandmatter.com.464 Chapter 7 Relativity