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11 S. Compare the light-gathering powers of a 3-cm-diameter telescope and
a 30-cm telescope.
12. S. One step on the Richter scale corresponds to a factor of 100 in terms
of the energy absorbed by something on the surface of the Earth, e.g. a
house. For instance, a 9.3-magnitude quake would release 100 times more
energy than an 8.3. The energy spreads out from the epicenter as a wave,
and for the sake of this problem we’ll assume we’re dealing with seismic
waves that spread out in three dimensions, so that we can visualize them as
hemispheres spreading out under the surface of the earth. If a certain 7.6-
magnitude earthquake and a certain 5.6-magnitude earthquake produce the
same amount of vibration where I live, compare the distances from my
house to the two epicenters.
13. In Europe, a piece of paper of the standard size, called A4, is a little
narrower and taller than its American counterpart. The ratio of the height
to the width is the square root of 2, and this has some useful properties. For
instance, if you cut an A4 sheet from left to right, you get two smaller sheets
that have the same proportions. You can even buy sheets of this smaller size,
and they’re called A5. There is a whole series of sizes related in this way, all
with the same proportions. (a) Compare an A5 sheet to an A4 in terms of
area and linear size. (b) The series of paper sizes starts from an A0 sheet,
which has an area of one square meter. Suppose we had a series of boxes
defined in a similar way: the B0 box has a volume of one cubic meter, two
B1 boxes fit exactly inside an B0 box, and so on. What would be the
dimensions of a B0 box.
14. Estimate the mass of a human hair, in units of kg.
15. According to folklore, every time you take a breath, you are inhaling
some of the air molecules exhaled in Caesar’s last words. Is this true. If so,
how many molecules.