215
Solutions to Selected
Problems
Chapter 0
6.
134mg
×
10
–3
g
1mg
×
10
–3
kg
1g
=1.34
×
10
–4
kg
8. (a) Let’s do 10.0 g and 1000 g. The arithmetic
mean is 505 grams. It comes out to be 0.505 kg,
which is consistent. (b) The geometric mean comes
out to be 100 g or 0.1 kg, which is consistent. (c) If
we multiply meters by meters, we get square
meters. Multiplying grams by grams should give
square grams! This sounds strange, but it makes
sense. Taking the square root of square grams (g
2
)
gives grams again. (d) No. The superduper mean of
two quantities with units of grams wouldn’t even be
something with units of grams! Related to this
shortcoming is the fact that the superduper mean
would fail the kind of consistency test carried out in
the first two parts of the problem.
Chapter 1
10.
1mm
2
×
1cm
10mm
2
=10
–2
cm
2
11. The bigger scope has a diameter that’s ten times
greater. Area scales as the square of the linear
dimensions, so its light-gathering power is a hun-
dred times greater (10x10).
12. Since they differ by two steps on the Richter
scale, the energy of the bigger quake is 10000 times
greater. The wave forms a hemisphere, and the
surface area of the hemisphere over which the
energy is spread is proportional to the square of its
radius. If the amount of vibration was the same, then
the surface areas much be in the ratio of 10000:1,
which means that the ratio of the radii is 100:1.
Chapter 2
4. 1 light-year= v
.
t
=
3.0x10
8
m/s
1year
×
365days
1year
24hours
1day
3600s
1hour
=
9.5x10
15
m
5. Velocity is relative, so having to lean tells you
nothing about the train’s velocity. Fullerton is moving
at a huge speed relative to Beijing, but that doesn’t
produce any noticeable effect in either city. The fact
that you have to lean tells you that the train is accel-
erating.
7. To the person riding the moving bike, bug A is
simply going in circles. The only difference between
the motions of the two wheels is that one is traveling
through space, but motion is relative, so this doesn’t
have any effect on the bugs. It’s equally hard for each
of them.
10. In one second, the ship moves v meters to the
east, and the person moves v meters north relative to
the deck. Relative to the water, he traces the diago-
nal of a triangle whose length is given by the
Pythagorean theorem, (v
2
+v
2
)
1/2
=2
1/2
v. Relative to the
water, he is moving at a 45-degree angle between
north and east.
Chapter 3
14.
x
v
t
t
15. Taking g to be 10 m/s, the bullet loses 10 m/s of
speed every second, so it will take 10 s to come to a
stop, and then another 10 s to come back down, for a
total of 20 s.
16.
.
x=
1
2
at
2
, so for a fixed value of
.
x, we have
t
.
1/a
. Decreasing a by a factor of 3 means that t
will increase by a factor of
3
.
Solutions to Selected Problems