16 CHAPTER 1 | Physics and Measurement
12. (a) Assume the equation x 5 At 3 1 Bt describes the motion 22. Let rAl represent the density of aluminum and rFe that
of a particular object, with x having the dimension of of iron. Find the radius of a solid aluminum sphere that
length and t having the dimension of time. Determine the balances a solid iron sphere of radius r Fe on an equal-arm
dimensions of the constants A and B. (b) Determine the balance.
dimensions of the derivative dx/dt 5 3At 2 1 B.
23. One gallon of paint (volume 5 3.78 3 10 –3 m3) covers an
Section 1.4 Conversion of Units area of 25.0 m2. What is the thickness of the fresh paint on
the wall?
13. A rectangular building lot has a width of 75.0 ft and a 24. An auditorium measures 40.0 m 3 20.0 m 3 12.0 m. The
length of 125 ft. Determine the area of this lot in square density of air is 1.20 kg/m3 . What are (a) the volume of the
meters. room in cubic feet and (b) the weight of air in the room in
14. Suppose your hair grows at the rate 1/32 in. per day. pounds?
Find the rate at which it grows in nanometers per second. 25. (a) At the time of this book’s printing, the U.S. national
Because the distance between atoms in a molecule is on debt is about $10 trillion. If payments were made at the
the order of 0.1 nm, your answer suggests how rapidly lay- rate of $1 000 per second, how many years would it take
ers of atoms are assembled in this protein synthesis. to pay off the debt, assuming no interest were charged?
15. A solid piece of lead has a mass of 23.94 g and a volume of (b) A dollar bill is about 15.5 cm long. How many dollar
2.10 cm3. From these data, calculate the density of lead in bills attached end to end would it take to reach the Moon?
SI units (kilograms per cubic meter). The front endpapers give the Earth–Moon distance. Note:
Before doing these calculations, try to guess at the answers.
16. An ore loader moves 1 200 tons/h from a mine to the sur- You may be very surprised.
face. Convert this rate to pounds per second, using 1 ton 5
26. A hydrogen atom has a diameter of 1.06 3 10210 m. The
2 000 lb.
nucleus of the hydrogen atom has a diameter of approxi-
17. Why is the following situation impossible? A student’s dormitory mately 2.40 3 10215 m. (a) For a scale model, represent the
room measures 3.8 m by 3.6 m, and its ceiling is 2.5 m high. diameter of the hydrogen atom by the playing length of
After the student completes his physics course, he displays an American football field (100 yards 5 300 ft) and deter-
his dedication by completely wallpapering the walls of the mine the diameter of the nucleus in millimeters. (b) Find
room with the pages from his copy of volume 1 (Chap- the ratio of the volume of the hydrogen atom to the vol-
ters 1–22) of this textbook. He even covers the door and ume of its nucleus.
window.
Section 1.5 Estimates and Order-of-Magnitude Calculations
18. A pyramid has a height of 481 ft, and its base covers an
area of 13.0 acres (Fig. P1.18). The volume of a pyramid is Note: In your solutions to Problems 27 through 30, state
given by the expression V 5 13 Bh, where B is the area of the the quantities you measure or estimate and the values
base and h is the height. Find the volume of this pyramid in you take for them.
cubic meters. (1 acre 5 43 560 ft 2)
27. Find the order of magnitude of the number of table-tennis
balls that would fit into a typical-size room (without being
Adam Sylvester/Photo Researchers, Inc.
crushed).
28. (a) Compute the order of magnitude of the mass of a bath-
tub half full of water. (b) Compute the order of magnitude
of the mass of a bathtub half full of copper coins.
29. To an order of magnitude, how many piano tuners reside
in New York City? The physicist Enrico Fermi was famous
for asking questions like this one on oral Ph.D. qualifying
examinations.
Figure P1.18 Problems 18 and 19. 30. An automobile tire is rated to last for 50 000 miles. To an
order of magnitude, through how many revolutions will it
19. The pyramid described in Problem 18 contains approxi- turn over its lifetime?
mately 2 million stone blocks that average 2.50 tons each.
Find the weight of this pyramid in pounds. Section 1.6 Significant Figures
20. Assume it takes 7.00 min to fill a 30.0-gal gasoline tank. Note: Appendix B.8 on propagation of uncertainty may
(a) Calculate the rate at which the tank is filled in gal- be useful in solving some problems in this section.
lons per second. (b) Calculate the rate at which the tank
31. The tropical year, the time interval from one vernal equinox
is filled in cubic meters per second. (c) Determine the time
to the next vernal equinox, is the basis for our calendar. It
interval, in hours, required to fill a 1.00-m3 volume at the
contains 365.242 199 days. Find the number of seconds in a
same rate. (1 U.S. gal 5 231 in.3)
tropical year.
21. One cubic meter (1.00 m3) of aluminum has a mass of 32. How many significant figures are in the following numbers?
2.70 3 103 kg, and the same volume of iron has a mass of (a) 78.9 6 0.2 (b) 3.788 3 109 (c) 2.46 3 1026 (d) 0.005 3
7.86 3 103 kg. Find the radius of a solid aluminum sphere 33. A rectangular plate has a length of (21.3 6 0.2) cm and
that will balance a solid iron sphere of radius 2.00 cm on a width of (9.8 6 0.1) cm. Calculate the area of the plate,
an equal-arm balance. including its uncertainty.
