[جنون الفزياء]

Problems 19
Which of the following equations are dimensionally
correct?
(a) vf $ vi'ax
(b) y $ (2 m)cos(kx), where k $ 2 m"1.
16. (a) A fundamental law of motion states that the acceleration
of an object is directly proportional to the resultant force exerted
on the object and inversely proportional to its mass. If
the proportionality constant is defined to have no dimensions,
determine the dimensions of force. (b) The newton is
the SI unit of force. According to the results for (a), how can
you express a force having units of newtons using the fundamental
units of mass, length, and time?
17. Newton’s law of universal gravitation is represented by
Here F is the magnitude of the gravitational force exerted by
one small object on another, M and m are the masses of the
objects, and r is a distance. Force has the SI units kg·m/s2.
What are the SI units of the proportionality constant G?
Section 1.5 Conversion of Units
18. A worker is to paint the walls of a square room 8.00 ft high
and 12.0 ft along each side. What surface area in square
meters must she cover?
19. Suppose your hair grows at the rate 1/32 in. per day. Find
the rate at which it grows in nanometers per second. Because
the distance between atoms in a molecule is on the
order of 0.1 nm, your answer suggests how rapidly layers of
atoms are assembled in this protein synthesis.
20. The volume of a wallet is 8.50 in.3 Convert this value to m3,
using the definition 1 in. $ 2.54 cm.
A rectangular building lot is 100 ft by 150 ft. Determine the
area of this lot in m2.
22. An auditorium measures 40.0 m ! 20.0 m ! 12.0 m. The
density of air is 1.20 kg/m3. What are (a) the volume of
the room in cubic feet and (b) the weight of air in the
room in pounds?
23. Assume that it takes 7.00 minutes to fill a 30.0-gal gasoline
tank. (a) Calculate the rate at which the tank is filled in
gallons per second. (b) Calculate the rate at which the
tank is filled in cubic meters per second. (c) Determine
the time interval, in hours, required to fill a 1-m3 volume
at the same rate. (1 U.S. gal $ 231 in.3)
24. Find the height or length of these natural wonders in kilometers,
meters and centimeters. (a) The longest cave system
in the world is the Mammoth Cave system in central Kentucky.
It has a mapped length of 348 mi. (b) In the United
States, the waterfall with the greatest single drop is Ribbon
Falls, which falls 1 612 ft. (c) Mount McKinley in Denali National
Park, Alaska, is America’s highest mountain at a
height of 20 320 ft. (d) The deepest canyon in the United
States is King’s Canyon in California with a depth of 8 200 ft.
A solid piece of lead has a mass of 23.94 g and a volume of
2.10 cm3. From these data, calculate the density of lead in
SI units (kg/m3).
25.
21.
F $
GMm
r 2
15. 26. A section of land has an area of 1 square mile and contains
640 acres. Determine the number of square meters in
1 acre.
27. An ore loader moves 1 200 tons/h from a mine to the surface.
Convert this rate to lb/s, using 1 ton $ 2 000 lb.
28. (a) Find a conversion factor to convert from miles per
hour to kilometers per hour. (b) In the past, a federal law
mandated that highway speed limits would be 55 mi/h.
Use the conversion factor of part (a) to find this speed in
kilometers per hour. (c) The maximum highway speed is
now 65 mi/h in some places. In kilometers per hour, how
much increase is this over the 55 mi/h limit?
At the time of this book’s printing, the U.S. national debt
is about $6 trillion. (a) If payments were made at the rate
of $1 000 per second, how many years would it take to pay
off the debt, assuming no interest were charged? (b) A
dollar bill is about 15.5 cm long. If six trillion dollar bills
were laid end to end around the Earth’s equator, how
many times would they encircle the planet? Take the radius
of the Earth at the equator to be 6 378 km. (Note: Before
doing any of these calculations, try to guess at the answers.
You may be very surprised.)
30. The mass of the Sun is 1.99 ! 1030 kg, and the mass of an
atom of hydrogen, of which the Sun is mostly composed, is
1.67 ! 10"27 kg. How many atoms are in the Sun?
One gallon of paint (volume$3.78 ! 10"3 m3) covers
an area of 25.0 m2. What is the thickness of the paint on
the wall?
32. A pyramid has a height of 481 ft and its base covers an area
of 13.0 acres (Fig. P1.32). If the volume of a pyramid is
given by the expression V $ Bh, where B is the area of
the base and h is the height, find the volume of this pyramid
in cubic meters. (1 acre $ 43 560 ft2)
13
31.
29.
Figure P1.32 Problems 32 and 33.
Sylvain Grandadam/Photo Researchers, Inc.
33. The pyramid described in Problem 32 contains approximately
2 million stone blocks that average 2.50 tons each.
Find the weight of this pyramid in pounds.
34. Assuming that 70% of the Earth’s surface is covered with
water at an average depth of 2.3 mi, estimate the mass of
the water on the Earth in kilograms.
35. A hydrogen atom has a diameter of approximately
1.06 ! 10"10 m, as defined by the diameter of the spherical
electron cloud around the nucleus. The hydrogen nucleus
has a diameter of approximately 2.40 ! 10"15 m.
(a) For a scale model, represent the diameter of the hydrogen
atom by the length of an American football field