Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Reference part 2- Appendix D-I
Document related concepts
Electromagnetic mass wikipedia , lookup
Special relativity wikipedia , lookup
Specific impulse wikipedia , lookup
Electrical resistance and conductance wikipedia , lookup
Woodward effect wikipedia , lookup
Weightlessness wikipedia , lookup
Classical mechanics wikipedia , lookup
Conservation of energy wikipedia , lookup
Potential energy wikipedia , lookup
Equations of motion wikipedia , lookup
Negative mass wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Electrostatics wikipedia , lookup
Mass versus weight wikipedia , lookup
Electromagnetism wikipedia , lookup
Newton's laws of motion wikipedia , lookup
Faster-than-light wikipedia , lookup
Anti-gravity wikipedia , lookup
Lorentz force wikipedia , lookup
Time in physics wikipedia , lookup
Speed of gravity wikipedia , lookup
Transcript
,
l
Equations
Chapter 2
Motion in One Dimension
~X=
DISPLACEMENT
Xf- Xi
~X-
Xf-Xi
Vavg= ~t- tf- ti
AVERAGE VELOCITY
~
AVERAGE SPEED
average speed
distance traveled
time of travel
AVERAGE ACCELERATION
~V
Vf-Vi
aavg= ~t- tf- ti
DISPLACEMENT
~ = -i_Cvi
These equations are valid only for constantly
accelerated, straight-line motion.
~ = vi ~ t + 2a(~t)
FINAL VELOCITY
Vf= Vi+ a~t
These equations are valid only for constantly
accelerated, straight-line motion.
Vf =vi +2a~
Chapter 3
1
+ Vf)~t
1
2
J
2
2
Two-Dimensional Motion and Vectors
PYTHAGOREAN THEOREM
c2
= a2 + b2
This equation is valid only for right triangles.
TANGENT, SINE, AND
COSINE FUNCTIONS
tan () = opp
adj
sin () = opp
hyp
These equations are valid only
for right triangles.
VERTICAL MOTION OF A PROJECTILE
THAT FALLS FROM REST
These equations assume that air resistance is
negligible, and apply only when the initial
vertical velocity is zero. On Earth's surface,
ay=-g=-9.81
2
Vy,f = 2ay~Y
~y = ~ay(~t) 2
mil.
HORIZONTAL MOTION OF A
Vx = Vx,i = constant
PROJECTILE
~=Vx ~ t
These equations assume that air resistance
is negligible.
Append ix D : Equations
Vy,f = ay~t
cos () = adj
hyp
PROJECTILES LAUNCHED
ATAN ANGLE
These equations assume that air resistance
is negligible. On Earth's surface,
ay=-g=-9.81 m/s 2.
Vx =Vi cos()= constant
Ax= (vi cos
B)~t
Vy,f = Vi sin () + ay~t
2
2
Vy,f = v?(sin 8) + 2ay~Y
~y =(vi sin B)~t + ~ay(~t) 2
RELATIVE VELOCITY
Chapter 4
Vac = Vab
+ Vbc
Forces and the Laws of Motion
NEWTON'S FIRST LAW
An object at rest remains at rest,
and an object in motion continues
in motion with constant velocity
(that is, constant speed in a straight
line) unless the object experiences a
net external force.
NEWTON'S SECOND LAW
IF=ma
I.F is the vector sum of all external forces
acting on the object.
NEWTON'S THIRD LAW
If two objects interact, the
magnitude of the force exerted on
object 1 by object 2 is equal to the
magnitude of the force exerted on
object 2 by object 1, and these two
forces are opposite in direction.
WEIGHT
Fg= mag
On Earth's surface, ag= g= 9.81 m!/.
COEFFICIENT OF STATIC FRICTION
Fs,max
Jls=----p;
COEFFICIENT OF KINETIC FRICTION
Fk
flk=Fn
The coefficient of kinetic friction varies with
speed, but we neglect any such variations here.
FORCE OF FRICTION
Ft = J1Fn
Appendix D: Equations
855
Chapter 5
Work and Energy
~
NET WORK
This equation applies only when the force is
constant.
W net= Fnetd COS
KINETIC ENERGY
KE= 2 mv
WORK-KINETIC ENERGY THEOREM
Wnet =ME
GRAVITATIONAL POTENTIAL ENERGY
PEg= mgh
1
()
2
1
~
2
ELASTIC POTENTIAL ENERGY
PEelastic = 2kx
MECHANICAL ENERGY
ME=KE+'LPE
CONSERVATION OF
MECHANICAL ENERGY
MEi =MEt
This equation is valid only if non mechanical
forms of energy (such as friction) are disregarded.
w
POWER
Chapter 6
P=-=Fv
flt
Momentum and Collisions
MOMENTUM
p =m v
IMPULSE-MOMENTUM THEOREM
Fflt = flp = mvf - mvi
This equation is valid only when the force
is constant.
CONSERVATION OF MOMENTUM
These equations are valid for a closed system,
that is, when no external forces act on the system
during the collision. When such external forces
are either negligibly small or act for too short
a time to make a significant change in the
momentum, these equations represent a good
approximation. The second equation is valid for
two-body collisions.
856
Append ix 0: Equations
Pi = Pt
m1 v1,i + m2v2,i = m1v1,f+ m2v2,f
1
CONSERVATION OF MOMENTUM FOR
A PERFECTLY INELASTIC COLLISION
This is a simplified version of the conservation of
momentum equation valid only for perfectly
inelastic collisions between two bodies.
mlvl,i + m2v2,i = (ml
+ m2) Vf
CONSERVATION OF KINETIC ENERGY
FOR AN ELASTIC COLLISION
No collision is perfectly elastic; some kinetic
energy is always converted to other forms of
energy. But if these losses are minimal, this
equation can provide a good approximation.
Chapter 7
1
2ml vl,i
2
1
+ 2m2v2,i
1
2m 1 vl,f
2
2
1
+ 2m2v2,f
2
Circular Motion and Gravitation
2
Vt
CENTRIPETAL ACCELERATION
ac=~
CENTRIPETAL FORCE
Fe= mvt
r
2
NEWTON'S LAW OF UNIVERSAL
GRAVITATION
The constant of universal gravitation (G) equals
6.673x 10- 11 N·m 2!kg2.
KEPLER'S LAWS OF
PLANETARY MOTION
Fg= Gmlm2
r2
First Law: Each planet travels in an
elliptical orbit around the sun, and
the sun is at one of the focal points.
Second Law: An imaginary line
drawn from the sun to any planet
sweeps out equal areas in equal time
intervals.
Third Law: The square of a planet's
orbital period ( T 2 ) is proportional
to the cube of the average distance
( r 3 ) between the planet and the sun,
or T 2 oc r 3.
PERIOD AND SPEED OF AN OBJECT
IN CIRCULAR ORBIT
T~21C.jfm
6.673X 10
The constant of universal gravitation (G) equals
11
N•m 2 /kg 2 .
v,~fcS
TORQUE
r= Fdsin ()
Appendix D: Equations
85 7
MECHANICAL ADVANTAGE
This equation disregards friction.
EFFICIENCY
This equation accounts for friction.
Chapter 8
MA =Pout- din
F· --d
m
out
eft=
Wout
Win
Fluid Mechanics
m
MASS DENSITY
p =-
BUOYANT FORCE
FE= Fg (displaced fluid)= mfg
The first equation is for an object that is
completely or partially submerged. The second
equation is for a floating object.
FE= Fg(object) = mg
PRESSURE
F
P=-
v
A
PASCAL'S PRINCIPLE
Pressure applied to a fluid in a closed
container is transmitted equally to
every point of the fluid and to the
walls of the container.
HYDRAULIC LIFT EQUATION
F2 =-F1
Al
FLUID PRESSURE AS A FUNCTION
P=Po+ pgh
A2
OF DEPTH
CONTINUITY EQUATION
A 1v 1 =A2 v2
BERNOULLI'S PRINCIPLE
The pressure in a fluid decreases as
the fluid's velocity increases.
Chapter 9
Heat
TEMPERATURE CONVERSIONS
9
Tp= 5Tc+ 32.0
T= Tc+273.15
858
Appendix D: Equations
,
CONSERVATION OF ENERGY
L1PE + L1KE + L1 U = 0
SPECIFIC HEAT CAPACITY
Q
Cp = mi1T
CALORIMETRY
Qw=-Qx
These equations assume that the energy transferred
to the surrounding container is negligible.
Cp,wmwi1Tw = -cp,xmxi1Tx
LATENT HEAT
Q =mL
Chapter 10
Thermodynamics
WORK DONE BY A GAS
This equation is valid only when the pressure is
constant. When the work done by the gas (W) is
negative, positive work is done on the gas.
W= PAd= PL1V
THE FIRST LAW OF
THERMODYNAMICS
i1U= Q - W
Q represents the energy added to the system as heat
and W represents the work done by the system.
CYCLIC PROCESSES
L1Unet= 0 and Qnet= Wnet
EFFICIENCY OF A HEAT ENGINE
eff = Wnet = Qh - Qc = 1 _ Qc
Qh
Chapter 11
Qh
Qh
Vibrations and Waves
HOOKE'S LAW
Felastic= - kx
PERIOD OF A SIMPLE PENDULUM IN
SIMPLE HARMONIC MOTION
This equation is valid only when the amplitude is
small (less than about 15°).
T=2rcjf
IN SIMPLE HARMONIC MOTION
T=2rcj¥
SPEED OF A WAVE
v=JA-
PERIOD OF A MASS-SPRING SYSTEM
Appendix D: Equations
859
Chapter 12
Sound
p
INTENSITY OF A SPHERICAL WAVE
J
This equation assumes that there is no absorption
in the medium.
intensity= nr2
HARMONIC SERIES OF A VIBRATING
v
fn = n- n = 1, 2, 3, ...
2L
STRING OR A PIPE OPEN AT BOTH
4
l
ENDS
HARMONIC SERIES OF A PIPE
CLOSED AT ONE END
v
fn = n L
BEATS
frequency difference = number of
beats per second
Chapter 13
n = 1, 3, 5, ...
4
Light and Reflection
SPEED OF ELECTROMAGNETIC
WAVES
c=fA
8
This book uses the value c = 3.00 x 10 m/s for the
speed of EM waves in a vacuum or in air.
LAW OF REFLECTION
~
angle of incidence ((}) = angle of
reflection ((}')
MIRROR EQUATION
This equation is derived assuming that the rays
incident on the mirror are very close to the
principal axis of the mirror.
MAGNIFICATION OF A CURVED
MIRROR
Chapter 14
Appendix D: Equations
1
1
h'
!i
M=-,;=- p
Refraction
INDEX OF REFRACTION
860
1
-+-=p q f
For any material other than a vacuum, the index
of refraction varies with the wavelength of light.
c
n=v
SNELL'S LAW
ni
sin
(}i
= nr sin
Br
THIN-LENS EQUATION
This equation is derived assuming that the
thickness of the lens is much less than the focal
length of the lens.
1
1
1
- +-=-
p
MAGNIFICATION OF A LENS
This equation can be used only when the index of
refraction of the first medium (nJ is greater than
the index of refraction of the second medium (nr)·
f
q
h'
h
q
p
M=-=-- (forni>nr)
CRITICAL ANGLE
This equation can be used only when the index of
refraction of the first medium (nJ is greater than
the index of refraction of the second medium (nr)·
Chapter 15
sin
ec=nrn-· (for ni > nr)
l
Interference and Diffraction
CONSTRUCTIVE AND DESTRUCTIVE
INTERFERENCE
The grating spacing multiplied by the sine of the
angle of deviation is the path difference between
two waves. To observe interference effects, the
sources must be coherent and have identical
wavelengths.
Constructive Interference:
dsin B=±mAm = 0, 1, 2, 3, . ..
Destructive Interference:
dsin B =±(m+~)A
m = 0, 1, 2, 3, ...
DIFFRACTION GRATING
See the equation above for
constructive interference.
LIMITING ANGLE OF RESOLUTION
e = 1.22-A.
This equation gives the angle e in radians and
applies only to circular apertures.
Chapter 16
D
Electric Forces and Fields
COULOMB'S LAW
This equation assumes either point charges or
spherical distributions of charge.
ELECTRIC FIELD STRENGTH DUE
TO A POINT CHARGE
7qlq2)
Felectric= kc (
q
E=kc2
r
Appendix D: Equations
861
Chapter 17
I
Electrical Energy and Current
ELECTRICAL POTENTIAL ENERGY
The displacement, d, is from the reference point
and is parallel to the field. This equation is valid
only for a uniform electric field.
PEezectric = -qEd
POTENTIAL DIFFERENCE
The second half of this equation is valid only for a
uniform electric field, and !1d is parallel to the
field.
!J. v = MEelectric = -E!J.d
q
POTENTIAL DIFFERENCE BETWEEN A
POINT AT INFINITY AND A POINT
q
r
!J. V= kc-
NEAR A POINT CHARGE
CAPACITANCE
c = _g_
!J.V
CAPACITANCE FOR A PARALLELPLATE CAPACITOR IN A VACUUM
The permittivity in a vacuum (co) equals
8.85x 10-12 C 2!(N· m2).
A
c =cod
j
ELECTRICAL POTENTIAL ENERGY
STORED IN A CHARGED CAPACITOR
. -
1
2
1
2C
There is a limit to the maximum energy (or
charge) that can be stored in a capacitor because
electrical breakdown ultimately occurs between
the plates of the capacitor for a sufficiently large
potential difference.
ELECTRIC CURRENT
I= !J.Q
!J.t
RESISTANCE
R=!J.V
I
OHM'S LAW
Ohm's law is not universal, but it does apply to
many materials over a wide range of applied
potential differences.
!J.V
-=constant
ELECTRIC POWER
P = I!J. V = I2R = (!J. V)
I
2
R
862
Appendix D: Equations
Q2
PEelectnc - 2Q!J. V = 2C (!J. V) = -
Chapter 18
Circuits and Circuit Elements
RESISTORS IN SERIES:
EQUIVALENT RESISTANCE
AND CURRENT
RESISTORS IN PARALLEL:
EQUIVALENT RESISTANCE
AND CURRENT
Chapter 19
Req = R 1 + R2 + R3 ...
The current in each resistor is the
same and is equal to the total current.
1
1
1
Req
R1
R2
1
-=-+-+-
R3 ...
The sum of the current in each
resistor equals the total current.
Magnetism
<PM= AB cos ()
MAGNETIC FLUX
MAGNITUDE OF A MAGNETIC FIELD
The direction ofFmagnetic is always perpendicular
to both B and v, and can be found with the righthand rule.
FORCE ON A CURRENT-CARRYING
CONDUCTOR PERPENDICULAR TO
B
Fmagnetic
qv
Fmagnetic= BI f
A MAGNETIC FIELD
This equation can be used only when the current
and the magnetic field are at right angles to each
other.
Chapter 20
Electromagnetic Induction
FARADAY'S LAW OF MAGNETIC
INDUCTION
emf = _ NL1<PM
11t
N is assumed to be a whole number.
EMF PRODUCED BY A GENERATOR
emf= NAB OJ sin mt
N is assumed to be a whole number.
maximum emf= NABOJ
FARADAY'S LAW FOR MUTUAL
INDUCTANCE
emf=-M/11
11t
Appendix D: Equations
863
RMS CURRENT AND POTENTIAL
Imax = 0.707 Imax
\12
Irms=
DIFFERENCE
~Vrms=
TRANSFORMERS
N2
~V2=-~Vl
N is assumed to be a whole number.
Chapter 21
~Vmax=
\12 0.707 ~V
Nl
Atomic Physics
ENERGY OF A LIGHT QUANTUM
E=hf
MAXIMUM KINETIC ENERGY
KEmax = hf- hft
OF A PHOTOELECTRON
WAVELENGTH AND FREQUENCY
h
h
p
mv
li = - = -
OF MATTER WAVES
34
Planck's constant (h) equals 6. 63 X 10- J•s.
E
f=h
Chapter 22
Subatomic Physics
RELATIONSHIP BETWEEN REST
ER = mc 2
ENERGY AND MASS
BINDING ENERGY OF A NUCLEUS
Ebind
MASS DEFECT
~m
=~mc
2
= Z( atomic mass of H)
+ Nmn- atomic mass
ACTIVITY (DECAY RATE)
..
~
activity=--= liN
~t
HALF-LIFE
864
Appendix D: Equations
T112
=
0.693
-li
j
Appendix J
Advanced Topics
CONVERSION BETWEEN RADIANS
n
AND DEGREES
8(rad) =-8(deg)
180°
ANGULAR DISPLACEMENT
118= !1s
This equation gives 118 in radians.
r
!18
AVERAGE ANGULAR VELOCITY
Wavg=M
AVERAGE ANGULAR ACCELERATION
aavg=--;;;
ROTATIONAL KINEMATICS
m1 = mi
These equations apply only when the angular
acceleration is constant. The symbol m represents
instantaneous rather than average angular velocity.
!1m
+ a!J.t
!18 = mi!J.t + ~a(!1t)
m/ = m?
2
+ 2a(!18)
1
!18 = 2( mi + mf)!J.t
TANGENTIAL SPEED
Vt= rm
For this equation to be valid, m must be in rad/s.
TANGENTIAL ACCELERATION
at= ra
For this equation to be valid, a must be in rad!s 2.
NEWTON'S SECOND LAW FOR
r=Ia
ROTATING OBJECTS
ANGULAR MOMENTUM
L=Im
ROTATIONAL KINETIC ENERGY
KErot=im
IDEAL GAS LAW
PV=NkBT
1
2
Boltzmann's constant (kB) equals 1.38 x 10-23 J/K.
BERNOULLI'S EQUATION
p + ~pv 2 + pgh =constant
Appendix D: Equations
865
~
SI Units
Sl Base Units Used in This Book
Sl Prefixes
Symbol
Name
Quantity
A
ampere
current
a
atto
10-18
K
kelvin
absolute temperature
f
femto
10-15
kg
kilogram
mass
p
pico
10-12
m
meter
length
time
n
nano
10-9
second
~
micro
10-6
m
milli
10-3
c
centi
10-2
d
deci
10-1
k
kilo
10 3
M
mega
106
G
giga
109
T
tera
1012
p
peta
1015
E
exa
1018
Symbol
Name
Numerical equivalent
j
I
J
Other Commonly Used Units
Symbol
Name
Quantity
atm
standard atmosphere
pressure
Btu
British thermal unit
energy
1.013 250 X 10 5 Pa
1.055 X 10 3 J
Cal
food calorie
energy
= 1 kcal = 4.186 x 103 J
cal
calorie
energy
4.186
Ci
curie
decay rate or activity
3.7 x 10 10 s- 1
op
degree Fahrenheit
temperature
0.5556°C
ft
foot
length
0.3048 m
ft · lb
foot-pound
work and energy
1.356 J
g
gram
mass
0.001 kg
gal
gallon
volume
3.785 x 10-3 m 3
hp
horsepower
power
746W
in
inch
length
2.54 x 10-2 m
kcal
kilocalorie
energy
4.186
lb
pound
force
4.45 N
mi
mile
length
1.609 x 10 3 m
rev
revolution
angular displacement
2nrad
0
degrees
angular displacement
Appendix E: Sl Units
Conversions
=(
I
J
X
!
10 3 J
2'360:.) rad =
I. 745 x
w-2 rad
Other Units Acceptable with Sl
Symbol
Name
Quantity
Conversion
Bq
becquerel
decay rate or activity
c
oc
coulomb
electric charge
degree Celsius
temperature
1K
dB
decibel
relative intensity (sound)
(unitless)
eV
electron volt
energy
1.60 X 10- 19 J
F
farad
capacitance
H
henry
inductance
A2•s4
c
1--=
12
V
kg•m
2
kg•m
J
1--=1A2•s2
A2
h
hour
time
Hz
hertz
frequency
1 A•s
3.600 X 10 3 S
s
joule
work and energy
2
kg•m
1 - 2--= 1 N•m
s
kW•h
kilowatt-hour
energy
3.60 X 10
L
liter
volume
10-3m3
min
minute
time
6.0x 10 1 s
N
newton
force
kg•m
1-s2
Pa
pascal
pressure
kg
N
1 - -2= 1 -2
m•s
m
-6
J
-
rad
radian
angular displacement
(unitless)
T
tesla
magnetic field strength
u
unified mass unit
mass (atomic masses)
kg
N
V •s
1 - -2= 1 - - = 1 A•s
A•m
m2
1.660 538 86 X 10-2? kg
v
volt
electric potential difference
w
watt
power
Q
ohm
resistance
2
kg•m
J
1 - -3= 1 A•s
C
2
kg•m
J
1-=
1s3
s
--2
V
kg•m
1 -2- =
13
A •s
A
Appendix E: Sl Units
867
Useful Tables
Fundamental Constants
Symbol
Quantity
Established value
Value used for
calculations in this book
c
speed of light in a vacuum
299 792 458 m/s
3.00 x 10 8 m/s
e
elementary charge
1.602 176 53
e1
base of natural logarithms
2.718 2818 28
X
1.60 X 10- 19 C
10- 19 C
2.72
12
2
2
8.85 x 10- 12 C2 /(N •m 2 )
eo
(Greek epsilon) permittivity of
a vacuum
8.854187 817 x 10-
G
constant of universal gravitation
6.672 59 X 10-ll N•m 2 /kg 2
6.673
g
free-fall acceleration
at Earth's surface
9.806 65 m/s 2
9.81 m/s 2
h
Planck's constant
6.626 0693 x 10-34 J • s
6.63 x 10-34 J •s
kB
Boltzmann's constant (RINA)
1.380 6505
10-23 J/K
1.38 X 10-23 J/K
kc
Coulomb constant
8.987 551 787 x 109 N · m 2;c
R
molar (universal) gas constant
8.314 472 J/(mol• K)
8.31 J/(mol •K)
n
(Greek pi) ratio of the circumference to the diameter of a circle
3.141 592 654
calculator value
X
C /(N •m
2
)
X
10-ll N•m 2 /kg 2
8.99 x 109 N •m 2/C 2
Coefficients of Friction (Approximate Values)
l's
l'k
l's
steel on steel
0.74
0.57
waxed wood on wet snow
aluminum on steel
0.61
0.47
waxed wood on dry snow
rubber on dry concrete
1.0
0.8
metal on metal (lubricated)
0.14
l'k
0.1
0.04
0.15
0.06
rubber on wet concrete
-
0.5
ice on ice
0.1
0.03
wood on wood
0.4
0.2
Teflon on Teflon
0.04
0.04
glass on glass
0.9
0.4
synovial joints in humans
0.01
0.003
Useful Astronomical Data
Symbol
Quantity
Value used for
calculations in this book
IE
moment of inertia of Earth
8.03 x 10 37 kg•m 2
ME
mass of Earth
5.97 X 1024 kg
RE
radius of Earth
6.38 x 106 m
Average Earth-moon distance
3.84 x 108 m
Average Earth-sun distance
1.50 X 10 11 m
mass of the moon
7.35
mass of the sun
1.99 X 10 30 kg
period of Earth's orbit
3.16 X 10 7 S
yr
Appendix F: Useful Tables
X
10 22 kg
The Moment of Inertia for a Few Shapes
Shape
Moment of inertia
thin hoop about
symmetry axis
MR 2
thin hoop about
diameter
2
I.MR
2
point mass about axis
MR 2
disk or cylin~er about
symmetry ax1s
I_MR2
Shape
gt~
~
thin rod about
perpendicular axis
through center
_!_M/'2
I
thin rod about
perpendicular axis
through end
I.Mf 2
solid sphere
about diameter
5MR
thin spherical shell
about diameter
'?:.MR 2
~I
2
Densities of Some Common
Substances*
Substance
p (kg/m
hydrogen
Moment of inertia
12
3
2
2
3
Specific Heat Capacities
3
Substance
Cp
0.0899
aluminum
8.99 X 102
helium
0.179
copper
3.87 X 102
steam (100°C)
0.598
glass
8.37 X 10 2
air
1.29
gold
1.29 X 10 2
oxygen
1.43
carbon dioxide
1.98
ice
2.09 X 10 3
ethanol
0.806 X 10 3
iron
4.48 X 10 2
ice
0.917 X 10 3
lead
1.28 X 10 2
fresh water (4°C)
1.00 X 10 3
mercury
1.38 X 10 2
sea water (15°C)
1.025 X 10 3
silver
2.34 X 10 2
glycerine
1.26 X 10 3
steam
2.01 X 10 3
aluminum
2.70 X 10 3
water
4.186 X 10 3
iron
7.86 X 10 3
copper
8.92 X 10 3
silver
10.5 X 10 3
lead
11.3 X 10 3
mercury
13.6 X 10 3
gold
19.3 X 10 3
)
(J/kg • °C)
"All densities are measured at 0°C and 1 atm unless otherwise noted.
Appendix F: Useful Tables
869
Latent Heats of Fusion and Vaporization at Standard Pressure
Substance
L1 (J/kg)
Melting point (OC)
Boiling point (OC)
Lv (J/kg)
4
-195.81
2.01
10 5
nitrogen
-209.97
2.55 X 10
oxygen
-2 18.79
1.38 X 104
-182.97
2.13 X 10 5
ethyl alcohol
-114
1.04 X 10 5
78
8.54 X 10 5
water
0.00
3.33
100.00
2.26 X 106
lead
327.3
2.45 X 104
1745
8.70 X 10 5
aluminum
660.4
3.97 X 10 5
2467
1.14 X 10 7
X
10 5
X
Speed of Sound in Various Media
Medium
v(m/s)
Gases
air (0°C)
331
Medium
v(m/s)
Liquids at 25°C
methyl alcohol
Medium
1140
Solids
aluminum
5100
air (25°C)
346
sea water
1530
copper
3560
air (100°C)
366
water
1490
iron
5130
lead
1320
helium (0°C)
hydrogen (0°C)
oxygen (0°C)
972
1290
vulcanized rubber
Intensity (W/m 2 )
Decibel level (dB)
Examples
1.0 X 10- 12
0
1.0 X 10-ll
10
rustling leaves
1.0
X 10- 10
20
quiet whisper
1.0
X 10- 9
30
whisper
1.0 X 10-S
40
mosquito buzzing
1.0 X 10-7
50
normal conversation
1.0 X 10- 6
60
air conditioning at 6 m
1.0 X 10-5
70
vacuum cleaner
1.0 X 10- 4
80
busy traffic, alarm clock
1.0 X 10-3
90
lawn mower
2
100
subway, power motor
1
110
auto horn at 1 m
1.0 X 10°
120
threshold of pain
1.0 X 10
1
130
thunderclap, machine gun
1.0 X 10
3
150
nearby jet airplane
1.0 X 101.0 X 10-
I
54
317
Conversion of Intensity to Decibel Level
870
v(m/s)
Appendix F: Useful Tables
l
threshold of hearing
I
1
Indices of Refraction for Various Substances*
Solids at 20°C
n
Liquids at 20°C
n
cubic zirconia
2.20
benzene
1.501
diamond
2.419
carbon disulfide
1.628
fluorite
1.434
carbon tetrachloride
1.461
fused quartz
1.458
ethyl alcohol
1.361
glass, crown
1.52
glycerine
1.473
glass, flint
1.66
water
1.333
ice (at 0°C)
1.309
polystyrene
1.49
sodium chloride
1.544
zircon
1.923
Gases at
ooc,
1 atm
n
air
1.000 293
carbon dioxide
1.000 450
--
*measured with light of vacuum wavelength= 589 nm
Useful Atomic Data
Symbol
Quantity
Established value
Value used for calculations
in this book
me
mass of electron
9.109 3826 X 10-3 1 kg
5.485 799 0945 X 10-4 u
0.510 998 918 MeV
9.109 X 10-31 kg
5.49 X 10-4 U
5.110 x 10- 1 MeV
mn
mass of neutron
1.674 927 28 X 10- 27 kg
1.008 664 915 60 u
939.565 360 MeV
1.675 X 10-27 kg
1.008 665 u
9.396 X 102 MeV
mp
mass of proton
1.672 621 71 X 10-27 kg
1.007 276 466 88 u
938.272 029 MeV
1.673 X 10-27 kg
1.007 276 u
9.383 X 10 2 MeV
Appendix F: Useful Tables
871
Periodic Table of the Elements
J
1
H
Key:
Hydrogen
1.007 94
1s 1
n
---
Atomic number
Group 1
Group 2
3
4
21
Li
I
u•;,m
6.941
I
c
Symbol
Carbon ~
Name
Be
Beryllium
9.012182
2
[He~
6
~
r~;i~~~;)
Average atomic mass
Electron configuration
I
11
Na
31
11
Sodium
22.989 770
[Ne)3s 1
I
I
41
1
L .;.!!!Jj
19
20
K
Ca
J
Group 3
, ~21Sc
:I
i
Potassium
39.0983
Group 4
Group 5
22
23
I
Ti
Scandium
44.955 910
IArJ3d14s2
[Ar~
v
Group 7
Group 6
.I
Cr
I Mn
Group 8
25
24
i
I Fe
26
l
Group 9
il
~
27
Co
I
37
Rb
51
Rubidium
85.4678
[Kr)5s 1
38
I
Sr
...
~
55
61
71
...
_.
_1
I
Cs
Ba
Cesium
132.905 43
[Xej6sl
Barium
137.327
(Xe)6s2
88
Fr
Ra
Francium
(223)
[Rn)7s 1
Radium
(226)
_1
I
l""J--
57
56
87
,--·- --
j
I
,.-,.- --
La
Hf
Ta
Hafnium
178.49
Tantalum
180.9479
(Xe)4f'45d~2
(Xe)4f'4stf~2
-
_1
I
73
72
lanthanum
138.9055
(Xe)5d 16s2
li'
$,2
'
104
105
Ac
Rf
Db
Actinium
(227}
(Rn)6d 17s 2
Rutherfordium
(261}
[Rn)Sf14&# 27s2
Dubnium
(262}
[Rn)5f 1 4&d~s2
1
,....._ ., ..
_1
I
,..... _-
cj
I
~·-··--
_1
I
,.... ,._-
_j
74
I
I
106
107
Sg
Bh
Seaborgium
(266)
(Rn)5f14/s 2
Bohrium
(264)
(Rn)S f 14Js 2
J
108
j
~
109
Hs
Mt
Hassium
(277)
[Rn)5f 14&f'7s 2
Meitnerium
(268)
(Rn)Sf14&# 77s 2
* The systematic names and symbols
for elements greater than 11 0 will
be used until the approval of trivial
names by IUPAC.
I
58
59
60
61
62
Ce
Pr
Nd
Pm
Sm
Cerium
140.116
(Xe)4 f'S!t'~2
•.
"'.
Visit the HRW Web site for updates
on the periodic table.
"'~
872
~~~-"""' ---~~
-
~
-.......-
90
'·
\..
,•_....._...,
Appendix G: Periodic Table of the Elements
I
Th
Thoriurr
J
PraseodymitJn
140.907 65
(Xe)4fl&s2
j
Neodymium
144.24
(Xe)4f4&s2
j
Promethium
(145)
. [Xe)4f5fis2
J
Samanurr,
150.36
[Xe~f'is2
J
J
Hydrogen
Semiconductors
(also known as metalloids)
Group 18
2
Metals
Alkali metals
Alkaline-earth metals
Transition metals
Other metals
He
Helium
4.002 602
Group 13
Nonmetals
Halogens
Noble gases
Other nonmetals
B
Boron
~~~~·
Group 14
Group 12
Group 11
28
29
Ni
Cu
46
47
I
30
Zn
Pd
1
I
Carbon
14
Si
Aluminum
Silicon
26.98~ 5~8 J 28.0~5~3p
[NeJ3s 3p
[NeJ3s
.
Ga i
I
~
Auorine
'
50
51
Sn
Sb
Tin
118.710
(Kr)4tf105sl5p2
Antimony
121.760
[KrJ4d'ossl5pJ
I
I
33
As
49
18
34
Se ,
Ne
Neon
32
~~
17
18
Cl
Ar
Chlorine
35.4535
Argon
39.948,
(Ne)3sl]p
I
uz
35
Br
f
53
J
I
I
I
lNells~
36
Kr
54
Xe
Xenon
131.293
(Krl4d"Ss~
I
85
At
W"
II
86
Rn
Gold
966 55
~''6s'
[XeJ4f'~'
Ds
I
32
Ge
Au
Platinum
195.078
ji
l l l6 J
80
Pt
Darmstadtium
(281)
1Rnl5f'4&1'7s'
15
I
In
(Kr)4d~
110
Oxygen
Group 17
I P . S
Phosphorus
·
Sulfur
J . 30.973..761__ , ' '·'' 3~ .• ':·
.;.: •!~~
48
Palladium
106.42
78
l0
N
Nitrogen
Cd
I
Group 16
I i;l +,i~J.tflOI",:':1 "i l'~~-i ;·-~,ilfm.~ ~,!>s
AI
31
t
C
1
I
13
Group 10
Group 15
j
111
Uuu*
Unununium
(272)
(Rn)5f14&# 107s 1
A team at Lawrence Berkeley National Laboratories reported the discovery of elements 116 and 118 in June 1999.
The same team retracted the discovery in July 2001. The discovery of elements 113, 114, and 115 has been reported but not confirmed.
63
i
Eu '
95
Am
~
{243)
(Rn)5f7s2
64
65
Gd
Tb
Gadolinium
157.25
[Xe)4f5d'6sz
Terbium
158.925 34
txeJ41'&s2
96
l;
i
97
Cm
Bk
1Rn)Sf76d17s2
(Rn)5f'7s 2
~
~ ~
{247)
{247)
I
1
j
66
Dy
67
I
Ho I
68
69
70
Er
Tm
Yb
Erbium
167.259
[Xe)4fl'fs2
Thulium
168.934 21
[Xel4f'36f2
Ytterbium
173.04
[Xe)41'46f2
101
102
Dysprosium
162.500
(Xe)4110fisl
Holmium
164.930 32
(Xe)41n6Sz
98
99
Cf
Es
Fm
Md
No
. (Rn)Sf...,s2
{Rn)Sf117s1
(Rn)51'~s2
[RnJ5f'7s 2
(Rn)5f'fJs2
I
~
j ~
j
{251)
{252)
100
I
~
j ~
j ~
{257)
{258)
{259)
I~1
Lu
Lutetium
174.967
[Xe)41'~'6sz
l~
I
103
Lr
{262)
(Rn)5f1"6d17s 2
The atomic masses listed in this table reflect the precision of current measurements. (Values
listed in parentheses are those of the element's most stable or most common isotope.)
Appendix G: Periodic Table of the Elements
873
Abbreviated Table of Isotopes and
Atomic Masses
Z
0
2
Element
Symbol
(Neutron)
n
Hydrogen
Deuterium
Tritium
H
D
T
Helium
He
Average
atomic
mass (u)
Mass number
( * indicates
Atomic
mass (u)
Percent
abundance
radioactive) A
10.4 m
1*
1.008 665
1.0079
1
2
3*
1.007 825
2.014 102
3.016 049
99.985
0.015
4.002 60
3
4
6*
3.016 029
4.002 602
6.018 886
0.000 14
99.999 86
7.5
92.5
3
Lithium
Li
6.941
6
7
6.015 121
7.016 003
4
Beryllium
Be
9.0122
7*
8*
9
10*
7.016 928
8.005 305
9.012 174
10.013 584
12.33 y
0.81 s
53.3 d
6.7 X 10-l ? S
100
5
Boron
B
10.81
10
11
10.012 936
11.009 305
6
Carbon
c
12.011
10*
11 *
12
13
14*
10.016 854
11.011433
12.000 000
13.003 355
14.003 242
13*
14
15
16*
13.005 738
14.003 074
15.000 108
16.006 100
99.63
0.37
15*
16
17
18
19*
15.003 065
15.994 915
16.999 132
17.999 160
19.003 577
99.761
0.039
0.200
18*
19
20*
18.000 937
18.998 404
19.999 982
100
19*
20
21
22
19.001 880
19.992 435
20.993 841
21.991 383
22*
23
24*
21.994 434
22.989 767
23.990 961
23*
24
25
26
22.994 124
23.985 042
24.985 838
25.982 594
78.99
10.00
11.01
26*
27
25.986 892
26.981 534
100
7
8
9
Nitrogen
Oxygen
Fluorine
10 Neon
11 Sodium
12 Magnesium
13 Aluminum
N
0
F
Ne
Na
Mg
Al
14.0067
15.9994
18.998 40
20.180
22.989 87
24.305
26.981 54
Appendix H: Abbreviated Table of Isotopes and Atomic Masses
Half-life
(if radioactive)
T 112
1.5 X 106 y
19.9
80.1
19.3 s
20.4m
~
'
98.9
1.10
5715 y
996m
7.13 s
122 s
26.9 s
109.8 m
1l.Os
17.2 s
90.48
0.27
9.25
2.61 y
100
14.96 h
11.3s
7.4 X 10 5 y
~
Z
Element
Symbol
Average
atomic
mass (u)
Mass number
( * indicates
Atomic
mass (u)
Percent
abundance
radioactive) A
T112
14 Silicon
Si
28.086
28
29
30
27.976 927
28.976 495
29.973 770
92.23
4.67
3.10
15 Phosphorus
p
30.973 76
30*
31
32*
29.978 307
30.973 762
31.973 907
100
32
33
34
35*
31.972 071
32.971 459
33.967 867
34.969 033
95.02
0.75
4.21
75.77
16 Sulfur
s
32.066
2.50m
14.263 d
87.5 d
17 Chlorine
Cl
35.453
35
36*
37
34.968 853
35.968 307
36.975 893
18 Argon
Ar
39.948
36
37*
38
39*
40
35.967 547
36.966 776
37.962 732
38.964 314
39.962 384
0.337
35.04 d
0.063
269 y
99.600
K
39.0983
39
40*
41
38.963 708
39.964 000
40.961 827
93.2581
0.0117
6.7302
20 Calcium
Ca
40.08
40
41 *
42
43
44
39.962
40.962
41.958
42.958
43.955
96.941
41*
45
40.969 250
44.955 911
100
44*
47
48
43.959 691
46.951 765
47.947 947
7.3
73.8
22 Titanium
Sc
Ti
44.9559
47.88
591
279
618
767
481
60y
50.9415
50*
51
49.947 161
50.943 962
0.25
99.75
24 Chromium
Cr
51.996
48*
52
53
47.954 033
51.940 511
52.940 652
83.79
9.50
54*
55
53.940 361
54.938 048
100
54
55*
56
53.939 613
54.938 297
55.934 940
5.9
26 Iron
Fe
54.938 05
55.847
l.Oxl0 5 y
0.596 s
v
Mn
1.28 X 109 y
0.647
0.135
2.086
23 Vanadium
25 Manganese
3.0xl0 5 y
24.23
19 Potassium
21 Scandium
Half-life
(if radioactive)
1.5 X 10 17 y
21.6 h
312.1 d
2.7y
91.72
27 Cobalt
Co
58.933 20
59
60*
58.933 198
59.933 820
100
28 Nickel
Ni
58.793
58
59*
60
57.935 345
58.934 350
59.930 789
68.077
5.27y
7.5xl0 4 y
26.223
29 Copper
Cu
63.54
63
65
62.929 599
64.927 791
69.17
30.83
30 Zinc
Zn
65.39
64
66
67
68
63.929 144
65.926 035
66.927 129
67.924 845
48.6
27.9
4.1
18.8
Appendix H: Abbreviated Table of Isotopes and Atomic Masses
875
Z
Element
Symbol
Average
atomic
mass (u)
Mass number
( * indicates
radioactive) A
Percent
abundance
31 Gallium
Ga
69.723
69
71
68.925 580
70.924 703
60.108
39.892
32 Germanium
Ge
72.61
70
72
73
74
76
69.924 250
71.922 079
72.923 462
73.921 177
75.921402
21.23
27.66
7.73
35.94
7.44
33 Arsenic
As
74.9216
75
74.921 594
100
34 Selenium
Se
78.96
76
77
78
80
82*
75.919 212
76.919 913
77.917 397
79.916 519
81.916 697
9.36
7.63
23.78
49.61
8.73
50.69
49.31
35 Bromine
Br
79.904
79
81
78.918 336
80.916 287
36 Krypton
Kr
83.80
81*
82
83
84
85*
86
80.916 589
81.913 481
82.914 136
83.911 508
84.912 531
85.910 615
85
87*
84.911 793
86.909 186
72.17
27.83
86
87
88
9.86
7.00
82.58
90*
85.909 266
86.908 883
87.905 618
89.907 737
37 Rubidium
38 Strontium
Rb
Sr
85.468
87.62
89
88.905 847
100
91.224
90
91
92
93*
94
89.904 702
90.905 643
91.905 038
92.906 473
93.906 314
51.45
11.22
17.15
93
94*
92.906 376
93.907 280
100
92
93*
94
95
96
97
98
100
91.906 807
92.906 811
93.905 085
94.905 841
95.904 678
96.906 020
97.905 407
99.907 476
14.84
97*
96.906 363
97.907 215
98.906 254
Mo
95.94
Tc
98*
99*
I
4.75
X
10
10
1.5 X 10 6 y
17.38
2 X 104 y
y
~
f
~
3.5 X 10 3 y
9.25
15.92
16.68
9.55
24.13
9.63
2.6 X 106 y
4.2 X 106 y
2.1 X 10 5 y
44 Ruthenium
Ru
101.07
99
100
101
102
104
98.905 939
99.904 219
100.905 558
101.904 348
103.905 558
12.7
12.6
17.1
31.6
18.6
45 Rhodium
Rh
102.9055
103
102.905 502
100
Appendix H: Abbreviated Table of Isotopes and Atom ic M asses
10 5 y
29.1 y
88.9058
42 Molybdenum
X
10.76 y
Zr
92.9064
1.4 X 1020 y
17.3
40 Zirconium
Nb
T 1;2
2.1
y
41 Niobium
Half-life
(if radioactive)
11.6
11.4
57.0
39 Yttrium
43 Technetium
876
Atomic mass
(u)
4
~
Z
Element
Symbol
Average
atomic
mass (u)
Mass number
( * indicates
radioactive) A
Atomic mass
(u)
Percent
abundance
46 Palladi urn
Pd
106.42
104
105
106
108
110
103.904 033
104.905 082
105.903 481
107.903 898
109.905 158
11.14
22.33
27.33
26.46
11.72
47 Silver
Ag
107.868
107
109
106.905 091
108.904 754
51.84
48.16
48 Cadmium
Cd
112.41
109*
110
111
112
113*
114
108.904 984
109.903 004
110.904 182
111.902 760
112.904 401
113.903 359
12.49
12.80
24.13
12.22
28.73
113
115*
112.904 060
114.903 876
4.3
95.7
116
117
118
119
120
121*
115.901 743
116.902 953
117.901 605
118.903 308
119.902 197
120.904 237
14.53
7.58
24.22
8.58
32.59
49 Indium
50 Tin
In
Sn
114.82
118.71
121.76
121
123
120.903 820
122.904 215
57.36
42.64
52 Tellurium
Te
127.60
125
126
128*
130*
124.904 429
125.903 309
127.904 468
129.906 228
7.12
18.93
31.79
33.87
126.9045
127
129*
126.904 474
128.904 984
100
131.29
129
131
132
134
136*
128.904 779
130.905 069
131.904 141
133.905 394
135.907 214
26.4
21.2
26.9
10.4
8.9
100
54 Xenon
Xe
9.3 X 10 15 y
4.4 X 10 14 y
55 y
Sb
I
T 1; 2
462 d
51 Antimony
53 Iodine
Half-life
(if radioactive)
55 Cesium
Cs
132.9054
133
135*
137*
132.905 436
134.905 891
136.907 078
56 Barium
Ba
137.33
133*
137
138
132.905 990
136.905 816
137.905 236
11.23
71.70
24
> 8 X 10 Y.:
< 1.25 X 10 21 y
1.6Xl0 7 y
> 2.36 X 10 21 y
2 X 10 6 y
30 y
10.5 y
57 Lanthanum
La
138.905
138*
139
137.907 105
138.906 346
0.0902
99.9098
58 Cerium
Ce
140.12
138
140
142*
137.905 986
139.905 434
141.909 241
0.25
88.43
11.13
59 Praseodymium
Pr
140.9076
141
140.907 647
100
60 Neodymium
Nd
144.24
142
143
144*
145
146
141.907 718
142.909 809
143.910 082
144.912 568
145.913 113
27.13
12.18
23.80
8.30
17.19
1.05 X 10 11 y
>5Xl0 16 y
2.3 X 10 15 y
Appendix H: Abbreviated Table of Isotopes and Atomic Masses
877
Z
878
Element
Symbol
61 Promethium
Pm
62 Samarium
Sm
63 Europium
Eu
Average
atomic
mass (u)
Mass number
( * indicates
radioactive) A
Atomic mass
(u)
Percent
abundance
145*
146*
144.912 745
145.914 968
150.36
147*
148*
149*
150
152
154
146.914 894
147.914 819
148.917 180
149.917 273
151.919 728
153.922 206
15.0
11.3
13.8
7.4
26.7
22.7
151.96
151
152*
153
150.919 846
151.921 740
152.921 226
47.8
14.80
20.47
15.65
24.84
21.86
64 Gadolinium
Gd
157.25
155
156
157
158
160
154.922 618
155.922 119
156.923 957
157.924 099
159.927 050
T112
17.7y
5.5 y
1.06 X lOlly
7 X 10 15 Y
>2x10 15 y
13.5 y
52.2
65 Terbium
Tb
158.9253
159
158.925 345
100
66 Dysprosium
Dy
162.5
161
162
163
164
160.926 930
161.926 796
162.928 729
163.929 172
18.9
25.5
24.9
28.2
67 Holmium
Ho
164.9303
165
164.930 316
100
68 Erbium
Er
167.26
166
167
168
170
165.930 292
166.932 047
167.932 369
169.935 462
33.6
22.95
27.8
14.9
69 Thulium
Tm
168.9342
169
171*
168.934 213
170.936 428
100
1.92 y
70 Ytterbium
Yb
173.04
171
172
173
174
176
170.936 324
171.936 379
172.938 209
173.938 861
175.942 564
14.3
21.9
16.12
31.8
12.7
71 Lutetium
Lu
174.967
175
176*
174.940 772
175.942 679
97.41
2.59
72 Hafnium
Hf
178.49
177
178
179
180
176.943 218
177.943 697
178.945 813
179.946 547
18.606
27.297
13.029
35.100
73 Tantalum
Ta
180.9479
181
180.947 993
99.988
74 Tungsten
w
183.85
182
183
184
186
181.948 202
182.950 221
183.950 929
185.954 358
26.3
14.28
30.7
28.6
75 Rhenium
Re
186.207
185
187*
184.952 951
186.955 746
37.40
62.60
76 Osmium
Os
190.2
188
189
190
192
187.955832
188.958 139
189.958 439
191.961 468
13.3
16.1
26.4
41.0
77 Iridium
Ir
192.2
191
193
190.960 585
192.962 916
37.3
62.7
Appendix H: Abbreviated Table of Isotopes and Atomic Masses
Half-life
(if radioactive)
3.78 X 10 10 y
4.4 X 10 10 y
Z
Element
78 Platinum
Symbol
Pt
Average
atomic
mass (u)
Mass number
( * indicates
radioactive) A
Atomic mass
(u)
Percent
abundance
32.9
33.8
25.3
195.08
194
195
196
193.962 655
194.964 765
195.964 926
79 Gold
Au
196.9665
197
196.966 543
100
80 Mercury
Hg
200.59
198
199
200
201
202
197.966 743
198.968 253
199.968 299
200.970 276
201.970 617
9.97
16.87
23.10
13.10
29.86
81 Thallium
Tl
204.383
203
204*
205
208*
202.972 320
203.073 839
204.974 400
207.981 992
29.524
Half-life
(if radioactive)
T 1; 2
3.78 y
70.476
3.053 m
82 Lead
Pb
207.2
206
207
208
212*
205.974 440
206.974 871
207.976 627
211.991 872
24.1
22.1
52.4
83 Bismuth
Bi
208.9803
209
212*
208.980 374
211.991 259
100
84 Polonium
Po
209*
212*
216*
208.982 405
211.988 842
216.001 889
102 y
0.30 flS
0.145 s
85 Astatine
At
218*
219*
218.008 685
219.01l 294
1.6s
0.9m
86 Radon
Rn
220*
222*
220.011 369
222.017 571
55.6 s
3.823 d
10.64 h
60.6m
87 Francium
Fr
223*
223.019 733
22m
88 Radium
Ra
224*
226*
228*
224.020 187
226.025 402
228.031 064
3.66 d
1.6X 10 3 y
5.75y
89 Actinium
Ac
227*
228*
227.027 701
228.028 716
18.72 y
1.913 y
90 Thorium
Th
232*
234*
232.038 051
234.043 593
91 Protactinium
Pa
231*
234*
231.035 880
234.043 300
92 Uranium
u
234*
235*
238*
234.040 946
235.043 924
238.050 784
93 Neptunium
Np
236*
237*
236.046 560
237.048 168
1.15 X 10 5 y
2.14 X 10 6 y
94 Plutonium
Pu
239*
244*
239.052 157
244.064 200
2.412 X 10 5 y
8.1 X 10 7 y
100
1.40 X 10 10 y
24.1 d
32.760 y
6.7h
0.0055
0.720
99.2745
2.46 X 10 5 y
7.04 X 10 8 y
4.47 X 10 9 y
Appendix H: Abbreviated Table of Isotopes and Atomic Masses
879
Additional Problems
Chapter 1 The S cience of Physics
1. Mt. Waialeale in Hawaii gets 1.168 x 10 3 em of
rainfall per year. Express this quantity in meters.
2. An acre is equal to about 4.0469 x 10 3 m 2.
Express this area in square kilometers.
4
3
3. A group drinks about 6.4 x 10 cm of water per
person per year. Express this in cubic meters.
16. A small rocket launched from rest travels
12.4 m upward in 2.0 s. What is the rocket's
net acceleration?
17. A jet slows uniformly from 153 km/h to 0 km/h
over 42.0 m. What is the jet's acceleration?
18. A softball thrown straight up at 17.5 m/s is
caught 3.60 slater. How high does the ball rise?
4. The largest stone jar on the Plain of Jars in Laos
has a mass of 6.0 x 10 3 kg. Express this mass in
milligrams.
19. A child, starting from rest, sleds down a snow-
5. Half of a sample of the radioactive isotope
beryllium-8 decays in 6.7 x 10-l? s. Express this
time in picoseconds.
20. A sky diver opens her parachute and drifts down
covered slope in 5.50 s. If the child's final speed
is 14.0 m/s, what the length of the slope?
for 34.0 s with a constant velocity of 6.50 m/s.
What is the sky diver's displacement?
21. In a race, a tortoise runs at 10.0 cm/s and a hare
Chapter 2 Motion in One Dimension
6. The fastest airplane is the Lockheed SR-71. If an
SR-71 flies 15.0 km west in 15.3 s, what is its
average velocity in kilometers per hour?
7. Except for a 22.0 min rest stop, Emily drives with
a constant velocity of 89.5 km/h, north. How
long does the trip take if Emilis average velocity
is 77.8 km/h, north?
8. A spaceship accelerates uniformly for 1220 km.
How much time is required for the spaceship to
increase its speed from 11.1 km/s to 11.7 km/s?
9. A polar bear initially running at 4.0 m/s accelerates uniformly for 18 s. If the bear travels 135m
in this time, what is its maximum speed?
10. A walrus accelerates from 7.0 km/h to 34.5 km/h
over a distance of 95 m. What is the magnitude
of the walrus's acceleration?
11. A snail can move about 4.0 min 5.0 min. What is
the average speed of the snail?
12. A crate is accelerated at 0.035 m!s 2 for 28.0 s
along a conveyor belt. If the crate's initial speed
is 0.76 m/s, what is its final speed?
13. A person throws a ball vertically and catches it
after 5.10 s. What is the balrs initial velocity?
14. A bicyclist accelerates -0.870 m!s 2 during a
3.80 s interval. What is the change in the velocity
of the bicyclist and bicycle?
15. A hockey puck slides 55.0 min 1.25 s with a uniform acceleration. If the puck's final speed is
43.2 m/s, what was its initial speed?
Appendix 1: Additional Problems
runs at 200.0 cm/s. Both start at the same time,
but the hare stops to rest for 2.00 min. The tortoise wins by 20.0 em. At what time does the
tortoise cross the finish line?
22. What is the length of the race in problem 21?
23. The cable pulling an elevator upward at 12.5 m/s
breaks. How long does it take for the elevator to
come to rest?
24. A disk is uniformly accelerated from rest for
0.910 s over 7.19 km. What is its final speed?
25. A tiger accelerates 3.0 m!s 2 for 4.1 s to reach a
final speed of 55.0 km/h. What was its initial
speed in kilometers per hour?
26. A shark accelerates uniformly from 2.8 km/h to
32.0 km/h in 1.5 s. How large is its acceleration?
27. The 1903 Wright flyer was accelerated at 4.88 m/s 2
along a track that was 18.3 m long. How long did
it take to accelerate the flyer from rest?
28. A drag racer starts at rest and reaches a speed of
386.0 km/h with an average acceleration of
16.5 m /s2• How long does this acceleration take?
29. A hummingbird accelerates at -9.20 m/s 2 such
that its velocity changes from +50.0 km/h to
0 km/h. What is its displacement?
30. A train backs up from an initial velocity of
-4.0 m /s and an average acceleration of
2
-0.27 m/s • What is the train's velocity after 17 s?
31. A cross-country skier skiing with an initial velocity of +4.42 m/s slows uniformly at -0.75 m/s 2.
How long does it take the skier to stop?
32. What is the skier's displacement in problem 31?
47. Find the displacement direction in problem 46.
33. A speedboat uniformly increases its speed from
48. A train travels 478 km southwest along a straight
25 m/s west to 35 m/s west. How long does it
take the boat to travel 250 m west?
34. A ship accelerates at -7.6 x 10-2 m!s 2 so that it
comes to rest at the dock 255 m away in 82.0 s.
What is the ship's initial speed?
35. A student skates downhill with an average acceleration of 0.85 m!s 2 . Her initial speed is 4.5 m/s,
and her final speed is 10.8 m/s. How long does
she take to skate down the hill?
36. A wrench dropped from a tall building is caught
in a safety net when the wrench has a velocity of
-49.5 m/s. How far did it fall?
37. A rocket sled comes to a complete stop from a
speed of 320 km/h in 0.18 s. What is the sled's
average acceleration?
38. A racehorse uniformly accelerates 7.56 m!s 2 ,
reaching its final speed after running 19.0 m. If
the horse starts at rest, what is its final speed?
39. An arrow is shot upward at a speed of 85.1 m/s.
How long does the archer have to move from the
launching spot before the arrow returns to Earth?
40. A handball strikes a wall with a forward speed of
13.7 m/s and bounces back with a speed of
11.5 m/s. If the ball changes velocity in 0.021 s,
what is the handball's average acceleration?
stretch. If the train is displaced south by 42 km,
what is the train's displacement to the west?
49. Find the displacement direction in problem 48.
50. A ship's total displacement is 7400 km at 26°
south of west. If the ship sails 3200 km south,
what is the western component of its journey?
51. The distance from an observer on a plain to the
top of a nearby mountain is 5.3 km at 8.4° above
the horizontal. How tall is the mountain?
52. A skyrocket travels 113m at an angle of 82.4°
with respect to the ground and toward the south.
What is the rocket's horizontal displacement?
53. A hot-air balloon descends with a velocity of
55 km/h at an angle of 37° below the horizontal.
What is the vertical velocity of the balloon?
54. A stretch of road extends 55 km at 37° north of
east, then continues for 66 km due east. What is
a driver's resultant displacement along this road?
55. A driver travels 4.1 km west, 17.3 km north, and
finally 1.2 km at an angle of 24.6° west of north.
What is the driver's displacement?
56. A tornado picks up a car and hurls it horizontally 125m with a speed of 90.0 m/s. How long
does it take the car to reach the ground?
41. A ball accelerates at 6.1 m/s 2 from 1.8 m/s to
9.4 m!s. How far does the ball travel?
57. A squirrel knocks a nut horizontally at a speed of
42. A small sandbag is dropped from rest from a
58. A flare is fired at an angle of 35° to the ground at
hovering hot-air balloon. After 2.0 s, what is the
sandbag's displacement below the balloon?
43. A hippopotamus accelerates at 0.678 m!s 2 until
it reaches a speed of 8.33 m/s. If the hippopotamus runs 46.3 m, what was its initial speed?
44. A ball is hit upward with a speed of 7.5 m/s. How
long does the ball take to reach maximum height?
45. A surface probe on the planet Mercury falls
17.6 m downward from a ledge. If free-fall acceleration near Mercury is -3.70 m/s2, what is the
probe's velocity when it reaches the ground?
Chapter 3 Two-Dimensional M otio n
a nd Vectors
46. A plane moves 599 m northeast along a runway.
If the northern component of this displacement
is 89 m, how large is the eastern component?
10.0 cm/s. If the nut lands at a horizontal distance of 18.6 em, how high up is the squirrel?
an initial speed of 250 m/s. How long does it
take for the flare to reach its maximum altitude?
59. A football kicked with an initial speed of 23.1 m/s
reaches a maximum height of 16.9 m. At what
angle was the ball kicked?
60. A bird flies north at 58.0 km/h relative to the
wind. The wind is blowing at 55.0 km/h south
relative to Earth. How long will it take the bird to
fly 1.4 km relative to Earth?
61. A race car moving at 286 km/h is 0.750 km
behind a car moving at 252 km/h. How long will
it take the faster car to catch up to the slower car?
62. A helicopter flies 165m horizontally and then
moves downward to land 45 m below. What is
the helicopter's resultant displacement?
63. A toy parachute floats 13.0 m downward. If the
parachute travels 9.0 m horizontally, what is the
resultant displacement?
Appendix 1: Additional Problems
881
64. A billiard ball travels 2.7 mat an angle of 13°
with respect to the long side of the table. What
are the components of the ball's displacement?
65. A golf ball has a velocity of 1.20 m/s at 14.0° east
of north. What are the velocity components?
66. A tiger leaps with an initial velocity of 55.0 km/h
at an angle of 13.0° with respect to the horizontal.
What are the components of the tiger's velocity?
67. A tramway extends 3.88 km up a mountain from
a station 0.8 km above sea level. If the horizontal
displacement is 3.45 km, how far above sea level
is the mountain peak?
68. A bullet travels 850 m, ricochets, and moves
another 640 mat an angle of 36° from its previous forward motion. What is the bullet's resultant displacement?
79. What is the range of an arrow shot horizontally
at 85.3 m/s from 1.50 m above the ground?
80. A drop of water in a fountain takes 0.50 s to
travel 1.5 m horizontally. The water is projected
upward at an angle of 33°. What is the drop's initial speed?
81. A golf ball is hit up a 41.0° ramp to travel4.46 m
horizontally and 0.35 m below the edge of the
ramp. What is the ball's initial speed?
82. A flare is fired with a velocity of 87 km/h west
from a car traveling 145 km/h north. With
respect to Earth, what is the flare's resultant displacement 0.45 s after being launched?
83. A sailboat travels south at 12.0 km/h with
respect to the water against a current 15.0° south
of east at 4.0 km/h. What is the boat's velocity?
69. A bird flies 46 km at 15° south of east, then 22 km
at 13° east of south, and finally 14 km at 14° west
of south. What is the bird's displacement?
70. A ball is kicked with a horizontal speed of
9.37 m/s off the top of a mountain. The ball
moves 85.0 m horizontally before hitting the
ground. How tall is the mountain?
71. A ball is kicked with a horizontal speed of
1.50 m/s from a height of 2.50 x 102 m. What is its
horizontal displacement when it hits the ground?
72. What is the velocity of the ball in problem 71
when it reaches the ground?
73. A shingle slides off a roof at a speed of 2.0 m!s
and an angle of 30.0° below the horizontal. How
long does it take the shingle to fall45 m?
74. A ball is thrown with an initial speed of 10.0 m/s
and an angle of 37.0° above the horizontal. What
are the vertical and horizontal components of
the ball's displacement after 2.5 s?
75. A rocket moves north at 55.0 km/h with respect
to the air. It encounters a wind from 17.0° north
of west at 40.0 km/h with respect to Earth. What
is the rocket's velocity with respect to Earth?
76. How far to the north and west does the rocket in
problem 75 travel after 15.0 min?
77. A cable car travels 2.00 x 10 2 m on level ground,
then 3.00 x 10 2 m at an incline of 3.0°, and then
2
2.00 x 10 m at an incline of 8.8°. What is the
final displacement of the cable car?
78. A hurricane moves 790 km at 18° north of west,
then due west for 150 km, then north for 470 km,
and finally 15° east of north for 240 km. What is
the hurricane's resultant displacement?
882
Appendix 1: Additional Problems
Chapter 4 Forces and the Laws
of Motion
84. A boat exerts a 9.5 x 104 N force 15.0° north of
west on a barge. Another exerts a 7.5 x 104 N
force north. What direction is the barge moved?
85. A shopper exerts a force on a cart of 76 Nat an
angle of 40.0° below the horizontal. How much
force pushes the cart in the forward direction?
86. How much force pushes the cart in problem 85
against the floor?
87. What are the magnitudes of the largest and
smallest net forces that can be produced by combining a force of 6.0 N and a force of 8.0 N?
88. A buoyant force of 790 N lifts a 214 kg sinking
boat. What is the boat's net acceleration?
89. A house is lifted by a net force of 2850 N and
moves from rest to an upward speed of 15 cm/s
in 5.0 s. What is the mass of the house?
90. An 8.0 kg bag is lifted 20.0 em in 0.50 s. If it is
initially at rest, what is the net force on the bag?
91. A 90.0 kg skier glides at constant speed down a
17.0° slope. Find the frictional force on the skier.
92. A snowboarder slides down a 5.0° slope at a constant speed. What is the coefficient of kinetic
friction between the snow and the board?
93. A 2.00 kg block is in equilibrium on a 36.0°
incline. What is the normal force on the block?
94. A 1.8 x 10 3 kg car is parked on a hill on a 15.0°
incline. A 1.25 x 104 N frictional force holds the
car in place. Find the coefficient of static friction.
95. The coefficient of kinetic friction between a jar
109. A traffic signal is supported by two cables, each
slid across a table and the table is 0.20. What is
the magnitude of the jar's acceleration?
of which makes an angle of 40.0° with the vertical. If each cable can exert a maximum force
2
of 7.50 x 10 N, what is the largest weight they
can support?
96. A force of 5.0 N to the left causes a 1.35 kg book
2
to have a net acceleration of 0.76 m!s to the
left. What is the frictional force on the book?
97. A child pulls a toy by exerting a force of 15.0 N
at an angle of 55.0° with respect to the floor.
What are the components of the force?
98. A car is pulled by three forces: 600.0 N to the
north, 750.0 N to the east, and 675 N at 30.0°
south of east. What direction does the car move?
99. Suppose a catcher exerts a force of -65.0 N to
stop a baseball with a mass of 0.145 kg. What is
the ball's net acceleration as it is being caught?
100. A 2.0 kg fish pulled upward by a fisherman
rises 1.9 min 2.4 s, starting from rest. What is
the net force on the fish during this interval?
101. An 18.0 N force pulls a cart against a 15.0 N
frictional force. The speed of the cart increases
1.0 m/s every 5.0 s. What is the cart's mass?
110. A certain cable of an elevator is designed to
exert a force of 4.5 x 104 N. If the maximum
acceleration that a loaded car can withstand is
3.5 m/s 2, what is the combined mass of the car
and its contents?
11 I. A frictional force of 2400 N keeps a crate of
machine parts from sliding down a ramp with
an incline of 30.0°. The coefficient of static friction between the box and the ramp is 0.20. What
is the normal force of the ramp on the box?
112. Find the mass of the crate in problem 111.
113. A 5.1 x 102 kg bundle of bricks is pulled up a
ramp at an incline of 14° to a construction site.
The force needed to move the bricks up the
ramp is 4.1 x 10 3 N. What is the coefficient of
static friction between the bricks and the ramp?
102. A 47 kg sled carries a 33 kg load. The coefficient
of kinetic friction between the sled and snow is
0.075. What is the magnitude of the frictional
force on the sled as it moves up a hill with a 15°
incline?
103. Ice blocks slide with an acceleration of 1.22 m/s 2
down a chute at an angle of 12.0° below the horizontal. What is the coefficient of kinetic friction
between the ice and chute?
104. A 1760 N force pulls a 266 kg load up a 17°
incline. What is the coefficient of static friction
between the load and the incline?
105. A 4.26 x 10 7 N force pulls a ship at a constant
speed along a dry dock. The coefficient of kinetic friction between the ship and dry dock is
0.25. Find the normal force exerted on the ship.
106. If the incline of the dry dock in problem 105 is
10.0°, what is the ship's mass?
107. A 65.0 kg skier is pulled up an 18.0° slope by
2
a force of 2.50 x 10 N. If the net acceleration
uphill is 0.44 m/s 2, what is the frictional force
between the skis and the snow?
108. Four forces are acting on a hot-air balloon:
F1 = 2280.0 N up, F2 = 2250.0 N down, F3 =
85.0 N west, and F4 = 12.0 N east. What is the
direction of the net external force on the balloon?
Chapter 5 Work and Energy
114. If 2.13 x 106 J of work must be done on a
2
roller-coaster car to move it 3.00 x 10 m, how
large is the net force acting on the car?
115. A force of 715 N is applied to a roller-coaster
4
car to push it horizontally. If 2.72 x 10 J of
work is done on the car, how far has it been
pushed?
116. In 0.181 s, through a distance of 8.05 m, a test
pilot's speed decreases from 88.9 m/s to 0 m/s.
If the pilot's mass is 70.0 kg, how much work is
done against his body?
117. What is the kinetic energy of a disk with a mass
of 0.20 g and a speed of 15.8 km/s?
118. A 9.00 x 10 2 kg walrus is swimming at a speed
of 35.0 km/h. What is its kinetic energy?
119. A golf ball with a mass of 47.0 g has a kinetic
energy of 1433 J. What is the ball's speed?
120. A turtle, swimming at 9.78 m/s, has a kinetic
energy of 6.08 x 104 J. What is the turtle's mass?
121. A 50.0 kg parachutist is falling at a speed of
47.00 m/s when her parachute opens. Her speed
upon landing is 5.00 m/s. How much work is
done by the air to reduce the parachutist's speed?
122. An 1100 kg car accelerates from 48.0 km/h to
59.0 km/h over 100.0 m. What was the magnitude of the net force acting on it?
Appendix 1: Additional Problems
883
123. What is the gravitational potential energy of a
64.0 kg person at 5334 m above sea level?
124. A spring has a force constant of 550 N/m. What
is the elastic potential energy stored in the
spring when the spring is compressed 1.2 em?
125. What is the kinetic energy of a 0.500 g raindrop
that falls 0.250 km? Ignore air resistance.
126. A 50.0 g projectile is fired upward at 3.00 x
10 2 m/sand lands at 89.0 m/s. How much
mechanical energy is lost to air resistance?
127. How long does it take for 4.5 x 106 J of work to
be done by a 380.3 kW engine?
128. A ship's engine has a power output of 13.0 MW.
How much work can it do in 15.0 min?
129. A catcher picks up a baseball from the ground
with a net upward force of 7.25 X 1o- 2 N so
that 4.35 x 10-2 J of net work is done. How far
is the ball lifted?
130. A crane does 1.31 x 10 3 Jof net work when lifting cement 76.2 m. How large is the net force
doing this work?
131. A girl exerts a force of 35.0 Nat an angle of
20.0° to the horizontal to move a wagon 15.0 m
along a level path. What is the net work done
on it if a frictional force of 24.0 N is present?
132. The Queen Mary had a mass of 7.5 x 10 7 kg
and a top cruising speed of 57 km/h. What was
the kinetic energy of the ship at that speed?
133. How fast is a 55.0 kg sky diver falling when her
kinetic energy is 7.81 x 104 J?
134. A hockey puck with an initial speed of 8.0 m/s
coasts 45 m to a stop. If the force of friction on
the puck is 0.12 N, what is the puck's mass?
139. A ball falls 3.0 m down a vertical pipe, the end
of which bends horizontally. How fast does the
ball leave the pipe if no energy is lost to friction?
140. A spacecraft's engines do 1.4 x 10 13 Jof work in
8.5 min. What is the power output of these engines?
141. A runner exerts a force of 334 N against the
ground while using 2100 W of power. How long
does it take him to run a distance of 50.0 m?
142. A high-speed boat has four 300.0 kW motors.
How much work is done in 25 s by the motors?
143. A 92 N force pushes an 18 kg box of books, initially at rest, 7.6 m across a floor. The coefficient of kinetic friction between the floor and
the box is 0.35. What is the final kinetic energy
of the box of books?
144. A guardrail can be bent by 5.00 em and then
restore its shape. What is its force constant
if struck by a car with 1.09 x 104 Jof kinetic
energy?
145. A 25.0 kg trunk strikes the ground with a speed of
12.5 m/s. If no energy is lost from air resistance,
what is the height from which the trunk fell?
146. Sliding a 5.0 kg stone up a frictionless ramp with
a 25.0° incline increases its gravitational potential energy by 2.4 x 102 J. How long is the ramp?
147. A constant 4.00 x 102 N force moves a 2.00 x
2
10 kg iceboat 0.90 km. Frictional force is negligible, and the boat starts at rest. Find the boat's
final speed.
148. A 50.0 kg circus clown jumps from a platform
into a net 1.00 m above the ground. The net is
stretched 0.65 m and has a force constant of 3.4 x
104 N/m. What is the height of the platform?
135. How far does a 1.30 x 104 kg jet travel if it is
slowed from 2.40 x 10 2 km/h to 0 km/h by an
acceleration of -30.8 m/s 2?
136. An automobile is raised 7.0 m, resulting in an
increase in gravitational potential energy of
6.6 x 104 J. What is the automobile's mass?
137. A spring in a pogo stick has a force constant of
1.5 x 10'1 N/m. How far is the spring compressed
when its elastic potential energy is 120 J?
138. A 100.0 g arrow is pulled back 30.0 em against
a bowstring. The bowstring's force constant is
1250 N/m. What speed will the arrow leave
the bow?
Chapter 6 Momentum and Collisions
149. If a 50.0 kg cheetah, initially at rest, runs 274m
north in 8.65 s, what is its momentum?
150. If a 1.46 x 10 5 kg whale has a momentum of
9.73 x 10 5 kg•m/s to the south, what is its
velocity?
151. A star has a momentum of 8.62 x 10 36 kg•m/s
and a speed of 255 km/s. What is its mass?
152. A 5.00 g projectile has a velocity of 255 m/s right.
Find the force to stop this projectile in 1.45 s.
153. How long does it take a 0.17 kg hockey puck to
decrease its speed by 9.0 mls if the coefficient
of kinetic friction is 0.050?
884
Appendix 1: Additional Problems
I
154. A 705 kg race car driven by a 65 kg driver moves
with a velocity of 382 km/h right. Find the force
to bring the car and driver to a stop in 12.0 s.
155. Find the stopping distance in problem 154.
156. A 50.0 g shell fired from a 3.00 kg rifle has a
speed of 400.0 m!s. With what velocity does the
rifle recoil in the opposite direction?
157. A twig at rest in a pond moves with a speed of
0.40 cm/s opposite a 2.5 g snail, which has a
speed of 1.2 cm/s. What is the mass of the twig?
158. A 25.0 kg sled holding a 42.0 kg child has a
speed of 3.50 m/s. They collide with and pick
up a snowman, initially at rest. The resulting
speed of the snowman, sled, and child is
2.90 m!s. What is the snowman's mass?
159. An 8500 kg railway car moves right at 4.5 m/s,
and a 9800 kg railway car moves left at 3.9 m/s.
The cars collide and stick together. What is the
final velocity of the system?
160. What is the change in kinetic energy for the
two railway cars in problem 159?
161. A 55 g clay ball moving at 1.5 m/s collides with a
55 g clay ball at rest. By what percentage does the
kinetic energy change after the inelastic collision?
162. A 45 g golf ball collides elastically with an identical ball at rest and stops. If the second ball's
final speed is 3.0 m!s, what was the first ball's
initial speed?
163. A 5.00 X 10 2 kg racehorse gallops with a
momentum of 8.22 x 10 3 kg•m/s to the west.
What is the horse's velocity?
164. A 3.0 x 10 7 kg ship collides elastically with a
2.5 x 10 7 kg ship moving north at 4.0 km/h.
After the collision, the first ship moves north at
3.1 km/h and the second ship moves south at
6.9 km/h. Find the unknown velocity.
165. A high-speed train has a mass of 7.10 x 10 5 kg
and moves at a speed of 270.0 km/h. What is
the magnitude of the train's momentum?
166. A bird with a speed of 50.0 km/h has a
momentum of magnitude of 0.278 kg •m/s.
What is the bird's mass?
167. A 75 N force pulls a child and sled initially at
rest down a snowy hill. If the combined mass of
the sled and child is 55 kg, what is their speed
after 7.5 s?
168. A student exerts a net force of -1.5 N over a
period of 0.25 s to bring a falling 60.0 g egg to a
stop. What is the egg's initial speed?
169. A 1.1 x 10 3 kg walrus starts swimming east
from rest and reaches a velocity of 9.7 m/s in
19 s. What is the net force acting on the walrus?
170. A 12.0 kg wagon at rest is pulled by a 15.0 N
force at an angle of 20.0° above the horizontal.
If an 11.0 N frictional force resists the forward
force, how long will the wagon take to reach a
speed of 4.50 m/s?
171. A 42 g meteoroid moving forward at 7.82 x
10 3 m/s collides with a spacecraft. What force is
needed to stop the meteoroid in 1.0 x 10-6 s?
172. A 455 kg polar bear slides for 12.2 s across the
ice. If the coefficient of kinetic friction between
the bear and the ice is 0.071, what is the change
in the bear's momentum as it comes to a stop?
173. How far does the bear in problem 172 slide?
17 4. How long will it take a -1.26 x 104 N force to
stop a 2.30 x 10 3 kg truck moving at a speed of
22.2 m/s?
175. A 63 kg skater at rest catches a sandbag moving
north at 5.4 m/s. The skater and bag then move
north at 1.5 m/s. Find the sandbag's mass.
176. A 1.36 x 104 kg barge is loaded with 8.4 x 10 3 kg
of coal. What was the unloaded barge's speed if
the loaded barge has a speed of 1.3 m/s?
177. A 1292 kg automobile moves east at 88.0 km/h.
If all forces remain constant, what is the car's
velocity if its mass is reduced to 1255 kg?
178. A 68 kg student steps into a 68 kg boat at
rest, causing both to move west at a speed of
0.85 m/s. What was the student's initial velocity?
179. A 1400 kg automobile, heading north at
45 km/h, collides inelastically with a 2500 kg
truck traveling east at 33 km/h. What is the
vehicles' final velocity?
180. An artist throws 1.3 kg of paint onto a 4.5 kg
canvas at rest. The paint-covered canvas slides
backward at 0.83 m/s. What is the change in the
kinetic energy of the paint and canvas?
181. Find the change in kinetic energy if a 0.650 kg
fish leaping to the right at 15.0 m/s collides
inelastically with a 0.950 kg fish leaping to the
left at 13.5 m/s.
182. A 10.0 kg cart moving at 6.0 m/s hits a 2.5 kg cart
moving at 3.0 m/s in the opposite direction. Find
the carts' final speed after an inelastic collision.
183. A ball, thrown right 6.00 m/s, hits a 1.25 kg panel
at rest, then bounces back at 4.90 m/s. The panel
moves right at 1.09 m/s. Find the ball's mass.
Appendix 1: Additional Problems
885
184. A 2150 kg car, moving east at 10.0 m/s, collides
and joins with a 3250 kg car. The cars move
east together at 5.22 m/s. What is the 3250 kg
car's initial velocity?
185. Find the change in kinetic energy in problem 184.
186. A 15.0 g toy car moving to the right at 20.0 cm/s
collides elastically with a 20.0 g toy car moving
left at 30.0 cm/s. The 15.0 g car then moves left
at 37.1 cm/s. Find the 20.0 g car's final velocity.
187. A remora swimming right at 5.0 m/s attaches to a
150.0 kg shark moving left at 7.00 m!s. Both
move left at 6.25 m/s. Find the remora's mass.
197. A 2.05 x 108 kg asteroid has an orbit with a
7378 km radius. The centripetal force on the
asteroid is 3.00 x 10 9 N. Find the asteroid's tangential speed.
198. Find the gravitational force between a 0.500 kg
mass and a 2.50 x 10 12 kg mountain that is
10.0 km away.
199. The gravitational force between Ganymede
and Jupiter is 1.636 x 10 22 N. Jupiter's mass is
1.90 x 10 27 kg, and the distance between the
two bodies is 1.071 x 10 6 km. What is
Ganymede's mass?
200. At the sun's surface, the gravitational force on
188. A 6.5 x 10 12 kg comet, moving at 420 m/s,
catches up to and collides inelastically with
a 1.50 x 10 13 kg comet moving at 250 m/s.
Find the change in the comets' kinetic energy.
1.00 kg is 274 N. The sun's mass is 1.99 x 1030 kg.
If the sun is assumed spherical, what is the sun's
radius?
189. A 7.00 kg ball moves east at 2.00 m/s, collides
20 I. At the surface of a red giant star, the gravitational
with a 7.00 kg ball at rest, and then moves 30.0°
north of east at 1.73 m/s. What is the second
ball's final velocity?
190. A 2.0 kg block moving at 8.0 m/s on a frictionless surface collides elastically with a block at
rest. The first block moves in the same direction
at 2.0 m/s. What is the second block's mass?
force on 1.00 kg is only 2.19 x 10-3 N. If its mass
equals 3.98 x 1031 kg, what is the star's radius?
202. Uranus has a mass of 8.6 x 1025 kg. The mean
distance between the centers of the planet and
its moon Miranda is 1.3 x 10 5 km. If the orbit
is circular, what is Miranda's period in hours?
203. What is the tangential speed in problem 202?
204. The rod connected halfway along the 0.660 m
radius of a wheel exerts a 2.27 x 10 5 N force.
How large is the maximum torque?
Chapter 7 Circular Motion and
Gravitation
205. A golfer exerts a torque of 0.46 N •m on a golf
191. A pebble that is 3.81 m from the eye of a tornado has a tangential speed of 124 m/s. What
is the magnitude of the pebble's centripetal
acceleration?
192. A race car speeds along a curve with a tangential
speed of 75.0 m/s. The centripetal acceleration on
the car is 22.0 m!s2. Find the radius of the curve.
193. A subject in a large centrifuge has a radius
of 8.9 m and a centripetal acceleration of 20g
(g = 9.81 m/s 2 ). What is the tangential speed of
the subject?
194. A 1250 kg automobile with a tangential speed of
48.0 km/h follows a circular road that has a radius
of 35.0 m. How large is the centripetal force?
195. A rock in a sling is 0.40 m from the axis of rotation
and has a tangential speed of 6.0 m!s. What is the
2
rock's mass if the centripetal force is 8.00 x 10 N?
196. A 7.55 x 10 13 kg comet orbits the sun with a
speed of 0.173 km/s. If the centripetal force on
the comet is 505 N, how far is it from the sun?
886
Appendix 1: Additional Problems
club. If the club exerts a force of 0.53 Non a stationary golf ball, what is the length of the club?
206. What is the orbital radius of the Martian moon
Deimos if it orbits 6.42 x 1023 kg Mars in 30.3 h?
207. A 4.00 x 10 2 N •m torque is produced applying
a force 1.60 m from the fulcrum and at an angle
of 80.0° to the lever. How large is the force?
208. A customer 11 m from the center of a revolving
restaurant has a speed of 1.92 x 10-2 m/s. How
large a centripetal acceleration acts on the
customer?
209. A toy train on a circular track has a tangential
speed of 0.35 m/s and a centripetal acceleration
2
of 0.29 m!s • What is the radius of the track?
210. A person against the inner wall of a hollow
cylinder with a 150m radius feels a centripetal
acceleration of 9.81 m/s 2. Find the cylinder's
tangential speed.
2 11. The tangential speed of 0.20 kg toy carts is 5.6 m/s
when they are 0.25 m from a turning shaft. How
large is the centripetal force on the carts?
212. A 1250 kg car on a curve with a 35.0 m radius has
a centripetal force from friction and gravity of
8.07 x 10 3 N. What is the car's tangential speed?
228. A block of ebony with a volume of 2.5 x 10-3 m 3
is placed in fresh water. If the apparent weight of
the block is 7.4 N, what is the density of ebony?
213. Two wrestlers, 2.50 x 10-2 m apart, exert a 2.77 x
229. One piston of a hydraulic lift holds 1.40 x 10 3 kg.
214. A 1.81 x 10 5 kg blue whale is 1.5 m from a
230. A hydraulic-lift piston raises a 4.45 x 104 N
10-3 N gravitational force on each other. One
has a mass of 157 kg. What is the other's mass?
4
2.04 x 10 kg whale shark. What is the gravitational force between them?
215. Triton's orbit around Neptune has a radius of
3.56 x 10 5 km. Neptune's mass is 1.03 x 1026 kg.
What is Triton's period?
The other holds an ice block (p = 917 kg!m 3 )
that is 0.076 m thick. Find the first piston's area.
weight by 448 m. How large is the force on the
other piston if it is pushed 8.00 m downward?
231. A platinum flute with a density of 21.5 g/cm 3 is
submerged in fresh water. If its apparent weight
is 40.2 N, what is the flute's mass?
216. Find the tangential speed in problem 215.
217. A moon orbits a 1.0 x 1026 kg planet in 365 days.
What is the radius of the moon's orbit?
218. What force is required to produce a 1.4 N •m
torque when applied to a door at a 60.0° angle
and 0.40 m from the hinge?
219. What is the maximum torque that the force in
problem 218 can exert?
220. A worker hanging 65.0° from the vane of a
windmill exerts an 8.25 x 10 3 N •m torque. If the
worker weighs 587 N, what is the vane's length?
Chapter 8 Fluid Mechanics
221. A cube of volume 1.00 m 3 floats in gasoline,
3
which has a density of 675 kg/m . How large a
buoyant force acts on the cube?
222. A cube 10.0 em on each side has a density of
4
3
2.053 x 10 kg/m . Its apparent weight in fresh
water is 192 N. Find the buoyant force.
223. A 1.47 x 106 kg steel hull has a base that is 2.50 x
10 3 m 2 in area. If it is placed in sea water (p =
1.025 x 10 3 kg!m 3 ), how deep does the hull sink?
224. What size force will open a door of area 1.54 m 2
if the net pressure on the door is 1.013 x 10 3 Pa?
225. Gas at a pressure of 1.50 x 106 Pa exerts a force
of 1.22 x 10 4 Non the upper surface of a piston. What is the piston's upper surface area?
226. In a barometer, the mercury column's weight
equals the force from air pressure on the mercury's surface. Mercury's density is 13.6 x
10 3 kg/m 3 . What is the air's pressure if the
column is 760 mm high?
227. A cube of osmium with a volume of 166 cm 3 is
placed in fresh water. The cube's apparent weight
is 35.0 N. What is the density of osmium?
Chapter 9 Heat
232. Surface temperature on Mercury ranges from
463 K during the day to 93 K at night. Express
this temperature range in degrees Celsius.
233. Solve problem 233 for degrees Fahrenheit.
234. The temperature in Fort Assiniboine, Montana,
went from -5°F to +37°F on January 19, 1892.
Calculate this change in temperature in kelvins.
235. An acorn falls 9.5 m, absorbing 0.85 of its initial potential energy. If 1200 J/kg will raise the
acorn's temperature 1.0°C, what is its temperature increase?
236. A bicyclist on level ground brakes from 13.4 m/s
to 0 m!s. What is the cyclist's and bicycle's mass
if the increase in internal energy is 5836 J?
237. A 61.4 kg roller skater on level ground brakes
from 20.5 m/s to 0 m/s. What is the total
change in the internal energy of the system?
238. A 0.225 kg tin can (cp = 2.2 x 10 3 J/kg•°C) is
4
cooled in water, to which it transfers 3.9 x 10 J
of energy. By how much does the can's temperature change?
239. What mass of bismuth (cp = 121 J/kg•°C)
increases temperature by 5.0°C when 25 J are
added by heat?
240. Placing a 0.250 kg pot in 1.00 kg of water raises
the water's temperature 1.00°C. The pot's temperature drops 17 .5°C. Find the pot's specific
heat capacity.
241. Lavas at Kilauea in Hawaii have temperatures of
2192°F. Express this quantity in degrees Celsius.
242. The present temperature of the background
radiation in the universe is 2. 7 K. What is this
temperature in degrees Celsius?
Appendix 1: Additional Problems
887
243. The human body cannot survive at a temperature of 42°C for very long. Express this quantity
in kelvins.
4
244. Two sticks rubbed together gain 2.15 x 10 J
245. A stone falls 561.7 m. When the stone lands, the
internal energy of the ground and the stone
increases by 105 J. What is the stone's mass?
floor from 5.7 m/s to 0 m/s. If 3.3 x 105 J cause
1.0 kg of ice to melt, how much of the ice melts?
247. Placing a 3.0 kg skillet in 5.0 kg of water raises
the water's temperature 2.25°C and lowers the
skillet's temperature 29.6°C. Find the skillet's
specific heat.
6
air's temperature increases 55°C when 45 x 10 J
are added to it by heat, what is the air's mass?
249. A 0.23 kg tantalum part has a specific heat
0
capacity of 140 J/kg • C. By how much does
the part's temperature change if it gives up
4
3.0 x 10 J as heat?
Chapter 10 Thermodynamics
250. A volume of air increases 0.227 m 3 at a net
pressure of 2.07 x 10 7 Pa. How much work is
done on the air?
6
251. The air in a hot-air balloon does 3.29 x 10 J
of work, increasing the balloon's volume by
2190 m 3 . What is the net pressure in the balloon?
252. Filling a fire extinguisher with nitrogen gas at a
net pressure of 25.0 kPa requires 472.5 J of work
on the gas. Find the change in the gas's volume.
253. The internal energy of air in a closed car rises
873 J. How much heat energy is transferred to
the air?
254. A system's initial internal energy increases from
39 J to 163 J. If 114 J of heat are added to the
system, how much work is done on the system?
255. A gas does 623 J of work on its surroundings
when 867 J are added to the gas as heat. What is
the change in the internal energy of the gas?
256. An engine with an efficiency of 0.29 takes in 693 J
as heat. How much work does the engine do?
257. An engine with an efficiency of 0.19 does 998 J
of work. How much energy is taken in by heat?
Appendix 1: Additional Problems
259. A 5.4 x 10-4 m 3 increase in steam's volume does
260. A pressure of 655 kPa does 393 J of work inflating a bike tire. Find the change in volume.
261. An engine's internal energy changes from 8093 J
to 2.0920 x 104 J. If 6932 J are added as heat, how
much work is done on or by the system?
262. Steam expands from a geyser to do 192 kJ of
246. A 2.5 kg block of ice at 0.0°C slows on a level
888
5 71 J as heat and loses 463 J as heat per cycle.
1.3 J of work on a piston. What is the pressure?
from kinetic energy and lose 33 percent of it to
the air. How much does the sticks' internal
energy change?
248. Air has a specific heat of 1.0 x 103 J/kg • 0 C. If
258. Find the efficiency of an engine that receives
work. If the system's internal energy increases by
786 kJ, how much energy is transferred as heat?
263. If 632 kJ are added to a boiler and 102 kJ of
work are done as steam escapes from a safety
valve, what is the net change in the system's
internal energy?
264. A power plant with an efficiency of 0.35 percent requires 7.3 7 x 10 8 J of energy as heat.
How much work is done by the power plant?
1
265. An engine with an efficiency of 0.11 does 1150 J
of work. How much energy is taken in as heat?
266. A test engine performs 128 J of work and
receives 581 J of energy as heat. What is the
engine's efficiency?
Chapter 11 Vibrations and Waves
267. A scale with a spring constant of 420 N/m is
compressed 4.3 em. What is the spring force?
268. A 669 N weight attached to a giant spring
stretches it 6.5 em. What is the spring constant?
269. An archer applies a force of 52 N on a bowstring with a spring constant of 490 N/m. What
is the bowstring's displacement?
270. On Mercury, a pendulum 1.14 m long would
have a 3.55 s period. Calculate ag for Mercury.
271. Find the length of a pendulum that oscillates
with a frequency of 2.5 Hz.
272. Calculate the period of a 6.200 m long pendulum in Oslo, Norway, where ag= 9.819 m/s 2•
273. Find the pendulum's frequency in problem 272.
274. A 24 kg child jumps on a trampoline with a
spring constant of 364 N/m. What is the oscillation period?
275. A 32 N weight oscillates with a 0.42 s period
when on a spring scale. Find the spring constant.
~
276. Find the mass of a ball that oscillates at a period
of 0.079 s on a spring with a constant of 63 N/m.
277. A dolphin hears a 280kHz sound with a wave-
295. A 1.53 m long pipe that is closed on one end
has a seventh harmonic frequency of 466.2 Hz.
What is the speed of the waves in the pipe?
296. A pipe open at both ends has a fundamental
length of 0.51 em. What is the wave's speed?
278. If a sound wave with a frequency of 20.0 Hz
has a speed of 331 m/s, what is its wavelength?
279. A sound wave has a speed of 2.42 x 104 m/sand a
wavelength of 1.1 m. Find the wave's frequency.
frequency of 125 Hz. If the pipe is 1.32 m long,
what is the speed of the waves in the pipe?
297. Traffic has a power output of 1.57 x 10-3 W. At
what distance is the intensity 5.20 x 10-3 W/m 2?
298. If a mosquito's buzzing has an intensity of 9.3 x
280. An elastic string with a spring constant of
65 N/m is stretched 15 em and released. What
is the spring force exerted by the string?
281. The spring in a seat compresses 7.2 em under a
620 N weight. What is the spring constant?
282. A 3.0 kg mass is hung from a spring with a spring
constant of 36 N/m. Find the displacement.
283. Calculate the period of a 2.500 m long pendu2
lum in Quito, Ecuador, where ag= 9.780 m!s •
10-8 W/m 2 at a distance of 0.21 m, how much
sound power does the mosquito generate?
299. A note from a flute (a pipe with a closed end)
has a first harmonic of 392.0 Hz. How long is
the flute if the sound's speed is 331 m/s?
300. An organ pipe open at both ends has a first
harmonic of 370.0 Hz when the speed of sound
is 331 m/s. What is the length of this pipe?
284. How long is a pendulum with a frequency of
Chapter 13 Light and Reflection
0.50 Hz?
285. A tractor seat supported by a spring with a
3
spring constant of 2.03 x 10 N/m oscillates
at a frequency of 0.79 Hz. What is the mass
on the spring?
286. An 87 N tree branch oscillates with a period of
0.64 s. What is the branch's spring constant?
287. What is the oscillation period for an 8.2 kg baby
in a seat that has a spring constant of 221 N/m?
288. An organ creates a sound with a speed of 331 m/s
and a wavelength of 10.6 m. Find the frequency.
289. What is the speed of an earthquakes-wave
with a 2.3 x 10 4 m wavelength and a 0.065 Hz
frequency?
Chapter 12 Sound
290. What is the distance from a sound with 5.88 x
10-s W power if its intensity is 3.9 x 10- 6 W/m 2?
291. Sound waves from a stereo have a power output
of 3.5 W at 0.50 m. What is the sound's intensity?
292. What is a vacuum cleaner's power output if the
sound's intensity 1.5 m away is 4.5 x 10-4 W/m 2?
293. Waves travel at 499 m/s on a 0.850 m long cello
string. Find the string's fundamental frequency.
294. A mandolin string's first harmonic is 392 Hz.
How long is the string if the wave speed on it is
329 m/s?
301. A 7.6270 x 108 Hz radio wave has a wavelength
of 39.296 em. What is this wave's speed?
302. An X ray's wavelength is 3.2 nm. Using the speed
of light in a vacuum, calculate the frequency of
the Xray.
303. What is the wavelength of ultraviolet light with
a frequency of 9.5 x 10 14 Hz?
304. A concave mirror has a focal length of 17 em.
Where must a 2.7 em tall coin be placed for its
image to appear 23 em in front of the mirror's
surface?
305. How tall is the coin's image in problem 304?
306. A concave mirror's focal length is 9.50 em. A
3.0 em tall pin appears to be 15.5 em in front of
the mirror. How far from the mirror is the pin?
307. How tall is the pin's image in problem 306?
308. A convex mirror's magnification is 0.11. Suppose
you are 1.75 m tall. How tall is your image?
309. How far in front of the mirror in problem 308 are
you if your image is 42 em behind the mirror?
310. A mirror's focal length is -12 em. What is the
object distance if an image forms 9.00 em
behind the surface of the mirror?
311. What is the magnification in problem 310?
312. A metal bowl is like a concave spherical mirror.
You are 35 em in front of the bowl and see an
image at 42 em. What is the bowl's focal length?
Appendix 1: Additional Problems
889
313. For problem 312, find the bowl's radius of
curvature.
314. A concave spherical mirror on a dressing table
has a focal length of 60.0 em. If someone sits
35.0 em in front of it, where is the image?
315. What is the magnification in problem 314?
316. An image appears 5.2 em behind the surface of a
convex mirror when the object is 17 em in front
of the mirror. What is the mirror's focal length?
317. If the object in problem 316 is 3.2 em tall, how
tall is its image?
318. In order for someone to observe an object, the
wavelength of the light must be smaller than the
object. The Bohr radius of a hydrogen atom is
5.291 770 x 10- 11 m. What is the lowest frequency that can be used to locate a hydrogen atom?
319. Meteorologists use Doppler radar to watch the
movement of storms. If a weather station uses
electromagnetic waves with a frequency of
2.85 x 10 9 Hz, what is the wavelength of the
radiation?
320. PCS cellular phones have antennas that use radio
frequencies from 1800-2000 MHz. What range
of wavelengths corresponds to these frequencies?
321. Suppose you have a mirror with a focal length
of 32.0 em. Where would you place your right
hand so that you appear to be shaking hands
with yourself?
322. A car's headlamp is made of a light bulb in
front of a concave spherical mirror. If the bulb
is 5.0 em in front of the mirror, what is the
radius of the mirror?
323. Suppose you are 19 em in front of the bell of
your friend's trumpet and you see your image
at 14 em. If the trumpet's bell is a concave mirror, what would be its focal length?
324. A soup ladle is like a spherical convex mirror
with a focal length of 27 em. If you are 43 em in
front of the ladle, where does the image appear?
If your nose is 6.0 em long, how long does the
image appear?
329. How fast does microwave radiation that has a
frequency of 1.173 06 x 10 11 Hz and a wavelength of 2.5556 mm travel?
330. Suppose the microwaves in your microwave
oven have a frequency of 2.5 x 10 10 Hz. What is
the wavelength of these microwaves?
331. You place an electric heater 3.00 min front of a
concave spherical mirror that has a focal length of
30.0 em. Where would your hand feel warmest?
332. You see an image of your hand as you reach for
a doorknob with a focal length of 6.3 em. How
far from the doorknob is your hand when the
image appears at 5.1 em behind the doorknob?
333. What is the magnification of the image in
problem 332?
Chapter 14 Refraction
334. A ray of light in air enters an amethyst crystal
(n = 1.553). If the angle of refraction is 35°,
what is the angle of incidence?
335. Light passes from air at an angle of incidence
of 59.2° into a nephrite jade vase (n = 1.61).
Determine the angle of refraction in the jade.
336. Light entering a pearl travels at a speed of
1.97 x 10 8 m/s. What is the pearl's index of
refraction?
337. An object in front of a diverging lens of focal
length 13.0 em forms an image with a magnification of +5.00. How far from the lens is the
object placed?
338. An object with a height of 18 em is placed in
front of a converging lens. The image height is
-9.0 em. What is the magnification of the lens?
339. If the focal length of the lens in problem 338 is
6.0 em, how far in front of the lens is the object?
325. What is the magnification in problem 324?
340. Where does the image appear in problem 339?
326. Just after you dry a spoon, you look into the con-
341. The critical angle for light traveling from a
vex part of the spoon. If the spoon has a focal
length of -8.2 em and you are 18 em in front of
the spoon, where does the image appear?
327. The base of a lamp is made of a convex spherical mirror with a focal length of -39 em. Where
does the image appear when you are 16 em
from the base?
890
328. Consider the lamp and location in problem 327.
Appendix 1: Additional Problems
green tourmaline gemstone into air is 37.8°.
What is tourmaline's index of refraction?
342. Find the critical angle for light traveling from
ruby (n = 1.766) into air.
343. Find the critical angle for light traveling from
emerald (n =1.576) into air.
~
344. Malachite has two indices of refraction:
n 1 = 1.91 and n2 = 1.66. A ray of light in air
enters malachite at an incident angle of 35.2°.
Calculate both of the angles of refraction.
345. A ray of light in air enters a serpentine figurine
(n = 1.555). If the angle of refraction is 33°,
what is the angle of incidence?
346. The critical angle for light traveling from an
aquamarine gemstone into air is 39.18°. What is
the index of refraction for aquamarine?
347. A 15 em tall object is placed 44 em in front of a
diverging lens. A virtual image appears 14 em in
front of the lens. What is the lens's focal length?
348. What is the image height in problem 347?
349. A lighthouse converging lens has a focal length
of 4 m. What is the image distance for an object
placed 4 m in front of the lens?
350. What is the magnification in problem 349?
351. Light moves from olivine (n = 1.670) into onyx.
If the critical angle for olivine is 62.85°, what is
the index of refraction for onyx?
352. When light in air enters an opal mounted on a
ring, the light travels at a speed of 2.07 x 108
m/s. What is opal's index of refraction?
353. When light in air enters albite, it travels at a
velocity of 1.95 x 10 8 m/s. What is albite's index
of refraction?
354. A searchlight is constructed by placing a 500 W
bulb 0.5 m in front of a converging lens. The
focal length of the lens is 0.5 m. What is the
image distance?
355. A microscope slide is placed in front of a converging lens with a focal length of 3.6 em. The lens
forms a real image of the slide 15.2 em behind the
lens. How far is the lens from the slide?
356. Where must an object be placed to form an
image 12 em in front of a diverging lens with a
focal length of 44 em?
C hapter 1 5 Interference and
Diffraction
359. Light with a 587.5 nm wavelength passes through
two slits. A second-order bright fringe forms
0.130° from the center. Find the slit separation.
360. Light passing through two slits with a separa-
tion of 8.04 X 10-6 m forms a third bright fringe
13.1° from the center. Find the wavelength.
361. Two slits are separated by 0.0220 em. Find the
angle at which a first-order bright fringe is
observed for light with a wavelength of 527 nm.
362. For 546.1 nm light, the first-order maximum
for a diffraction grating forms at 75.76°. How
many lines per centimeter are on the grating?
363. Infrared light passes through a diffraction grating
of 3600 lines/em. The angle of the third-order
maximum is 76.54°. What is the wavelength?
364. A diffraction grating with 1950 lines/em is used
to examine light with a wavelength of 497.3 nm.
Find the angle of the first-order maximum.
365. At what angle does the second-order maximum
in problem 364 appear?
366. Light passes through two slits separated by 3.92 x
10-6 m to form a second-order bright fringe at
an angle of 13.1 °. What is the light's wavelength?
367. Light with a wavelength of 430.8 nm shines on
two slits that are 0.163 mm apart. What is the
angle at which a second dark fringe is observed?
368. Light of wavelength 656.3 nm passes through two
slits. The fourth-order dark fringe is 0.548° from
the central maximum. Find the slit separation.
369. The first-order maximum for light with a wavelength of 447.1 nm is found at 40.25°. How
many lines per centimeter does the grating have?
370. Light through a diffraction grating of
9550 lines/em forms a second-order maximum
at 54.58°. What is the wavelength of the light?
357. The critical angle for light traveling from
almandine garnet into air ranges from 33.1° to
35.3°. Calculate the range of almandine garnet's
index of refraction.
358. Light moves from a clear andalusite (n = 1.64)
crystal into ivory. If the critical angle for
andalusite is 69.9°, what is the index of
refraction for ivory?
Chapter 16 Electric Forces and Fields
37 1. Charges of -5.31J.C and +5.31J.C are separated
by 4.2 em. Find the electric force between them.
372. A dog's fur is combed, and the comb gains a
charge of 8.0 nC. Find the electric force between
the fur and comb when they are 2.0 em apart.
11
373. Two equal charges are separated by 6.5 x 10- m.
If the magnitude of the electric force between the
charges is 9.92 x 10-4 N, what is the value of q?
Appendix I: Additional Problems
891
374. Two point charges of -13.0 ~C and -16.0 ~C
exert repulsive forces on each other of 12.5 N.
What is the distance between the two charges?
375. Three equal point charges of 4.00 nC lie 4.00 m
apart on a line. Calculate the magnitude and
direction of the net force on the middle charge.
389. Find the electric force vector on a 5.0 nC charge
in a 1500 N/C electric field directed along the
y-axis.
390. What electric charge experiences an 8.42 X 1o-9 N
electric force in an electric field of 1663 N/C?
376. A proton is at each corner of a square with sides
391. Two 3.00 ~C charges lie 2.00 m apart on the
x-axis. Find the resultant electric field vector at
1.52 x 10- m long. Calculate the resultant force
vector on the proton at the upper right corner.
a point 0.250 m on they-axis, above the charge
on the left.
9
377. Three 2.0 nC charges are located at coordinates
(0 m, 0 m), (1.0 m, 0 m), and (1.0 m, 2.0 m).
Find the resultant force on the first charge.
378. Charges of 7.2 nC and 6.7 nC are 32 em apart.
Find the equilibrium position for a -3.0 nC
charge.
379. A -12.0 ~C charge is between two 6.0 ~C
charges, 5.0 em away from each. What electric
force keeps the central charge in equilibrium?
380. A 9.0 N/C electric field is directed along the x-axis.
Find the electric force vector on a -6.0 C charge.
381. What charge experiences an electric force
of 6.43 x 10-9 N in an electric field of
4.0 x 10 3 N/C?
382. A 5.00 ~C charge is 0.500 m above a 15.0 ~C
charge. Calculate the electric field at a point
1.00 m above the 15.0 mC charge.
383. Two static point charges of 99.9 ~C and 33.3 ~C
exert repulsive forces on each other of 87.3 N.
What is the distance between the two charges?
384. Two particles are separated by 9.30 x 10- 11 m. If
the magnitude of the electric force between the
charges is 2.66 x 10-8 N, what is the value of q?
385. A -23.4 nC charge is 0.500 m below a 4.65 nC
charge and 1.00 m below a 0.299 nC charge. Find
the resultant force vector on the -23.4 nC charge.
392. Two electrons are 2.00 x 10- 10 m and 3.00 x
10- 10 m, respectively, from a point. Where with
respect to that point must a proton be placed so
that the resultant electric field strength is zero?
393. A -7.0 C charge is in equilibrium with a 49 C
charge 18m to the right and an unknown charge
25 m to the right. What is the unknown charge?
394. Suppose two pions are separated by 8.3 x 10-10 m.
If the magnitude of the electric force between the
charges is 3.34 x 10-10 N, what is the value of q?
395. Suppose two muons having equal but opposite
charge are separated by 6.4 x 1o- 8 m. If the
magnitude of the electric force between the
charges is 5.62 x 10- 14 N, what is the value of q?
396. Consider four electrons at the corners of a
square. Each side of the square is 3.02 x
10-5 m. Find the magnitude and direction of
the resultant force on q3 if it is at the origin.
397. A charge of 5.5 nC and a charge of 11 nC are
separated by 88 em. Find the equilibrium position for a -22 nC charge.
398. Three charges are on they-axis. At the origin is a
charge, q1 = 72 C; an unknown charge, q2, is at
y = 15 mm. A third charge, q3 = -8.0 C, is placed
at y = -9.0 mm so that it is in electrostatic equilibrium with q1 and q2. What is the charge on ql
386. Three point charges are on the corners of a triangle: q1 =-9.00 nC is at the origin; q2 = -8.00 nC
is at x = 2.00 m; and q3 = 7.00 nC is at y = 3.00 m.
Find the magnitude and direction of the resultant force on ql.
387. Charges of -2.50 nC and -7.50 nC are 20.0 em
apart. Find a 5.0 nC charge's equilibrium
position.
388. A -4.6 C charge is in equilibrium with a -2.3 C
charge 2.0 m to the right, and an unknown charge
4.0 m to the right. What is the unknown charge?
892
Appendix 1: Additional Problems
Chapter 17 Electrical Energy
and Current
399. A helium-filled balloon with a 14.5 nC charge
rises 290 m above Earth's surface. By how much
does the electrical potential energy change if
Earth's electric field is -105 N/C?
400. A charged airplane rises 7.3 km in a 3.4 x
10 5 N/C electric field. The electrical potential
energy changes by -1.39 X 10 11 J. What is the
charge on the plane?
j
401. Earth's radius is 6.4 x 106 m. What is Earth's
capacitance if it is regarded as a conducting
sphere?
402. A 0.50 pF capacitor is connected across a 1.5 V
battery. How much charge can this capacitor store?
403. A 76 C charge passes through a wire's crosssectional area in 19 s. Find the current in the
wire.
404. The current in a telephone is 1.4 A. How long does
98 C of charge take to pass a point in the wire?
405. What is a television's total resistance if it is
plugged into a 120 V outlet and carries 0.75 A
of current?
406. A motor with a resistance of 12.2 Q is plugged
into a 120.0 V outlet. What is the current in the
motor?
407. The potential difference across a motor with a
0.30 Q resistance is 720 V. How much power is
used?
408. What is a microwave oven's resistance if it uses
1750 W of power at a voltage of 120.0 V?
409. A 64 nC charge moves 0.95 m with an electrical
potential energy change of -3.88 x 10-5 J. What
is the electric field strength?
410. A -14 nC charge travels through a 156 N/C
electric field with a change of 2.1 x 10-6 J in the
electrical potential energy. How far does the
charge travel?
5
411. A 5.0 x 10- F polyester capacitor stores 6.0 x
4
10- C. Find the potential difference across the
capacitor.
412. Some ceramic capacitors can store 3 x 10-2 C
with a potential difference of 30 kV across them.
What is the capacitance of such a capacitor?
413. The area of the plates in a 4550 pF parallelplate capacitor is 6.4 x 10- 3 m 2. Find the plate
separation.
414. A television receiver contains a 14 )lF capacitor
charged across a potential difference of 1.5 x 104 V.
How much charge does this capacitor store?
415. A photocopier uses 9.3 A in 15 s. How much
charge passes a point in the copier's circuit in
this time?
416. A 114 )lC charge passes through a gold wire's
cross-sectional area in 0.36 s. What is the current?
417. If the current in a blender is 7.8 A, how long do
56 C of charge take to pass a point in the circuit?
419. A battery-powered lantern has a resistance of
6.4 Q. What potential difference is provided by
the battery if the total current is 0.75 A?
420. The potential difference across an electric eel is
650 V. How much current would an electric eel
deliver to a body with a resistance of 1.0 x 102 Q?
421. If a garbage-disposal motor has a resistance of
25.0 Q and carries a current of 4.66 A, what is the
potential difference across the motor's terminals?
422. A medium-sized oscillating fan draws 545 rnA of
current when the potential difference across its
motor is 120 V. How large is the fan's resistance?
423. A generator produces a 2.5 x 104 V potential
difference across power lines that carry 20.0 A
of current. How much power is generated?
424. A computer with a resistance of 91.0 Q uses
230.0 W of power. Find the current in the
computer.
425. A laser uses 6.0 x 10 13 W of power. What is the
potential difference across the laser's circuit if
the current in the circuit is 8.0 x 10 6 A?
426. A blender with a 75 Q resistance uses 350 W of
power. What is the current in the blender's circuit?
Chapter 18 Circuits and Circuit
Elements
427. A theater has 25 surround-sound speakers
wired in series. Each speaker has a resistance of
12.0 Q. What is the equivalent resistance?
428. In case of an emergency, a corridor on an airplane has 57 lights wired in series. Each light
bulb has a resistance of 2.00 Q. Find the equivalent resistance.
429. Four resistors with resistances of 39 Q, 82 Q ,
12 Q, and 42 Q are connected in parallel across
a 3.0 V potential difference. Find the equivalent
resistance.
430. Four resistors with resistances of 33 Q, 39 Q,
4 7 Q, and 68 Q are connected in parallel across
a 1.5 V potential difference. Find the equivalent
resistance.
431. A 16 Q resistor is connected in series with another resistor across a 12 V battery. The current in
the circuit is 0.42 A. Find the unknown resistance.
432. A 24 Q resistor is connected in series with another resistor across a 3.0 V battery. The current in
the circuit is 62 rnA. Find the unknown resistance.
418. A computer uses 3.0 A in 2.0 min. How much
charge passes a point in the circuit in this time?
Appendix 1: Additional Problems
893
433. A 3.3 Q resistor and another resistor are connected in parallel across a 3.0 V battery. The
current in the circuit is 1.41 A. Find the
unknown resistance.
445. For the figure above, what is the current in the
3.0 Q resistors?
s.on
2.on
434. A 56 Q resistor and another resistor are connected in parallel across a 12 V battery. The
current in the circuit is 3.21 A. Find the
unknown resistance.
24.0V
435. Three bulbs with resistances of 56 Q , 82 Q, and
s.on
24 Q are wired in series. If the voltage across the
circuit is 9.0 V, what is the current in the circuit?
436. Three bulbs with resistances of 96 Q, 48 Q, and
29 Q are wired in series. What is the current
through the bulbs if the voltage across them is
115V?
437. A refrigerator (R 1 = 75 Q) wired in parallel
with an oven (R 2 = 91 Q) is plugged into a
120 V outlet. What is the current in the circuit
of each appliance?
438. A computer (R 1 = 82 Q) and printer (R2 = 24 Q)
are wired in parallel across a 120 V potential
difference. Find the current in each machine's
circuit.
5.o n
5.o n
446. For the figure above, calculate the equivalent
resistance of the circuit.
447. For the figure above, what is the total current in
the circuit?
448. For the figure above, what is the current in
either of the 8.0 Q resistors?
Chapter 19 Magnetism
449. A proton moves at right angles to a magnetic
field of 0.8 T. If the proton's speed is 3.0 x
10 7 m/s, how large is the magnetic force
exerted on the proton?
450. A weak magnetic field exerts a 1.9 x 10-22 N
force on an electron moving 3.9 x 106 m/s perpendicular to the field. What is the magnetic
field strength?
3.o n
1.5 n
451. A 5.0 x 10-5 T magnetic field exerts a 6.1 x
12.0V
439. For the figure above, what is the equivalent
resistance of the circuit?
10- 17 N force on a 1.60 x 10- 19 C charge, which
moves at a right angle to the field. What is the
charge's speed?
452. A 14 A current passes through a 2 m wire. A
440. For the figure above, find the current in the
circuit.
441. For the figure above, what is the potential difference across the 6.0 Q resistor?
442. For the figure above, what is the current
through the 6.0 Q resistor?
3.6 x 10-4 T magnetic field is at right angles to
the wire. What is the magnetic force on the wire?
453. A 1.0 m printer cable is perpendicular to a
1.3 x 10-4 T magnetic field. What current must
the cable carry to experience a 9.1 x 10-5 N
magnetic force?
454. A wire perpendicular to a 4.6 x 10-4 T magnetic
5.on
field experiences a 2.9 x 10-3 N magnetic force.
How long is the wire if it carries a 10.0 A current?
455. A 12 m wire carries a 12 A current. What mag-
3.on
15.0V
netic field causes a 7.3 x 10-2 N magnetic force
to act on the wire when it is perpendicular to
the field?
456. A magnetic force of 3.7 x 10- 13 N is exerted on
443. For the figure above, calculate the equivalent
resistance of the circuit.
444. For the figure above, what is the total current in
the circuit?
894
Appendix 1: Additional Problem s
an electron moving at 7.8 x 10 6 m/s perpendicular to a sunspot. How large is the sunspot's
magnetic field?
457. An electron moves with a speed of 2.2 x
10 6 m/sat right angles through a 1.1 x 10-2 T
magnetic field. How large is the magnetic force
on the electron?
458. A pulsar's magnetic field is 1 x 10-8 T. How fast
does an electron move perpendicular to this field
. c
soth at a 3.2 x 10-22 N magnetic
10rce acts on
the charge?
459. A levitation device designed to suspend 75 kg
uses 10.0 m of wire and a 4.8 x 10-4 T magnetic field, perpendicular to the wire. What
current is needed?
460. A power line carries 1.5 x 10 3 A for 15 km.
Earth's magnetic field is 2.3 x 10-5 T at a 45°
angle to the power line. What is the magnetic
force on the line?
470. A step-down transformer converts a 3.6 kV voltage to 1.8 kV. If the primary (input) coil has 58
turns, how many turns does the secondary have?
47 1. A step-up transformer converts a 4.9 kV voltage
to 49 kV. If the secondary (output) coil has 480
turns, how many turns does the primary have?
472. A 320-turn coil rotates from 0° to 90.0° in a 0.046
T magnetic field in 0.25 s, which induces an average emf of 4.0 V. What is the area of the coil?
473. A 180-turn coil with a 5.0 x 10-5 m 2 area is in a
magnetic field that decreases by 5.2 x 10-4 Tin
1.9 x 10-5 s. What is the induced current if the
coil's resistance is 1.0 x 102 W?
474. A generator provides a maximum ac current of
1.2 A and a maximum output emf of 211 V.
Calculate the rms potential difference.
475. Calculate the rms current for problem 474.
Chapter 20 Electromagnetic Induction
461. A coil with 540 turns and a 0.016 m 2 area is
rotated exactly from 0° to 90.0° in 0.050 s. How
strong must a magnetic field be to induce an
emf of 3.0V?
476. A generator can provide a maximum output emf
of 170 V. Calculate the rms potential difference.
477. A step-down transformer converts 240 V across
the primary to 5.0 V across the secondary.
What is the step-down ratio (N1 :N2 )?
462. A 550-turn coil with an area of 5.0 x 10-5 m 2 is in
a magnetic field that decreases by 2.5 X 1o-4 T in
2.1 X 10-5 s. What is the induced emf in the coil?
463. A 246-turn coil has a 0.40 m 2 area in a magnetic field that increases from 0.237 T to
0.320 T. What time interval is needed to induce
an emf of -9.1 V?
464. A 9.5 V emf is induced in a coil that rotates
from 0.0° to 90.0° in a 1.25 x 10-2 T ma~netic
field for 25 ms. The coil's area is 250 em . How
many turns of wire are in the coil?
465. A generator provides a rms emf of 320 V across
100 Q. What is the maximum emf?
466. Find the rms current in the circuit in problem 465.
467. Some wind turbines can provide an rms current of 1.3 A. What is the maximum ac current?
468. A transformer has 1400 turns on the primary and
140 turns on the secondary. What is the voltage
across the primary if secondaryvoltage is 6.9 kV?
469. A transformer has 140 turns on the primary
and 840 turns on the secondary. What is the
voltage across the secondary if the primary
voltage is 5.6 kV?
Chapter 21 Atomic Physics
478. Determine the energy of a photon of green
light with a wavelength of 527 nm.
479. Calculate the de Broglie wavelength of an
electron with a velocity of 2.19 x 106 m/s.
480. Calculate the frequency of ultraviolet (UV)
light having a photon energy of 20.7 eV.
481. X-ray radiation can have an energy of 12.4
MeV. To what wavelength does this correspond?
482. Light of wavelength 240 nm shines on a potassium surface. Potassium has a work function of
2.3 eV. What is the maximum kinetic energy of
the photoelectrons?
483. Manganese has a work function of 4.1 eV. What
is the wavelength of the photon that will just
have the threshold energy for manganese?
484. What is the speed of a proton with a de Broglie
wavelength of 2.64 x 10- 14 m?
485. A cheetah can run as fast as 28 m/ s. If the cheetah
has a de Broglie wavelength of 8.97 x 10-37 m,
what is the cheetah's mass?
486. What is the energy of a photon of blue light
with a wavelength of 430.8 nm?
Appendix 1: Additional Problems
895
487. Calculate the frequency of infrared (IR) light
with a photon energy of 1.78 eV.
488. Calculate the wavelength of a radio wave that
has a photon energy of 3.1 x 10-6 eV.
489. Light of frequency 6.5 x 10 14 Hz illuminates
a lithium surface. The ejected photoelectrons
are found to have a maximum kinetic energy
of 0.20 eV. Find the threshold frequency of
this metal.
490. Light of wavelength 519 nm shines on a rubidium surface. Rubidium has a work function of
2.16 eV. What is the maximum kinetic energy
of the photoelectrons?
491. The smallest known virus moves across a Petri
dish at 5.6 x 10-6 m/s. If the de Broglie wavelength of the virus is 2.96 x 10-8 m, what is the
virus's mass?
492. The threshold frequency of platinum is 1.36 x
10 15 Hz. What is the work function of platinum?
493. The ship Queen Elizabeth II has a mass of 7.6 x
10 7 kg. Calculate the de Broglie wavelength if
this ship sails at 35 m/s.
494. Cobalt has a work function of 5.0 eV. What is
the wavelength of the photon that will just have
the threshold energy for cobalt?
495. Light of frequency 9.89 x 10 14 Hz illuminates
a calcium surface. The ejected photoelectrons
are found to have a maximum kinetic energy
of 0.90 eV. Find the threshold frequency of
this metal.
496. What is the speed of a neutron with a de Broglie
wavelength of 5.6 x 10- 14 m?
499. Find the mass defect of i~Ni.
500. Complete this radioactive-decay formula:
212
s4Po ------7 ? + 42He.
501. Complete this radioactive-decay formula:
16 N-----7?+_0e+v.
1
7
502. Complete this radioactive-decay formula:
1
1
~ism ------7 ~6Nd +? .
503. A 3.29 x 10- 3 g sample of a pure radioactive
substance is found after 30.0 s to have only
8.22 x 10-4 g left undecayed. What is the halflife of the substance?
504. The half-life of ~~Cr is 21.6 h. A chromium-48
sample contains 6.5 x 10 6 nuclei. Calculate the
activity of the sample in mCi.
505. How long will it take a sample of lead-212
(which has a half-life of 10.64 h) to decay to
one-eighth its original strength?
506. Compute the binding energy of 1 ~~Sn.
507. Calculate the difference in the binding energy
o f 126C and 1680.
508. What is the mass defect of ~6Zn?
509. Complete this radioactive-decay formula:
(. ------7 131 Xe + _0e + -v.
54
1
510. Complete this radioactive-decay formula:
+<
16ow
74 ------7 1s6Hf
72
.•
511. Complete this radioactive-decay formula:
4
? ------7 107
52 Te + 2He.
512. A 4.14 x 10-4 g sample of a pure radioactive
substance is found after 1.25 days to have only
2.07 x 10-4 g left undecayed. What is the substance's half-life?
513. How long will it take a sample of cadmium-109
Chapter 22 Subatomic Physics
497. Calculate the binding energy of i§K.
498. Determine the difference in the binding energy
1
of ~~Ag and ~§cu.
896
Appendix 1: Additional Problems
with a half-life of 462 days to decay to one-fourth
its original strength?
514. The half-life of ~~Fe is 2.7 years. What is the
decay constant for the isotope?
