U NITS, PHYSICAL
QUANTITIES,
A ND VECTORS
1
L EARNING G OALS
B y studying this duJpter, you willll!tlm:
What the fundamental quantities
of mechanics are, and the units
physicists use to measure them.
? Being able to predid t he p ath of a hurricane is ess
9
ROTATION OF
RIGID BODIES
?All segments of a
rotating helicopter
blade have the same
angular velocity and
angular acceleration.
Compared to a given
blade segment, how
many times greater is
t he linear speed of a
second segment twice
as far from the axis
5
APPLYING
NEWTON'S LAWS
L EARNING G OALS
B y studying this chllpter, you Wll1I011m:
How to use Newton's first law to
solve problems involving the forces
that act on a body in equilibrium.
How to use Newton's second law
t o solve problems involving the
fo
N EWTON'S LAWS
OF M OTION
4
L EARNING G OALS
B y studying this duJpter, you willll!tlm:
What the concept of force means
in physics, and why forces are
vectors.
?The standing child
is pushing t he child
s eated o n t he swing.
Is t he s eated child
pushing
POTENTIAL ENERGY
A ND ENERGY
C ONSERVATION
7
L EARNING G OALS
B y studying this duJpter. you willll!tlm:
How t o use the concept of gravitational potential energy in problems
that involve vertical motion.
?As this diver enters
the water, is the force
of g
2
M OTION A LONG
A STRAIGHT LINE
L EARNING G OALS
B y studying this chllpter, you Wll1I011m:
How to describe straight-line
motion in terms of average velocity,
instantaneous velocity, average
acceleration, and instantaneous
acceleration.
How to interpret
QUANTUM MECHANICS
40
n2h 2 . 8mL2
40.1.
IDENTIFY and SET UP: The energy levels for a particle in a box are given by En = EXECUTE: (a) The lowest level is for n = 1, and E1 =
(1)(6.626 10-34 J s) 2 = 1.2 10-67 J. 8(0.20 kg)(1.5 m) 2
1 2E 2(1.2
ATOMIC STRUCTURE
41
L = l (l + 1) . Lz = ml . l = 0, 1, 2,., n - 1. ml = 0, 1, 2,., l . cos = Lz / L .
41.1.
IDENTIFY and SET UP:
EXECUTE: (a) l = 0 : L = 0 , Lz = 0 . l = 1: L = 2 , Lz = ,0, - . l = 2 : L = 6 , Lz = 2 , ,0, - , -2 . (b) In ea
NUCLEAR PHYSICS
43
43.1.
(a) (b) (c)
28 14 85 37
Si has 14 protons and 14 neutrons. Rb has 37 protons and 48 neutrons. Tl has 81 protons and 124 neutrons.
205 81
43.2.
(a) Using R = (1.2 fm)A1 3 , the radii are roughly 3.6 fm, 5.3 fm, and 7.1
PARTICLE PHYSICS AND COSMOLOGY
44
44.1.
(a) IDENTIFY and SET UP: Use Eq.(37.36) to calculate the kinetic energy K. 1 EXECUTE: K = mc 2 - 1 = 0.1547 mc 2 2 2 1- v / c
m = 9.109 10 -31 kg, so K = 1.27 10-14 J (b) IDENTIFY and SET UP: The tota
BRIEF CONTENTS
Mechanics
1
2
U nits, Physical Quantities, a nd Vectors
M otion Along a S traight Line
3
4
5
6
M otion i n Two o r T hree Dimensions
7
25
71
N ewton's Laws o f M otion
107
A pplying Newton's Laws
1 36
Work a nd Kinetic Energy
181
P otential
DETAILED CONTENTS
5
MECHANICS
5.1
1
UNITS, PHYSICAL
QUANTITIES, A ND VECTORS
1.1
T he N ature o f P hysics
S olving Physics Problems
S tandards and Units
U nit C onsistency and Conversions
U ncertainty a nd Significant Figures
E stimates a nd O rders o f
DETAILED CONTENTS
5
MECHANICS
5.1
1
UNITS, PHYSICAL
QUANTITIES, A ND VECTORS
1.1
T he N ature o f P hysics
S olving Physics Problems
S tandards and Units
U nit C onsistency and Conversions
U ncertainty a nd Significant Figures
E stimates a nd O rders o f
M OTION I N T WO
OR THREE DIMENSIONS
3
L EARNING G OALS
B y studying this duJpter. you willll!tlm:
How to represent the position of a
body in two or three dimensions
using vectors.
?If a car is going
around a curve a t
c onstant speed, is it
accelerating?
W ORK A ND
KINETIC ENERGY
6
L EARNING G OALS
B y sIIIdying this chapter, you willl.llm:
?
When a shotgun fires,
t he expanding gases in
t he barrel push t he
shell out. According t o
Newton's third law, t he
shell exerts a s much
force o n t he g ases a s
M OMENTUM, IMPULSE,
A ND COLLISIONS
8
L earning G oals
B y studying this duJpter. you willll!tlm:
?Which could potentially c ause y ou t he
g reater injury: being
tackled by a lightweight, fast-moving
football player, o r being
tackled by a player with
d
THE WAVE NATURE OF PARTICLES
39
hc
39.1.
IDENTIFY and SET UP: EXECUTE: (a) =
=
h h = . For an electron, m = 9.11 10 -31 kg . For a proton, m = 1.67 10 -27 kg . p mv
6.63 10-34 J s = 1.55 10-10 m = 0.155 nm (9.11 10-31 kg)(4.70 106 m/s)
PHOTONS, ELECTRONS, AND ATOMS
38
h f - . The e e
38.1.
IDENTIFY and SET UP: The stopping potential V0 is related to the frequency of the light by V0 = slope of V0 versus f is h/e. The value fth of f when V0 = 0 is related to by = hf th .
EXECU
RELATIVITY
37
Figure 37.1
37.1.
IDENTIFY and SET UP: Consider the distance A to O and B to O as observed by an observer on the ground (Figure 37.1).
(b) d = vt = (0.900) (3.00 108 m s) (5.05 10-6 s) = 1.36 103 m = 1.36 km. 37.3.
1 IDENTIFY an
ELECTRIC CHARGE AND ELECTRIC FIELD
21
21.1.
(a) IDENTIFY and SET UP: Use the charge of one electron ( -1.602 10 -19 C) to find the number of electrons required to produce the net charge. EXECUTE: The number of excess electrons needed to produce n
GAUSS'S LAW
22
^ E = E cos dA, where is the angle between the normal to the sheet n and the
22.1.
(a) IDENTIFY and SET UP:
electric field E . EXECUTE: In this problem E and cos are constant over the surface so
E = E cos dA = E cos A = (1
ELECTRIC POTENTIAL
23
ra = 0.150 m rb = (0.250 m) 2 + (0.250 m) 2 rb = 0.3536 m
23.1.
IDENTIFY: Apply Eq.(23.2) to calculate the work. The electric potential energy of a pair of point charges is given by Eq.(23.9). SET UP: Let the initial position
CAPACITANCE AND DIELECTRICS
24
24.1.
24.2.
24.3.
Q Vab SET UP: 1 F = 10 -6 F EXECUTE: Q = CVab = (7.28 10 -6 F)(25.0 V) = 1.82 10 -4 C = 182 C EVALUATE: One plate has charge + Q and the other has charge -Q . Q PA and V = Ed . IDENTIFY and SE
CURRENT, RESISTANCE, AND ELECTROMOTIVE FORCE
25
25.1.
25.2.
IDENTIFY: I = Q / t . SET UP: 1.0 h = 3600 s EXECUTE: Q = It = (3.6 A)(3.0)(3600 s) = 3.89 104 C. EVALUATE: Compared to typical charges of objects in electrostatics, this is a huge amou
DIRECT-CURRENT CIRCUITS
26
26.1.
26.2.
26.3.
IDENTIFY: The newly-formed wire is a combination of series and parallel resistors. SET UP: Each of the three linear segments has resistance R/3. The circle is two R/6 resistors in parallel. EXECUTE: T
MAGNETIC FIELD AND MAGNETIC FORCES
27
27.1.
! IDENTIFY and SET UP: Apply Eq.(27.2) to calculate F . Use the cross products of unit vectors from Section 1.10. ! ^ j EXECUTE: v = ( +4.19 104 m/s ) i + ( -3.85 104 m/s ) ^ ! ^ (a) B = (1.40 T ) i !
SOURCES OF MAGNETIC FIELD
28
28.1.
! ^ EXECUTE: (a) r = ( 0.500 m ) i , r = 0.500 m ! ! ^ v r = vr^ i = -vrk j ^
! IDENTIFY and SET UP: Use Eq.(28.2) to calculate B at each point. ! ! ! ! ! qv r 0 qv r ^ r ^ B= 0 = , since r = . 4 r 2 4 r 3
ELECTROMAGNETIC INDUCTION
29
29.1.
29.2.
IDENTIFY: Altering the orientation of a coil relative to a magnetic field changes the magnetic flux through the coil. This change then induces an emf in the coil. SET UP: The flux through a coil of N turns
INDUCTANCE
30
Apply Eq.(30.4). di (a) E2 = M 1 = (3.25 10-4 H)(830 A/s) = 0.270 V; yes, it is constant. dt
30.1.
IDENTIFY and SET UP: EXECUTE: (b) E1 = M
di2 ; M is a property of the pair of coils so is the same as in part (a). Thus E1 = 0.270 V.