Apphysicsbexamreview 090425125639-phpapp01

What’s the difference between distance and
displacement?
 Distance is the total amount an object has
traveled.
 Displacement is the object’s change in position

• A rock is thrown straight upward from the edge of a
30 m cliff, rising 10 m then falling all the way down to
the base of the cliff. Find the rock’s displacement.
• An infant crawls 5 m east, then 3 m north, then 1 m.
What is the infant’s DISTANCE and DISPLACEMENT
• An athlete runs exactly once around the track, a total
distance of 500 m. Find the runner’s displacement for
the race

S = d/t, or V = x/t
• If the infant in the previous example takes 20
seconds to complete his journey, find the
magnitude of his average velocity.
• Is it possible to move with constant speed but not
constant velocity? Is it possible to mov e with
constant velocity but not constant speed?

a = v/t
 A car is traveling in a straight line along a highway
at a constant speed of 80 miles per hour for 10
seconds. Find its acceleration.
 Spotting a police car ahead, a driver of a car
slows from 32 m/s to 20 m/s in 2 seconds. Find
the car’s average acceleration

( ) tvvx o += 2
1
2
2
1
attvx o +=
atvv o +=
axvv o 222
+=

• An object with an initial velocity of 4 m/s moves along a
straight axis under constant acceleration. Three
seconds later, its velocity is 14 m/s. How far did it
travel during this time? 27m
• A car that’s initially traveling at 10 m/s accelerates
uniformly for 4 seconds at a rate of 2 m/s2
in a straight
line. How far does the car travel during this time? 56m
• A rock is dropped off a cliff that’s 80 m high. If it strikes
the ground with an impact velocity of 40 m/s, what
acceleration did it experience during its descent? 10
m/s2

 The area under a velocity vs. time graph equals
the displacement.

 Gravity is 10 m/s2
 y = ½ at2

• A rock is dropped from an 80 m cliff. How long does it
take to reach the ground? 4s
• A baseball is thrown straight upward with an initial
speed of 20 m/s. How high will it go? 20m
• One second after being thrown straight down, an
object is falling with a speed of 20 m/s. How fast will
it be falling 2 seconds later? -40 m/s
• If an object is thrown straight upward with an initial
speed of 8 m/s and takes 3 seconds to strike the
ground, from what height was the object thrown? 21m

X-motion is INDEPENDENT of Y-motion
• An object is thrown horizontally with an initial speed of
10 m/s. It hits the ground 4 seconds later. How far
did it drop in 4 seconds? -80m
• From a height of 100 m, a ball is thrown horizontally
with an initial speed of 15 m/s. How far does it travel
horizontally in the first 2 seconds? 30m
• A rolling ball falls off a lab desk with a velocity of 2
m/s. The height of the lab desk is 1 m. How far away
does the ball land?

• Any push or pull is called a force (N)
- Tension
- Gravitational force
- Air resistance
- Normal force
- Frictional force
- Electrostatic force
- Nuclear forces

 Law of Inertia – A body at rest wants to stay at
rest or a body in motion wants to stay in motion
unless acted upon by an outside force

 F = ma
 Force is measure in Newtons (kg●m/s2
)

 For every action, there is an equal but
opposite reaction

• What net force is required to maintain a 5000 kg
object moving at a constant velocity of magnitude
7500 m/s?
• How much force is required to cause an object of
mass 2 kg to have an acceleration of 4 m/s2
? 8 N
• An object feels two forces; one of strength 8 N pulling
to the left and one of strength 20 N pulling to the right.
If the object’s mass is 4 kg, what is its acceleration? 3
m/s2
• A book whose mass is 2 kg rests on a table. Find the
magnitude of the force exerted by the table on the
book. 20 N

 A can of paint with a mass of 6 kg hangs from a
rope. If the can is to be pulled up to a rooftop with
a constant velocity of 1 m/s, what must the
tension in the rope be? 60 N
 What force must be exerted to lift a 50 N object
with an acceleration of 10 m/s2
? 100 N

 The force that is perpendicular to the surface
 A book whose mass is 2 kg rests on a table. Find
the magnitude of the normal force exerted by the
table on the book. 20 N

• Parallel to the surface and opposite the direction
of the intended motion
1) Static friction – the force that resists movement
Fs = μsFN
2) Kinetic friction – the force that acts on a moving
object
Fk = μkFN

 A crate of mass 20 kg is sliding across a wooden
floor. The coefficient of kinetic friction between
the crate and the floor is 0.3
◦ Determine the strength of the friction force acting on the
crate. 60 N
◦ If the crate is being pulled by a force of 90 N (parallel to
the floor), find the acceleration of the crate. 1.5 m/s2

• A block slides down a frictionless, inclined plane
that makes a 30 degree angle with the horizontal.
Find the acceleration of this block. 5 m/s2
• Suppose the same block slides down the same
inclined plane with a coefficient of kinetic friction of
0.3. Find the acceleration of the block

• Ac = v2
/r
• Fc = mv2
/r
• Anything pointing towards the center of the circle is
positive, anything pointing away is negative
• An object of mass 5 kg moves at a constant speed of
6 m/s in a circular path of radius 2 m. Find the
object’s acceleration and the net force responsible for
its motion. 18 m/s2
; 90 N
• An athlete who weighs 800 N is running around a
curve at a speed of 5.0 m/s with a radius of 5.0 m.
Find the centripetal force acting on him & what
provides the centripetal force? 400 N & static friction

• A roller-coaster car enters the circular loop portion
of the ride. At the very top of the circle, the speed
of the car is 15 m/s, and the acceleration points
straight down. If the diameter of the loop is 40 m
and the total mass of the car is 1200 kg, find the
magnitude of the normal force exerted by the track
on the car at this point. 1500 N
• How would the normal force change if the car was
at the bottom of the circle? 25,500 N

 τ = Frsinθ
Counterclockwise – Torque is positive
Clockwise – Torque is negative

 What is the net torque in the following picture? 5.6
N●m

 W = Fdcosθ
 A crate is moved along a horizontal floor by a
worker who’s pulling on it with a rope that makes a
30 degree angle with the horizontal. The tension
in the rope is 69 N and the crate slides a distance
of 10 m. How much work is done on the crate by
the worker? 600 J

• A box slides down an inclined plane with an angle
of 37 degrees. The mass of the block is 35 kg,
the coefficient of kinetic friction is 0.3, and the
length of the ramp is 8 m.
1. How much work is done by gravity? 1690 J
2. How much work is done by the normal force? 0 N
3. How much work is done by friction? -671 J
4. What is the total work done?

• KE = ½ mv2
• The energy an object possesses due to its motion
• A pool cue striking a stationary billiard ball (m =
0.25 kg) gives the ball a speed of 2 m/s. If the
average force of the cue on the ball was 200 N,
over what distance does this force act? 0.0025 m

 PE = mgh
 The energy an object possesses due to its
position
 A 60 kg stuntwoman scales a 40 m tall rock.
What is her gravitational potential energy? If she
were to jump off the cliff, what would her final
velocity be? 24,000 J; 28 m/s

• Ei = Ef
• KEi + PEi = KEf + Pef
• A ball of mass 2 kg is gently pushed off the edge of a
table that is 5 m above the floor. Find the speed of the
ball as it strikes the floor. 10 m/s
• A box is projected up a long ramp with an incline of 37
degrees with an initial speed of 10 m/s. If the surface
of the ramp is frictionless, how high up the ramp will
the box go? What distance along the ramp will it slide?

 A skydiver jumps from a hovering helicopter that’s
3000 m above the ground. If air resistance can be
ignored, how fast will he be falling when his
altitude is 2000 m? 140 m/s
 Wile E. Coyote (m = 40 kg) falls off a 50 m high
cliff. On the way down, the force of air resistance
has an average strength of 100 N. Find the speed
with which he crashes into the ground. 27 m/s

• The rate at which work is done
• P = W/t or P = Fv
• A mover pushes a large crate (m = 75 kg) from the
inside of the truck to the back end (distance of 6 m),
exerting a steady push of 300 N. If he moves the
crate this distance in 20 s, what is his power output?
90 W
• What must be the power output of an elevator motor
that can lift a total mass of 1000 kg and give the
elevator a constant speed of 8.0 m/s? 80,000 W or 80
kW

• p = mv
• F = ∆p/∆t = ∆mv/∆t
• Momentum is also conserved
• A golfer strikes a golf ball of mass 0.05 kg and the
time of impact between the golf club and the ball
is 1 ms. If the ball acquires a velocity of
magnitude 70 m/s, calculate the average force on
the ball. 3500 N

• J = F∆t
• An 80 kg stuntman jumps out of a window that’s 45 m
above the ground.
1. How fast is he falling when he reaches the ground? 30
m/s
2. He lands on an air bag, coming to rest in 1.5s. What
average force does he feel while coming to rest?
-1600 N
3. What if he had instead landed on the ground (impact
time 10 ms)? -240,000 N

• Elastic Collisions – Kinetic Energy is conserved
• Inelastic Collisions – Kinetic Energy is not conserved.
• Two balls roll toward each other. The red ball has a
mass of 0.5 kg and a speed of 4 m/s just before
impact. The green ball has a mass of 0.2 kg and a
speed of 2 m/s. After the head-on collision, the red
ball continues forward with a speed of 2 m/s. Find the
speed of the green ball after the collision. Was the
collision elastic? 3.0 m/s; no

F = Gm1m2 / r2
G = 6.67 x 10-11
N ● m2
/ kg2
 Given that the radius of the earth is 6.37 x 106
m,
determine the mass of the earth. 6.1 x 1024
kg
 An artificial satellite of mass m travels at a
constant speed in a circular orbit of radius R
around the earth (mass M). What is the speed of
the satellite? √GM/R

 F = -kx
 The stiffer the spring, the greater the k
 Force and acceleration are greatest when
displacement is greatest.
 A 12 cm long spring has a spring constant of 400
N/m. How much force is required to stretch the
spring to a length of 14 cm? 8 N

 PEelastic = ½ kx2
 PE is maximized when spring is at the endpoints,
KE is minimum
 PE is 0 when spring is passing through x=0
(equilibrium) and KE is maximum

 A 0.05 kg block oscillates on a spring whose force
(spring) constant is 500 N/m. The amplitude of
the oscillations is 4.0 cm. Calculate the maximum
speed of the block. 4 m/s
 A 2.0 kg block is attached to an ideal spring with a
force constant of 500 N/m. The amplitude is 8.0
cm. Determine the total energy of the oscillator
and the speed of the block when it’s 4.0 cm from
equilibrium. 1.6 J; 1.1 m/s

 f = 1/T
 T = 1/f
 T = 2∏√m/k
 w = 2∏f, 2∏/T, √k/m
 A block oscillating on the end of a spring moves from is
position of maximum stretch to maximum compression in
0.25 s. Determine the period and frequency. 0.5 s; 2 Hz
 A student observing an oscillating block counts 45.5 cycles
in one minute. Determine its frequency and period. .758 Hz;
1.32s

 A 2.0 kg block is attached to a spring whose
spring constant is 300 N/m. Calculate the
frequency and period. 1.9 Hz; 0.51 s
 A block is attached to a spring and set into
oscillatory motion and its frequency is measured.
If this block were removed and replaced by a
second block with ¼ the mass of the first block,
how would the frequency of the oscillations
compare? f increases by a factor of 2

 KE is maximum at the equilibrium position
 Frequency nor period depends on the amplitude
for any object in SHM
L
g
T
=
π2

 A simple pendulum has a period of 1s on Earth.
What would its period be on the moon, where g is
1/6th
of the earth’s value?2.4s

In the drawing, one cycle is shaded in color.
The amplitude A is the maximum excursion of a particle of the medium from
the particles undisturbed position.
The wavelength is the horizontal length of one cycle of the wave.
The period is the time required for one complete cycle.
The frequency is related to the period and has units of Hz, or s-1
.
T
f
1
=

 The period of a traveling wave is 0.5s, its
amplitude is 10 cm, and its wavelength is 0.4 m.
What are its frequency and wave speed? 2Hz; 0.8
m/s
λ
λ
f
T
v ==

 When 2 or more waves meet, they overlap
(interfere)
 2 Types of interference
◦ Constructive Interference (added together)
◦ Destructive Interference (subtracted from each other)
 2 waves, one with amplitude of 8 cm and the other
with an amplitude of 3 cm travel in the same
direction on a string and overlap. What are the
maximum and minimum amplitudes? 11cm; 5 cm

 L = n(1/2λ)
 f = nV/2L
 A string of length 12 m that’s fixed at both ends
supports a standing wave with a total of 5 nods.
What are the harmonic number and wavelength of
this standing wave?

LONGITUDINAL SOUND WAVES
The area of condensation is
the region of compression
with increased air pressure
The area of rarefaction is
the region behind the
condensation with
decreased air pressure

 Sound travels fastest in solids, then liquids, then
gases
ρ
adB
v =

 The change in frequency and wavelength that
occurs when the source and detector are in
relative motion.
◦ Relative motion toward each other results in a frequency
shift upward, and relative motion away from each other
results in a frequency shift downward

 p = m/v
 specific gravity = psubstance / pwater (1000 kg/m3
)
 A cork has a volume of 4 cm3
and weighs .01 N.
What is the specific gravity of the rock? 0.25

 P = F/A
 1 atm = 101,300 Pa (1.013 x 105
Pa)
 A vertical column made of cement has a base
area of 0.5 m2
. If the height is 2 m, and the sp.
Gravity of cement is 3, how much pressure does
this column exert on the ground? 6 x 104
Pa

 Fg = pvg
 Pliquid = pgh (depends only on density and depth)
 Ptotal = Patm + Pliquid
 What is the gauge pressure of a swimming pool at
a point 1 m below the surface? 1 x104
Pa

 What happens to the gauge pressure if we double
the depth below the surface of a liquid? What
happens to the total pressure? Gauge pressure
increases by a factor of 2; Total pressure
increases by less than a factor of 2
 A flat piece of wood of area 0.5 m2
is lying at the
bottom of a lake. If the depth of the lake is 30 m,
what is the force on the wood due to the
pressure? 2 x 105
N

 The net upward force of an object in a liquid is
called the buoyant force.
 Archimedes Principle - The strength of the
buoyant force is equal to the weight of the fluid
displaced by the object.
FB = pvg
Vsub = pobject
Vtotal pfluid

 If pobject < pfluid , then the object will float
 A brick with a specific gravity of 2 and volume of
1.5 x 10-3 m3, is dropped into a swimming pool
full of water. Explain why the brick will sink. When
the brick is lying on the bottom of the pool, what is
the magnitude of the normal force on the brick?
Specific gravity is greater than 1; 15 N

 A glass sphere of specific gravity 2.5 and volume
of 10-3
m3
is completely submerged in a large
container of water. What is the apparent weight
of the sphere while immersed? 15 N

 f = Av
 A1v1 = A2v2 (flow speed increases when the pipe narrows
or inversely proportional)
 A pipe carries water. At one point in the pipe, the radius is
2 cm and the flow speed is 6 m/s. What is the flow rate?
What is the flow speed where the pipe’s radius changes to
1 cm? 7.5 x 10-3
m3
/s; 24 m/s
 If the diameter of the pipe increases from 4 cm to 12 cm,
what will happen to the flow speed? 1/9 the flowrate

 States that energy is conserved for fluid flow
P1 + pgy1 + ½ pv1
2
= P2 + pgy2 + ½ pv2

 The pressure is lower where the flow speed is
greater (airplanes, hurricanes).

 Celsius to Fahrenheit
9/5C + 32 = F
 Fahrenheit to Celsius
(F-32)5/9 = C
 Celsius to Kelvin
C + 273 = K

 Q = mc∆T (how much heat is added of removed
in the system to change the temperature)
 Q = mL (changing phases)
 Sp. Heat of water = 4186 J/kg ·C
 Rate of heat transfer
( )
L
TkA
t
Q ∆
=

TLL o∆=∆ α
• A brass rod 5 m long and 0.01 m in diameter
increases in length by 0.05 m when its
temperature is increased by 500°C. A similar
brass rod of length 10 m has a diameter of 0.02 m.
By how much will this rod’s diameter increase if its
temperature is increased by 1000°C? 4 x 10-4
m

 An aluminum rod (p = 2.7 x 103 kg/m3 has a radius
of 0.01 m and an initial length of 2 m at a
temperature of 20°C. Heat is added to raise its
temperature to 90°C. Its coefficient of linear
expansion is = 25 x 10-6/°C, the specific heat is 900
J/kg°C, and a thermal conductivity of k = 200 J/s
m°C.
◦ What is the mass of the aluminum rod? 1.7 kg
◦ What is the amount of heat added to the rod? 107,100 J
◦ What is the new length of the rod? 0.0035 m
◦ If we were to use this rod to transfer heat between two
objects one side being at 20°C and the other side at 90°C,
what would the rate of heat transfer be? 2.2 J/s

 Pv = nRT
 Speed of molecules of a gas
 In order for the average speed of the molecules in
a given sample of gas to double, what must
happen to the temperature? Since v is
proportional to square root of T, the temperature
must quadruple
m
kT
vrms
3
=
M
RT
vrms
3
=

 A cylindrical container of radius 15 cm and height
30 cm contains 0.6 mole of gas at 433 K. How
much force does the confined gas exert on the lid
of the container? 35 N

 Zeroth Law – Heat flows from the warmer object to
the cooler one until they reach thermal equilibrium.
 First Law
◦ W = -P∆V
 Work is positive when work is done ON the system (volume
id decreaseing
 Work is positive when work is done ON the surroundings
(volume is increasing)
WQU −=∆

THE SECOND LAW OF THERMODYNAMICS:
THE LAW OF ENTROPY
Heat flows spontaneously from a substance at a
higher temperature to a substance at a lower
temperature and does not flow spontaneously in the
reverse direction.

CH QWQ +=
HH
C
H
C
Q
W
T
T
Q
Q
e =−=−= 11

 A heat engine draws 800 J of heat from its high
temperature source and discards 450 J of exhaust
heat into its cold-temperature reservoir. How
much work does this engine perform and what is
its thermal efficiency? 350 J; 44%
 An inventor proposes a design for a heat engine
that operates between a heat source at 500°C and
a cold reservoir at 25°C with an efficiency of 2/3.
What’s your reaction to the inventor’s claim?

4 types of thermal processes
An isobaric process is a process that occurs at
constant pressure.
An isochoric process is a process that occurs at
constant volume.
An isothermal process is a process that occurs at
constant temperature.
An adiabatic process is a process during which no
energy is transferred to or from the system as heatat.

 Consider two small spheres, one carrying a
charge of +1.5nC and the other a charge -2.0 nC,
separated by a distance of 1.5 cm. Find the
electric force between them. -1.2 x 10-4
N
2
21
r
qq
kF =
( ) 229
CmN1099.841 ⋅×== ok πε
( )2212
mNC1085.8 ⋅×= −
οε

 It is the surrounding charges that create the electric field at
a given point.
 The electrostatic force points in the direction of
attraction
 The electric field always points away from the
positive charge and towards the negative charge.
oq
F
E


=

 Electric field does not depend on the sign of the
test charge
2
r
q
kE =

 A charge q = +3.0 nC is placed at a location at
which the electric field strength is 400 N/C. Find
the force felt by charge q. 1.2 x 10-6
N
 A dipole is formed by two point charges, each of
magnitude 4.0 nC, separated by a distance of 6.0
cm. What is the strength of the electric field at a
point midway between them? 8.0 x 104
N/C

 An object of mass 5g is placed at a distance of 2
cm above a charged plate. If the strength of the
electric field is 106
N/C, how much charge would
the object need to have in order for the electrical
repulsion to balance the gravitational pull? 5 x 10-8
C

 Electric Field Lines Never Cross
 Always perpendicular to the surface and point
AWAY from the positive TOWARD the negative

 Conductors permit the flow of excess charge; they
conduct electricity well (metals)
◦ There can be no electrostatic field within the body of a
conductor. Why?
 Insulators do not conduct electricity well. Electrons
do not flow well
 A solid sphere of copper is given a negative charge.
Discuss the electric field inside and outside the
sphere.

o
AB
o
A
o
B
q
W
qq
−
=−
EPEEPE

 A positive charge q1 = 2 + 10-6
C is held stationary,
while a negative charge q2 = -1 x 10-8
C, is
released from rest at a distance of 10 cm from q1.
Find the kinetic energy change of charge q2 when
it’s 1 cm from q1. 0.016 J

 Let Q = 2 x 10-8 C. What is the potential at a
Point P that is 2 cm from Q? 900 V
 How much work is done as a charge moves along
an equipotential surface? 0
BAo
AB
AB
r
kq
r
kq
q
W
VV −=
−
=−
r
kq
V =

 Capacitors are storage devices for electricity.
q = CV
 Parallel plate capacitors
d
A
C oκε
=

 A 10 nF parallel plate capactior holds a charge of
50μC on each plate. What is the electric potential
difference between the plates? If the plates are
separated by a distance of 0.2 mm, what is the
area of each plate? 5000 V; 0.23 m2

 Amount of voltage the battery produces

 I = q/t (Amps, A)
 The direction of the current is taken to be the
direction that a positive charge would move

 Resistors are devices that control current
 R = V/I (Ohm’s Law)
 Notice that if the current is large, the resistance is
low. If the current is small, the resistance is high.
 Resistivity:
A
L
R ρ=
resistivity in units of ohm·meter

 A wire of radius 1mm and length 2 m is made of
platinum (resistivity = 1 x 10-7
Ω•m). If a voltage of
9 V is applied between the ends of the wire, what
will be the resulting current? 140 A

IVP =
( ) RIIRIP 2
==
R
V
V
R
V
P
2
=





=

 Combining Resistors
◦ Series (one after the other):
 Add as normal
◦ Parallel (side by side):
 Add as inverse
 Same voltage applied across each device
+++= 321 RRRRS
+++=
321
1111
RRRRP

 Calculate the equivalent resistance in the circuit

 Combining Capacitors
◦ Series (one after the other):
 Add as inverse
◦ Parallel (side by side):
 Add as normal
 C = q/V
+++= 321 CCCCP
+++=
321
1111
CCCCS

 Field lines travel away from the North poles and
travel toward the South poles.
X X X X X ● ● ● ● ●
X X X X X ● ● ● ● ●
X X X X X ● ● ● ● ●
X X X X X ● ● ● ● ●
(into the page) (out of the page)

 The magnetic force always remains
perpendicular to the velocity and is directed
toward the center of the circular path.
( )θsinvq
F
B
o
=

 Right Hand Rule #1 (for positive charges)
◦ Thumb – Direction particle is traveling
◦ Index – Direction of Magnetic Field
◦ Middle – Direction of Magnetic Force
 If the charge is NEGATIVE, the force is the
opposite direction

r
I
B o
π
µ
2
=
AmT104 7
⋅×= −
πµo

 c = 3.00 x 108
m/s (speed of light)
f
v
=λ

 Law of Reflection
◦ Incident angle is the same as the reflected angle
 n = c/v
 Snell’s Law – relates the angle of incidence and
the angle of refraction
 If n2<n1, light bends AWAY from the normal. If
n2>n1, light bends TOWARD the normal.
2211 sinsin θθ nn =

 A beam of light in air is incident upon a piece of
glass striking the surface at an angle of 30
degrees. If the index of refraction of the glass is
1.5, what are the angles of reflection and
refraction? 60°; 35°

 Critical Angle - The angle of incidence at which
the angle of refraction is 90°. No light is refracted
out and the beam is refracted along the surface.
◦ If the angle of incidence is greater than the critical angle,
no beams of light are refracted.
21
1
2
sin nn
n
n
c >=θ







=′
1
2
n
n
dd
Apparent depth,
observer directly
above object

Conceptual Example 4 On the Inside Looking Out
A swimmer is under water and looking up at the surface. Someone
holds a coin in the air, directly above the swimmer’s eyes. To the
swimmer, the coin appears to be at a certain height above the
water. Is the apparent height of the coin greater, less than, or the
same as its actual height?
Light rays are refracted AWAY from the normal
when going from a higher index of refraction to
a lower index of refraction.
When it is the opposite, the light bends
TOWARD the normal

 Concave Mirrors
1. An incident ray parallel to the axis that is reflected through the
focal point
2. An incident ray that passes through the focal point and
reflected parallel
3. An incident ray that strikes the vertex is reflected at an equal
angle to the axis
 Convex Mirrors
1. An incident ray parallel to the axis is reflected away from the
focal point
2. An incident ray directed towards the focal point is reflected
parallel to the axis
3. An incident ray that strikes the vertex is reflected at an equal
angle to the axis

 Mirror Equation
 Magnification Equation
fdd io
111
=+
o
i
o
i
d
d
h
h
m −==

Summary of Sign Conventions for Spherical Mirrors
mirror.concaveaforis +f
mirror.convexaforis −f
mirror.theoffrontinisobjecttheifis +od
mirror.thebehindisobjecttheifis −od
image).(realmirrortheoffrontinisobjecttheifis +id
image).(virtualmirrorthebehindisobjecttheifis −id
object.uprightanforis +m
object.invertedanforis −m

 An object of height 4 cm is placed 30 cm in front
of a concave mirror whose focal length is 10 cm.
◦ Where’s the image? 15 cm
◦ Is it real or virtual? real
◦ Is it upright or inverted? inverted
◦ What the height? -2cm

 An object of height 4 cm is placed in front of a
convex mirror whose focal length is -30cm.
◦ Where’s the image? – 12 cm
◦ Is it real or virtual? virtual
◦ Is it upright or inverted? upright
◦ What’s the height of the image? 2.4 cm

 Converging lenses cause rays of light to converge
to a focal point.
 Diverging lenses cause rays of light to diverge
away from the focal point

 Converging Lenses
◦ Incident ray parallel to the axis is refracted through the
focal point.
◦ Incident rays pass through the center point of the lens.
 Diverging Lenses
◦ An incident ray parallel to the axis is reflected away from
the focal point
◦ Incident rays pass through the center point of the lens.

Summary of Sign Conventions for Lenses (page 827)
lens.convergingaforis +f
lens.divergingaforis −f
lens.theofleftthetoisobjecttheifis +od
lens.theofrightthetoisobjecttheifis −od
image).(reallenstheofrightthetoformedimageanforis +id
image).(virtuallenstheofleftthetoformedimageanforis −id
image.uprightanforis +m
image.invertedanforis −m

of a converging lens with a focal length of 24 cm
◦ Where’s the image? 53 cm
◦ Is it real or virtual? real
◦ Is it upright or inverted? inverted
◦ What’s the height of the image? -13 cm

of a diverging lens with a focal length of -24.5 cm.
◦ Where’s the image? -16 cm
◦ Is it real or virtual? virtual
◦ Is it upright or inverted? upright
◦ What’s the height of the image? 3.7 cm

 Light behaves like a stream of photons, known as
the photoelectric effect.
◦ E = Energy of a photon
◦ h = Planck’s Constant 6.63 x 10-34
J•s
 Increasing the intensity of the incident energy
means bombardment with more photons and
results in the ejection of more photoelectrons
◦ Φ = work function
hfE =
KE=−φE

 The threshold frequency is the frequency at which
photons need to travel to eject electrons.
◦ f = φ/h
 New unit for photon energy is electronvolt (eV)
◦ 1eV = 1.6 x 10-19
J

Examples
• The work function for aluminum is 4.08 ev
– What is the threshold frequency required to produce
photoelectrons from aluminum? 9.86 x 1014
Hz
– Classify the electromagnetic radiation that can produce
photoelectrons. UV
– If light of frequency f = 4.00 x 1015
Hz is used to illuminate a
piece of aluminum,
• What is the KE of ejected photoelectrons? 12.5 eV
• What’s the maximum speed of the photoelectron? (Electron mass
= 9.11 x 10-31
kg) 2.1 x 106
m/s
– If the light described in part b were increased by a factor
of 2 in intensity, what would happen to the value of the
Kinetic Energy? Nothing

 Bohr theorized that a photon is emitted only when
the electron changes orbits from a larger one with
a higher energy to a smaller one with a lower
energy
◦ En = Ionization Energy – the minimum amount of
energy that must be supplied to release the atom’s
electron
◦ Z = number of protons
◦ n = energy level
( ) ,3,2,1J1018.2 2
2
18
=×−= −
n
n
Z
En
( ) ,3,2,1eV6.13 2
2
=−= n
n
Z
En

 How much energy must a ground state electron
(n=1) in a hydrogen atom absorb to be excited to
the n=4 energy level? 12.8 eV
 With the electron in the n=4 level, what
wavelengths are possible for the photon emitted
when the electron drops to a lower energy level?
In what regions of the EM spectrum do these
photons lie?

 Light exhibits both wave-like and particle-like
characteristics

◦ h = Planck’s Constant
◦ p = linear momentum (mv)
ph=λ


neutrons
ofNumber
protons
ofNumber
neutronsand
protonsofNumber
NZA +=
atomic
number
atomic mass
number

 How many protons and neutrons are contained in
◦ 29 Protons, 34 Neutrons
uC63
29

 Isotope – Contain the same number of protons but
different number of neutrons
 The element Neon (atomic number 10) has
several isotopes. The most abundant isotope
contains 10 neutrons, and two others contain 11
and 12. Write symbols for these three nuclides (a
nucleus with a specific number of protons and
neutrons

Example 3 The Binding Energy of the Helium Nucleus Revisited
The atomic mass of helium is 4.0026u and the atomic mass of hydrogen
is 1.0078u. Using atomic mass units, instead of kilograms, obtain the
binding energy of the helium nucleus.

u0304.0u0026.4u0330.4 =−=∆m
MeV5.931u1 ↔
MeV3.28energyBinding =

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