Physics Semester 2 Review – Final Exam
Circular Motion 6.2
• Angular speed describes how fast something rotates. Degrees per minute and rotations per minute (rpm) are two common units of
angular speed.
• Linear speed describes how fast a revolving object travels. Linear speed is often given in meters per second.
1.
A compact disc is spinning with an angular speed of 3.3 rotations per second.
a. What is its angular speed in degrees per second?
b. What is its angular speed in rotations per minute (rpm)?
2.
A compact disc has a radius of 6 centimeters.
a. What is its circumference in meters?
b. If the cd rotates 4 times per second, what is the linear speed of a point on the outer edge of the cd? Give your answer in
meters per second.
c. What is the linear speed of a point 3 centimeters from the center of the cd? (Assume the angular speed has not changed).
Universal Gravitation 6.3
The law of universal gravitation allows you to calculate the gravitational force between two objects from their masses and the distance
between them. The law includes a value called the gravitational constant, or “G.” This value is the same everywhere in the universe.
Calculating the force between small objects like grapefruits or huge objects like planets, moons, and stars is possible using this law.
3.
4.
5.
6.
7.
Calculate the force between two objects that have masses of 70 kilograms and 2,000 kilograms separated by a distance of 1 meter.
Calculate the force between two touching grapefruits each with a radius of 0.08 meters and a mass of 0.45 kilograms.
Calculate the force between one grapefruit as described above and Earth. Earth has a mass of 5.9742 × 1024 kg and a radius of
6.3710 × 106 meters. Assume the grapefruit is resting on Earth’s surface.
A man on the moon with a mass of 90 kilograms weighs 146 newtons. The radius of the moon is 1.74 × 106 meters. Find the
mass of the moon.
The mass of the sun is 1.99 × 1030 kilograms and its distance from Earth is 150 million kilometers (150 × 109 meters). What is the
gravitational force between the sun and Earth?
Calculating Gravitational Field Strength 18.2
If we know the mass and the radius of a planet, star, or other object, we can calculate the strength of its gravitational field using this
formula:
8.
9.
Earth has a gravitational field strength of 9.8 N/kg. Its radius is 6,378,000 meters. What is Earth’s mass?
The escape speed from a planet of mass 3.6 x 10 24 kg is 9.1 km/s. What is the planet’s radius?
Coulomb’s Law 15.2
There are many similarities and some differences between the equation of universal gravitation and the equation for Coulomb’s law. They
are both inverse square law
relationships, and they both have similar arrangements of variables.
10. What is the force between a 3 C charge and a 2 C charge separated by a distance of 5 meters?
11. The force between a pair of charges is 100 newtons. The distance between the charges is 0.01 meter. If one of the charges is 0.2
nC, what is the strength of the other charge?
12. The force between two charges is 1000 N. One has a charge of 20 μC, and the other has a charge of 5 μC. What is the distance
between them?
Calculating Electric Fields and Forces
13. What is the force of an electric field of strength 4.0 N/C on a charge of 0.5 C
14. If an object with a charge of 0.08 C experiences an electric force of 5.0 N, what is the electric field strength?
Ohm's Law 13.3
A German physicist, Georg S. Ohm, developed this mathematical relationship, which is present in most circuits. This relationship is known
as Ohm's law. This relationship states that if the voltage (energy) in a circuit increases, so does the current (flow of charges). If the
resistance increases, the current flow decreases.
15.
16.
17.
18.
A circuit contains a 1.5 volt battery and a bulb with a resistance of 3 ohms. Calculate the current.
What is the voltage of a circuit with 15 amps of current and toaster with 8 ohms of resistance?
A light bulb has a resistance of 4 ohms and a current of 2 A. What is the voltage across the bulb?
Use the diagram below to answer the following problems.
a.
b.
c.
d.
What is the total voltage in each circuit?
How much current would be measured in each circuit if the light bulb has a resistance of 6 ohms?
How much current would be measured in each circuit if the light bulb has a resistance of 12 ohms?
Is the bulb brighter in circuit A or circuit B? Why?
Series Circuits
19. For the circuit shown in the diagram to the left, what is the total resistance of
the circuit?
20. What is the current through each resistor?
21. Describe what would happen to the circuit if the wire to the Ω resistor
broke.
1
Parallel Circuits 14.2
A parallel circuit has at least one point where the circuit divides, creating more than
one path for current. Each path is called a branch. The current through a branch is
called branch current. If current flows into a branch in a circuit, the same amount of
current must flow out again, Because each branch in a parallel circuit has its own path
to the battery, the voltage across each branch is equal to the battery’s voltage. If you know the resistance and voltage of
a branch you can calculate the current with Ohm’s Law (I=V/R).
22. For the circuit shown in the diagram to the left, what is
the total resistance of the circuit?
23. What is the current through each resistor?
24. Describe what would happen to the circuit if the wire
to the 1Ω resistor broke.
25. For the circuit shown in the diagram to the right, what is the total resistance of the circuit?
26. What is the current through each resistor?
27. Describe what would happen to the circuit if the wire to the 1Ω resistor broke.
Electrical Power 14.3
During everyday life we hear the word watt mentioned in reference to things like light bulbs and electric bills. The watt is the unit that
describes the rate at which energy is used by an electrical device. Energy is never created or destroyed, so “used” means it is converted
from electrical energy into another form such as light or heat. And since energy is measured in joules, power is measured in joules per
second. One joule per second is equal to one watt. We can calculate the amount of electrical power by an appliance or other electrical
component by multiplying the voltage by the current.
Current x Voltage = Power, or P = IV
28. Your oven has a power rating of 5000 watts.
a. How many kilowatts is this?
b. If the oven is used for 2 hours to bake cookies, how many kilowatt-hours (kWh) are used?
c. If your town charges $0.15/kWh, what is the cost to use the oven to bake the cookies?
29. Calculate the power of a motor that draws a current of 2 A when connected to a 12 volt battery.
Period and Frequency
30. A speaker vibrates at a frequency of 200 Hz. What is its period?
31. A pendulum has a period of 0.3 second. What is its frequency?
32. You want to describe the harmonic motion of a swing. You find out that it take 2 seconds for the swing to complete one cycle.
What is the swing’s period and frequency?
33. A mass-spring system is in SHM in a horizontal direction. If the mass is 0.25 kg, the spring constant is 12 N/m, and the
amplitude is 15 cm,
a. What is the maximum speed of the mass?
b. Where does the maximum speed occur?
c. What would be the speed at a half-amplitude position?
34. In the space below, sketch and label both a transverse wave and a longitudinal wave.
Waves
35. On the graphic at right label the following
of a wave:
a. one wavelength
b. half of a wavelength
c. the amplitude
d. crest
e. trough
36. How many wavelengths are represented
in the wave above?
37. What is the amplitude of the wave shown
above?
38.
39.
40.
41.
parts
A water wave has a frequency of 2 hertz and a wavelength of 5 meters. Calculate its speed.
A wave has a speed of 50 m/sec and a frequency of 10 Hz. Calculate its wavelength.
A wave has a speed of 30 m/sec and a wavelength of 3 meters. Calculate its frequency.
A wave has a period of 2 seconds and a wavelength of 4 meters. Calculate its frequency and speed.
Source
Intensity
Intensity Level
# of Times Greater
Than TOH
Threshold of Hearing (TOH)
1*10-12 W/m2
0 dB
100
Whisper
1*10-10 W/m2
20 dB
102
Normal Conversation
1*10-6 W/m2
60 dB
106
Busy Street Traffic
1*10-5 W/m2
70 dB
107
Walkman at Maximum Level
1*10-2 W/m2
100 dB
1010
Front Rows of Rock Concert
1*10-1 W/m2
110 dB
1011
Threshold of Pain
1*101 W/m2
130 dB
1013
Instant Perforation of Eardrum
1*104 W/m2
160 dB
1016
42. How many times louder than city traffic does the front row at a rock concert sound?
43. How many times greater intensity is the sound in the front row at a rock concert than normal conversation?
The Electromagnetic Spectrum 24.1
Radio waves, microwaves, visible light, and x-rays are familiar kinds of electromagnetic waves. All of these waves have characteristic
wavelengths and frequencies. Wavelength is measured in meters. It describes the length of one complete oscillation. Frequency describes the
number of complete oscillations per second. It is measured
in hertz, which is another way of saying “cycles per second.” The higher the wave’s frequency, the more energy it carries.
44.
45.
46.
47.
48.
49.
Yellow light has a longer wavelength than green light. Which color of light has the higher frequency?
Green light has a lower frequency than blue light. Which color of light has a longer wavelength?
Calculate the wavelength of violet light with a frequency of 750 × 1012 Hz.
Calculate the frequency of yellow light with a wavelength of 580 × 10–9 m.
A star is moving away from Earth at 7 x 106 m/sec. Is the spectral line be shifted to a shorter or longer wavelength.
On a warm summer’s day a trumpet player sounds an A-note (440 Hz) while on one side of a narrow canyon. The sound of the
echo returns to her in 1.2 s.
a. If the air temperature is 89o F, how far away is the other canyon wall?
b. What is the wavelength of the sound wave produced?
c. Describe the change in the pitch of the sound for a bungee jumper who is falling away from the trumpet player, then
bouncing back toward her.
The Law of Reflection 23.1
The law of reflection works perfectly with light and the smooth surface of a mirror. It can also help you win a game of pool or pass a
basketball to a friend on the court. Use a protractor to make your angles correct in your diagrams.
50. Light strikes a mirror’s surface at 20 degrees to the normal. What will the angle of
reflection be?
51. Because a lot of her opponent’s balls are in the way for a straight shot, Amy is
planning to hit the cue ball off the side of the pool table so that it will hit the 8ball into the corner pocket. In the diagram, show the angles of incidence and
reflection for the path of the cue ball. How many degrees does each angle
measure?
Refraction 23.2
When light rays cross from one material to another they bend. This bending is called refraction. Refraction is a useful phenomenon. All
kinds of optics, from glasses to camera lenses to binoculars depend on refraction.
52. In each diagram, draw the "missing" ray (either incident or refracted) in order to appropriately show that the direction of bending
is towards or away from the normal.
53. The work function for three surfaces are as follows: mercury = 4.50 eV, magnesium = 3.68 eV, and lithium = 2.30 eV.
a. At what threshold frequency are electrons liberated from each of these surfaces?
b. What color of light corresponds to these threshold frequencies?
Nuclear Phyiscs: BONUS
54. Spent fuel rods contain strontium-90 whose half-life is 28.1 y. Josh works at a nuclear reactor and must safely store the spent
rods. If a spent fuel rod contains 1.00 x 1027 atoms of strongium-90 when stored in a sealed container, how many strontium-90
atoms will remain if the container is excavated by archeologists 1000. y later?
55. In the movie The Planet of the Apes, the forbidden zone was an area presumably contaminated by the radioactive plutonium fallout
from the detonation of nuclear weapons. If Zera finds a rock in the forbidden zone that is tainted with plutonium-239 whose
activity is 100. Bq, how many atoms of plutonium does the rock contain when it is discovered?
56. If the nuclear explosion occurred 500. y prior to Zera’s discovery, how many plutonium-239 atoms did the rock originally
contain?
PhET Simulation http://phet.colorado.edu/simulations/sims.php?sim=Color_Vision
Color addition:
Red, green, and blue are commonly referred to as the primary additive colors and are used in TV screens and computer monitors.
1)
What color does the man perceive when the red light is turned up to full intensity?
2)
What color does the man perceive if the light is turned up to just ¼ of full intensity?
3)
Return the red to full intensity. Based on what you know from elementary school art, what color would you expect if you were to add
green at full intensity?
4)
What color is actually seen when green is added at full intensity?
5)
What color is perceived when red and blue are viewed at full intensity?
6)
What color is perceived when green and blue are viewed at full intensity?
7)
Do these last few experiments have more to do with rainbows or paints? Why?
Color subtraction:
The primary subtractive colors are cyan, magenta, and yellow. Pigments produce colors by removing select wavelengths of light from the
incident beam.
8)
Select the single bulb tab from the top and change your beam from photons to a solid beam. What color is the incident light?
9)
What color does the man perceive with a yellow filter?
10) Turn your beam into photons. Explain why the man perceives yellow using the words absorb and transmit.
11) Select a monochromatic bulb type of yellow. What color does the man perceive?
12) Change your beam to photons and explain why this is the case.
13) What might happen if the filter is changed to red? What might happen if the light is changed to blue?
Physics Reference Sheet
Position
Average Acceleration
Final Velocity
Final Position, given velocity
on the horizontal axis, x
x  x0 t
a
US – Metric Conversion
Factors and Other Helpful
Hints

t
Quadratic Formula
−𝑏 ± √𝑏 2 − 4𝑎𝑐
𝑥=
2𝑎
   0  at
x  x0  1    0 t
2
Or on the vertical axis, y (Free fall)
Final Position, given acceleration
On the horizontal axis, x
or
On the vertical axis, y (Free fall)
Final Velocity, given acceleration and displacement
On the horizontal axis, x
or
On the vertical axis, y (Free fall)
Newton’s Second Law
Weight
Normal Force on a horizontal surface
Normal Force on an incline
Friction under static conditions
Kinetic friction (sliding)
Coefficient of Friction
Work done by a constant force
Work-Energy Theorem
Springs
Kinetic Energy
Gravitiational Potential Energy
Total Mechanical Energy
Power
y  y0  1   0 t
2
x  x0   0t  1 at 2
2
y  y0  v0t  1 gt 2
2
 2   0 2  2ax  x0 
 2   0 2  2 g  y  y0 
𝐹⃗𝑛𝑒𝑡 = 𝑚𝑎⃗
w = mg
𝐹𝑛𝑜𝑟𝑚 = 𝑚𝑔
𝐹𝑛𝑜𝑟𝑚 = 𝑚𝑔 sin 𝜃 = 𝑤 sin 𝜃
𝐹𝑠𝑡𝑎𝑡𝑖𝑐𝑓𝑟𝑖𝑐 = 𝜇𝑠 𝐹𝑛𝑜𝑟𝑚
𝐹𝑘𝑖𝑛𝑒𝑡𝑖𝑐𝑓𝑟𝑖𝑐 = 𝜇𝑘 𝐹𝑛𝑜𝑟𝑚
𝜇 = tan 𝜃
W=Fnetcosd
1
1
𝑊 = ∆𝐾𝐸 = 𝑚𝑣 2 − 𝑚𝑣02
2
2
𝑊 = ∆𝑃𝐸 = 𝑚𝑔ℎ − 𝑚𝑔ℎ0
Fspring = kx
Wspring = ½ kx2
PEspring = ½ kx
KE = ½ mv2
PEgrav = mgh
E0 = E
KE0 + PE0 = KEf + PEf
𝑃=
𝑊
𝑡
=
𝐹𝑐𝑜𝑠𝜃𝑑
𝑡
= 𝐹𝑣𝑎𝑣𝑔
Time
1 year = 365.25 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
Length
1 inch = 2.54 cm
1 foot = 0.305 m
1 mile = 5280 ft = 1609 m
Weight
1 pound = 4.45 N
On earth, 1 kg = 2.2 lb
Energy
1 horsepower = 745.7 Watts
Unit Symbols
Meter, m
Kilogram, kg
Second, s
Ampere, A
Hertz, Hz
Newton, N
Joule, J
Watt, W
Coulomb, C
Volt, V
Ohm, 
Tesla, T
Electron Volt, eV
Bequerel, Bq
Angular displacement
Angular velocity
Tangential velocity
Angular Acceleration
Centripetal Acceleration
Centripetal Force
1
𝜃 = (𝜔𝑓 − 𝜔0 )
2
1
𝜃 = 𝜔0 𝑡 + 𝛼𝑡 2
2
𝜔𝑓 = 𝜔0 + 𝛼𝑡
𝜔𝑓2 = 𝜔𝑓2 + 2𝛼𝜃
2𝜋𝑟
= 2𝜋𝑟 2 𝑓
𝜔𝑓 − 𝜔0 )
𝛼=
𝑡
4𝜋 2 𝑟
𝑣2
𝑎𝑐 = 2 = 4𝜋 2 𝑟𝑓 2 =
𝑇
𝑟
𝑣 = 𝜔𝑟 =
𝑇
𝑣2
= 𝑚𝑟𝜔2
𝑟
𝑀1 𝑀2
𝐹=𝐺 2
𝑟
𝐺𝑀
𝐺𝑀
𝑔= 2 =
𝑟
(𝑟 + ℎ)2
𝑚1 𝑚2
𝑈 = 𝑃𝐸 = −𝐺
𝑟
4𝜋 2 3
2
𝑇 =(
)𝑟
𝐺𝑀
𝑘𝑞1 𝑞2
𝐹𝑒 =
= 𝐸𝑄
𝑟2
𝑄 𝑉
𝐸=𝑘 2=
𝑟
𝑑
𝐹𝑚𝑎𝑔 = 𝑞𝑣𝐵𝑠𝑖𝑛𝜃
𝐹𝐶 = 𝑚𝑎𝑐 = 𝑚
Universal Gravitation
Gravitational Field Strength
Gravitational Potential Energy
Kepler’s Law
Electrical Force
Magnetic Force
Speed of Sound
Simple Harmonic Motion
Period of waves
331 m/s + 0.6(oC)
1
𝑇=
𝑓
𝑚
𝑘
Springs
𝑇𝑠 = 2𝜋√
And Pendula
𝑇𝑝 = 2𝜋√
Wave Speed
Wave Energy
DeBroglie Wavlength
Radioactivity
Radioactive Decay
𝑙
𝑔
velocity = f
E = hf = KE + W
ℎ
𝜆=
𝑚𝑣
Δ𝑁
𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦 =
= −kN
𝑡
𝑁 = 𝑁0 𝑒 −𝑘𝑡
Constants
Acceleration due to gravity
on earth, g = 9.8 m/s2
Speed of light in a vacuum
c = 3.00 x 108 m/s
G = 6.67x 10-11Nm2/kg2
MEarth=5.98 x 1024kg
REarth to Sun = 1.5 x 1011m
Rearth = 6.4 x 106 m
ke = 9.00 x 109Nm2/C2
me = 9.11 x 10-31kg
mp=1.67 x 10-27kg
e = 1.60 x 10-19C
h=6.63 x 10-34 Js
1eV = 1.60 x 10-19 J
Prefixes
109, giga, G
106, mega, M
103, kilo, k
10-2, centi, c
10-3, milli, m
10-6, micro, µ
10-9, nano, n
10-12, pico, p