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. Calculate the force between two objects that have masses of 70 kilograms and 2,000 kilograms separated by a distance of 1 meter.

4. Calculate the force between two touching grapefruits each with a radius of 0.08 meters and a mass of 0.45 kilograms.

5. 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.

6. 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.

7. 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 18.2If 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. Earth has a gravitational field strength of 9.8 N/kg. Its radius is 6,378,000 meters. What is Earth’s mass?

9. The escape speed from a planet of mass 3.6 x 1024 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 lawrelationships, 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 C14. 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 13.3A 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. A circuit contains a 1.5 volt battery and a bulb with a resistance of 3 ohms. Calculate the current.16. What is the voltage of a circuit with 15 amps of current and toaster with 8 ohms of resistance?17. A light bulb has a resistance of 4 ohms and a current of 2 A. What is the voltage across the bulb?18. Use the diagram below to answer the following problems.

a. What is the total voltage in each circuit?b. How much current would be measured in each circuit if the light bulb has a resistance of 6

ohms?c. How much current would be measured in each circuit if the light bulb has a resistance of

12 ohms?d. 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 14.2A 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 parts of a wave:

a. one wavelengthb. half of a wavelengthc. the amplituded. creste. trough

36. How many wavelengths are represented

in the wave above?37. What is the amplitude of the wave shown

above?

38. A water wave has a frequency of 2 hertz and a wavelength of 5 meters. Calculate its speed.39. A wave has a speed of 50 m/sec and a frequency of 10 Hz. Calculate its wavelength.40. A wave has a speed of 30 m/sec and a wavelength of 3 meters. Calculate its frequency.41. 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 24.1Radio 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 measuredin hertz, which is another way of saying “cycles per second.” The higher the wave’s frequency, the more energy it carries.

44. Yellow light has a longer wavelength than green light. Which color of light has the higher frequency?

45. Green light has a lower frequency than blue light. Which color of light has a longer wavelength?46. Calculate the wavelength of violet light with a frequency of 750 × 1012 Hz.47. Calculate the frequency of yellow light with a wavelength of 580 × 10–9 m.48. 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.49. 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 23.1The 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 8-ball 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 23.2When 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 x=x0+νΔtUS – Metric

Conversion Factors

and Other Helpful

HintsAverage Acceleration a= Δν

Δt Quadratic Formula

x=−b±√b2−4ac2a

Final Velocity ν=ν0+atFinal Position, given velocityon the horizontal axis, x

Or on the vertical axis, y (Free fall)x=x0+

12 (ν+ν0) t

y= y0+12 (ν+ν0) t

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

Final Position, given accelerationOn the horizontal axis, xorOn the vertical axis, y (Free fall)

x=x0+ν0 t+12 at

2

y= y0+v0 t−12 gt

2

Final Velocity, given acceleration and displacementOn the horizontal axis, xorOn the vertical axis, y (Free fall)

ν2=ν02

+2a ( x−x0)

ν2=ν02−2 g ( y− y0 )

Newton’s Second Law F⃗net=ma⃗Weight Normal Force on a horizontal surfaceNormal Force on an incline

w = mgFnorm=mgFnorm=mgsin θ=w sin θ

Friction under static conditionsKinetic friction (sliding)Coefficient of Friction

F staticfric=μs Fnorm

F kineticfric=μkFnorm

μ=tan θWork done by a constant forceWork-Energy Theorem

W=Fnetcosd

W=∆ KE=12mv2−1

2mv0

2

W=∆ PE=mgh−mgh0Springs Fspring = kx

Wspring = ½ kx2

PEspring = ½ kxKinetic Energy KE = ½ mv2

Gravitiational Potential Energy PEgrav = mghTotal Mechanical Energy E0 = E

KE0 + PE0 = KEf + PEf

PowerP=W

t= Fcosθd

t=F vavg

Volt, V

Ohm,

Tesla, T

Electron Volt, eV

Bequerel, Bq

Angular displacementθ=12

¿)

θ=ω0 t+12α t 2

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

Angular velocity

Tangential velocity

ωf=ω0+αtωf2=ωf

2+2αθ

v=ωr=2 πrT

=2π r2 f

Angular Acceleration

Centripetal Acceleration

Centripetal Force

α=ωf−ω0¿¿t

ac=4 π2rT2

=4 π2 r f 2= v2

r

FC=mac=m v2

r=mrω2

Universal Gravitation

Gravitational Field Strength

Gravitational Potential Energy

Kepler’s Law

F=GM 1M 2

r2

g=GMr 2

= GM(r+h)2

U=PE=−Gm1m2r

T 2=( 4 π2GM )r 3Electrical Force

F e=k q1q2r2

=EQ

E=k Qr 2

=Vd

Magnetic Force Fmag=qvBsinθ

Speed of Sound 331 m/s + 0.6(oC)Simple Harmonic MotionPeriod of waves

Springs

And Pendula

Wave SpeedWave EnergyDeBroglie Wavlength

T=1f

T s=2 π √mkT p=2π √ l

g

velocity = fE = hf = KE + W

λ= hmv

RadioactivityRadioactive Decay Activity= ΔN

t=−¿kN

N=N 0 e−kt

10-12, pico, p