Physics Semester 2 Review – Final Exam

Momentum Conservation

1. Tiger Woods hits 45.0-gram golf ball, giving it a speed of 75.0 m/sec. What momentum has Tiger given to the golf ball?p = mvp = (0.045 kg)(75.0 m/sec)p = 3.38 kg·m/sec

2. A 400-kilogram cannon fires a 10-kilogram cannonball at 20 m/sec. If the cannon is on wheels, at what velocity does it move backward? m1v1 + m2v2 = m3v3 + m4v4400 kg(0 m/sec) + 10 kg(0 m/sec) = 400 kg(v2) + 10 kg(20m/s)0 = 400 kg(v2) + 200 kg·m/sec(v2) = (-200 kg·m/sec)/400 kg(v2) = -0.50 m/sec

3. Two billion people jump up in the air at the same time with an average velocity of 7.0 m/sec. If the mass of an average person is 60 kilograms and the mass of Earth is 5.98 × 1024 kilograms:

a. What is the total momentum of the two billion people?b. What is the effect of their action on Earth?

a. P = (# of people)(mv); p =(2.0 × 109)(60 kg)(7.0 m/sec);p = 8.4 × 1011 kg·m/secb. p(before jumping) = p (after jumping)m1v1 + m2v2 = m3v3 + m4v40 = 8.4 × 1011 kg·m/sec + 5.98 × 1024(v4);(v4) = (-8.4 × 1011 kg·m/sec)/ 5.98 x 1024

Earth moves beneath their feet at the speed, v4 = -1.4 × 10-13 m/sec

Collisions and Conservation of Momentum 3.3• There are two main types of collisions: elastic and inelastic.• As long as there are no outside forces (such as friction), momentum is conserved in both elastic and inelastic collisions.• Conservation of momentum makes it possible to determine the motion of objects before and after colliding.• The steps from the text for using momentum to solve collision problems are provided in the graphic below.

4. What is the momentum of a 100-kilogram fullback carrying a football on a play at a velocity of 3.5 m/sec.p = mv; p = (100kg)(3.5m/s); p = 350kg·m/s

5. What is the momentum of a 75.0-kilogram defensive back chasing the fullback at a velocity of 5.00 m/secp = mv; p = (75.0kg)(5.00m/s); p = 375kg·m/s

6. Terry, a 70-kilogram tailback, runs through his offensive line at a speed of 7.0 m/sec. Jared, a 100-kilogram linebacker, running in the opposite direction at 6.0m/s, meets Jared head-on and “wraps him up.” What is the result of this tackle?p(before collision) = p(after collision)m1v1 + m2v2 = (m3+ m4)(v3+4)(2000 kg)(5m/s) + (6000 kg)(-3m/s) = (8000 kg)(v3+4)v3+4 = -1m/s or 1m/s west

7. A 4-kilogram ball moving at 8 m/sec to the right collides with a 1-kilogram ball at rest. After the collision, the 4-kilogram ball moves at 4.8 m/sec to the right. What is the velocity of the 1-kilogram ball?p(before collision) = p(after collision)m1v1 + m2v2 = m3v3 + m4v4(4 kg)(8m/s) + (1 kg)(0m/s) = (4 kg)(4.8m/s) + (1kg)v4v4 = (32kgm/s - 19.2kg-m/s)/(1kg); v4 = 12.8m/s

8. A 0.10-kilogram piece of modeling clay is tossed at a motionless 0.10-kilogram block of wood and sticks. The block slides across a frictionless table at 15 m/sec.

a. At what speed was the clay tossed?b. The clay is replaced with a “bouncy” ball tossed with the same speed.

The bouncy ball rebounds from the wooden block at a speed of 10 meters per second. What effect does this have on the wooden block?

a. p(before toss) = p(after toss)m1v1 + m2v2 = (m3+ m4)(v3+4)(0.10 kg)(v1) + (0.10 kg)(0 m/s) = (0.20 kg)(15 m/s)(v1) = (0.30 kg·m/s)(0.10 kg)(v1) = 30 m/sb. p(before collision) = p(after collision)m1v1 + m2v2 = m3v3 + m4v4(0.10 kg)(30 m/s) + (0.10 kg)(0 m/s) = (0.10 kg)(v3) +(0.10 kg)(-40 m/s)(v3) = (3.0 kg·m/s + 4.0 kg·m/s)/(0.10 kg)(v3) = 70 m/sThe block slides away at a much higher speed of (v3) = 70 m/s. The “bouncy ball, by rebounding, has experienced a greater change in momentum. The block will experience this change in momentum as well.

9. In a railroad switchyard, a 45-ton freight car is sent at 8.0 mi/h toward a 28-ton car that is moving in the same direction at 3.4 mi/h. What is the speed of the pair after they couple together? p(before collision) = p(after collision)m1v1 + m2v2 = (m1+m2)v3[45ton(2000lb/ton)(1kg/2.2lb)]x[8.0mi/h(1609m/mi)(1h/3600s)]+[28ton((2000lb/ton)(1kg/2.2lb)]]x[3.4mi/h(1609m/mi)(1h/3600s)] = [(45ton+28ton)(2000lb/ton)(1kg/2.2lb)]v340909kgx3.58m/s + 25453kgx1.52m/s=(66362)v3v3=2.79m/s in original direction

10. A meteorite plunges to Earth, embedding itself 75 cm in the ground. If it does 140MJ of work in the process, what average force does the meteorite exert on the ground?

**Refer to pumpkin on the post problemW=Fxd; F=W/dF = 140 x 106 J/0.75m = 1.9 x 108N (assuming it strikes perpendicular to the ground and the work is in the same direction as the force).

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.

11. 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)?

a. 1,188°/secondb. 200 rpm

12. 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).a. 0.38 meterb. 1.52 m/secc. 0.75 m/sec

Universal Gravitation 6.3The 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.

13. Calculate the force between two objects that have masses of 70 kilograms and 2,000 kilograms separated by a distance of 1 meter.F=6.67 x10-11Nm2/kg2(70 kg x 2000 kg)/(1m)2= 9.338 x 106N

14. Calculate the force between two touching grapefruits each with a radius of 0.08 meters and a mass of 0.45 kilograms.F =Gm1m2/r2= 6.67 x10-11Nm2/kg2(0.45 kg x 0.45 kg)/(0.08m)2= 2.11 x 10-9 N

15. 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.F= F =Gm1m2/r2 = 6.67 x10-11Nm2/kg2(0.45 kg x 5.9742 x 1024 kg)/(6.3710 x 10 6m)2= 4.42 N

16. 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.mmoon= Fr2/Gmman = (146Nx (1.74 x 106m)2 )/(6.67 x 10-11x90kg) = 7.36 x 10 22 kg

17. 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?F =Gm1m2/r2 = 6.67 x 10 -11(1.99 x 1030kg)(5.9742 x 1024kg)/(150 x 109m)2 = 3.52 x 1022N

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:

18. Earth has a gravitational field strength of 9.8 N/kg. Its radius is 6,378,000 meters. What is Earth’s mass?g = Gm/r2= 9.8 m/s2 =6.67 x 10-11(mearth)/(6378000m)2

m= (9.8 m/s2)(6378000m)2/6.67 x 10-11 = 6.0 x 1024 kg

19. The escape speed from a planet of mass 3.6 x 1024 kg is 9.1 km/s. What is the planet’s radius?g = Gm/r2 and vesc=√2 gr … so substituting for g

vesc=√ 2 Gmrr2 =√ 2 Gm

rsolve for r…

r=2 Gmvesc

2 =2 (6.67 x 10−11)(3.6 x 1024)

(9.1 x10¿¿3m / s)❑2=1.01 x 107 m¿

Coulomb’s Law 15.2There 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.

20. What is the force between a 3 C charge and a 2 C charge separated by a distance of 5 meters?F = 2.16 x 109N

21. 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?Q2= 0.006 C or 6 mC

22. 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?d = 0.9m

Calculating Electric Fields and Forces

23. What is the force of an electric field of strength 4.0 N/C on a charge of 0.5 CF = 2.0 N

24. If an object with a charge of 0.08 C experiences an electric force of 5.0 N, what is the electric field strength?E = 63 N/C

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.

25. A circuit contains a 1.5 volt battery and a bulb with a resistance of 3 ohms. Calculate the current.I = V/R = 1.5 V/3Ω = 0.5 A

26. What is the voltage of a circuit with 15 amps of current and toaster with 8 ohms of resistance?V = IR = (15A)(8Ω)=120V

27. A light bulb has a resistance of 4 ohms and a current of 2 A. What is the voltage across the bulb?

V = IR = (2A)(4Ω) = 8V28. 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?

a. Circuit A: 6 V; Circuit B: 12 Vb. Circuit A: 1 A; Circuit B: 2 Ac. Circuit A: 0.5 A; Circuit B: 1 Ad. It is brighter in circuit B because there is a greater voltage and greater current (and more power is consumed since power equals current times voltage).

Series Circuits

29. For the circuit shown in the diagram to the left, what is the total resistance of the circuit? 6Ω

30. What is the current through each resistor?1.5A

31. Describe what would happen to the circuit if the wire to the Ω resistor broke. The current would stop because the circuit is no longer complete

123 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’sLaw (I=V/R).

32. For the circuit shown in the diagram to the left, what is the total resistance of the circuit? 0.55Ω

33. What is the current through each resistor? 16.4 A

34. Describe what would happen to the circuit if the

wire to the 1Ω resistor broke. The current would flow through the other resistors (2 and 3 ohms).

35. For the circuit shown in the diagram to the right, what is the total resistance of the circuit?

36. What is the current through each resistor?37. Describe what would happen to the circuit if

the wire to the 1Ω resistor broke.

Electrical Power 14.3During 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

38. 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?a. 5 kWb. 10 kWhc. $1.50

39. Calculate the power of a motor that draws a current of 2 A when connected to a 12 volt battery. 24 W

Period and Frequency

40. A speaker vibrates at a frequency of 200 Hz. What is its period? 0.005 s

41. A pendulum has a period of 0.3 second. What is its frequency? 3.33 Hz42. 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?T = 2 s; f = 0.5 Hz

43. 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?

(a) (b) at the equilibrium position (c)

44. In the space below, sketch and label both a transverse wave and a longitudinal wave.

Waves

45. On the graphic at right label the following parts of a wave:

a. one wavelength

b. half of a wavelength

c. the amplituded. creste. trough

46. How many wavelengths are representedin the wave above? 2 wavelengths

47. What is the amplitude of the wave shown

above? 5 cm

48. A water wave has a frequency of 2 hertz and a wavelength of 5 meters. Calculate its speed. v = 10m/s

49. A wave has a speed of 50 m/sec and a frequency of 10 Hz. Calculate its wavelength. = 5 m

50. A wave has a speed of 30 m/sec and a wavelength of 3 meters. Calculate its frequency.f = 10 Hz

51. A wave has a period of 2 seconds and a wavelength of 4 meters. Calculate its frequency and speed.f = 0.5Hz; v = 2 m/s

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

52. How many times louder than city traffic does the front row at a rock concert sound? 1011 : 107 = 104 = 10000 times louder, or 40 dB

53. How many times greater intensity is the sound in the front row at a rock concert than normal conversation?1011 : 106 = 105 = 100000 times louder, or 50 dB

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.

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

55. Green light has a lower frequency than blue light. Which color of light has a longer wavelength? green light has a longer wavelength

56. Calculate the wavelength of violet light with a frequency of 750 × 1012 Hz. 4x10-7m

57. Calculate the frequency of yellow light with a wavelength of 580 × 10–9

m. 5.2 x 1014Hz

58. A star is moving away from Earth at 7 x 106 m/sec. Will the spectral line be shifted to a shorter or longer wavelength. the wavelength will seem to be longer as the star is moving away from Earth

59. 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? d = vt = (331m/s+0.6(31.667))(0.6s) = 210m away

b. What is the wavelength of the sound wave produced? 0.80 mc. 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 pitch will seem higher as the bungee jumper approaches the sound and it will appear to be lower as the bungee jumper falls away from the trumpet player

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.

60. Light strikes a mirror’s surface at 20 degrees to the normal. What will the angle of reflection be? the angle of reflection will be 20 degrees to the normal

61. 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?The angle is 96 degrees. There for the angles of incidence and reflection will each be 48 degrees.

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.

62. 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.

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?