# Cp physics - Spring Final Review (second semester topics)

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1 Name: Class: _ Date: _ Cp physics - Spring Final Review (second semester topics) Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following is a direct cause of a substance s temperature increase? a. Energy is removed from the particles of the substance. b. Kinetic energy is added to the particles of the substance. c. The number of atoms and molecules in a substance changes. d. The volume of the substance decreases. 2. What happens to the internal energy of an ideal gas when it is heated from 0 C to 4 C? a. It increases. c. It remains constant. b. It decreases. d. It is impossible to determine. 3. Which of the following is proportional to the kinetic energy of atoms and molecules? a. elastic energy c. potential energy b. temperature d. thermal equilibrium 4. As the temperature of a substance increases, its volume tends to increase due to a. thermal equilibrium. c. thermal expansion. b. thermal energy. d. thermal contraction. 5. What is the temperature of a system in thermal equilibrium with another system made up of water and steam at 1 atm of pressure? a. 0 F c. 0 K b. 273 K d. 100 C 6. Energy transferred as heat occurs between two bodies in thermal contact when they differ in which of the following properties? a. mass c. density b. specific heat d. temperature 7. Which of the following terms describes a transfer of energy? a. heat c. temperature b. internal energy d. kinetic energy 8. The use of fiberglass insulation in the outer walls of a building is intended to minimize heat transfer through what process? a. conduction c. convection b. radiation d. vaporization 9. How is energy transferred as heat always directed? a. from an object at low temperature to an object at high temperature b. from an object at high temperature to an object at low temperature c. from an object at low kinetic energy to an object at high kinetic energy d. from an object with higher mass to an object of lower mass 10. What three properties of a substance affect the amount of energy transferred as heat to or from the substance? a. volume, temperature change, specific heat capacity b. density, temperature change, specific heat capacity c. mass, temperature change, specific heat capacity d. mass, temperature change, latent heat 1

2 Name: 11. A slice of bread contains about J of energy. If the specific heat capacity of a person is J/kg C, by how many degrees Celsius would the temperature of a 70.0 kg person increase if all the energy in the bread were converted to heat? a C c C b C d C 12. Which of the following is true during a phase change? a. Temperature increases. c. Temperature decreases. b. Temperature remains constant. d. There is no transfer of energy as heat. 13. The figure above shows how the temperature of 10.0 g of ice changes as energy is added. Which of the following statements is correct? a. The water absorbed energy continuously, but the temperature increased only when all of the water was in one phase. b. The water absorbed energy sporadically, and the temperature increased only when all of the water was in one phase. c. The water absorbed energy continuously, and the temperature increased continuously. d. The water did not absorb energy. 14. At what point on the figure above does the substance undergo a phase change? a. A c. C b. B d. E 15. Using the figure above, determine which value equals the latent heat required to change the liquid water into steam. a J c J b J d J 16. At what point on the figure above is the amount of energy transferred as heat approximately J? a. A c. C b. B d. D 2

3 Name: 17. When an ideal gas does positive work on its surroundings, which of the gas s quantities increases? a. temperature c. pressure b. volume d. internal energy 18. An ideal gas system is maintained at a constant volume of 4 L. If the pressure is constant, how much work is done by the system? a. 0 J c. 8 J b. 5 J d. 30 J 19. Which thermodynamic process takes place at a constant temperature so that the internal energy of a system remains unchanged? a. isovolumetric c. adiabatic b. isobaric d. isothermal 20. Which thermodynamic process takes place at constant volume so that no work is done on or by the system? a. isovolumetric c. adiabatic b. isobaric d. isothermal 21. In an isovolumetric process for an ideal gas, the system s change in the energy as heat is equivalent to a change in which of the following? a. temperature c. pressure b. volume d. internal energy 22. How is conservation of internal energy expressed for a system during an adiabatic process? a. Q = W = 0, so ΔU = 0 and U i = U f b. Q = 0, so ΔU = W c. ΔT = 0, so ΔU = 0; therefore, ΔU = Q W = 0, or Q = W d. ΔV = 0, so PΔV = 0 and W = 0; therefore, ΔU = Q 23. How is conservation of internal energy expressed for a system during an isovolumetric process? a. Q = W = 0, so ΔU = 0 and U i = U f b. Q = 0, so ΔU = W c. ΔT = 0, so ΔU = 0; therefore, ΔU = Q W = 0, or Q = W d. ΔV = 0, so PΔV = 0 and W = 0; therefore, ΔU = Q 24. How is conservation of internal energy expressed for a system during an isothermal process? a. Q = W = 0, so ΔU = 0 and U i = U f b. Q = 0, so ΔU = W c. ΔT = 0, so ΔU = 0; therefore, ΔU = Q W = 0, or Q = W d. ΔV = 0, so PΔV = 0 and W = 0; therefore, ΔU = Q 25. An ideal gas system undergoes an adiabatic process in which it expands and does 20 J of work on its environment. What is the change in the system s internal energy? a. 20 J c. 0 J b. 5 J d. 20 J 26. An ideal gas system undergoes an isovolumetric process in which 20 J of energy is added as heat to the gas. What is the change in the system s internal energy? a. 20 J c. 5 J b. 0 J d. 20 J 27. A repelling force occurs between two charged objects when the charges are of a. unlike signs. c. equal magnitude. b. like signs. d. unequal magnitude. 3

4 Name: 28. When a glass rod is rubbed with silk and becomes positively charged, a. electrons are removed from the rod. c. protons are added to the silk. b. protons are removed from the silk. d. the silk remains neutral. 29. Charge is most easily transferred in a. nonconductors. c. semiconductors. b. conductors. d. insulators. 30. In the diagram shown above, the circles represent small balls that have electric charges. Ball 1 has a negative charge, and ball 2 is repelled by ball 1. Next, you see that ball 2 repels ball 3 and that ball 3 attracts ball 4. What is the electric charge on ball 4? a. Ball 4 may have either a positive or negative charge. b. Ball 4 has a negative charge. c. Ball 4 has a positive charge. d. It is not possible to determine the charge on ball The process of charging a conductor by bringing it near another charged object and then grounding the conductor is called a. contact charging. c. polarization b. induction. d. neutralization. 32. Two point charges, initially 2 cm apart, are moved to a distance of 10 cm apart. By what factor does the resulting electric force between them change? a. 25 c. 1 5 b. 5 d Two positive charges, each of magnitude q, are on the y-axis at points y = +a and y = a. Where would a third positive charge of the same magnitude be located for the net force on the third charge to be zero? a. at the origin c. at y = 2a b. at y = 2a d. at y = a 34. Which is the most correct statement regarding the drawing of electric field lines? a. Electric field lines always connect from one charge to another. b. Electric field lines always form closed loops. c. Electric field lines can start on a charge of either polarity. d. Electric field lines never cross each other. 4

5 Name: 35. The electric field just outside a charged conductor in electrostatic equilibrium is a. zero. b. at its minimum level. c. the same as it is in the center of the conductor. d. perpendicular to the conductor s surface. 36. For a conductor that is in electrostatic equilibrium, any excess charge a. flows to the ground. b. resides entirely on the conductor s outer surface. c. resides entirely on the conductor s interior. d. resides entirely in the center of the conductor. 37. Electric field strength depends on a. charge and distance. c. Coulomb constant and mass. b. charge and mass. d. elementary charge and radius. 38. When a positive charge moves in the direction of the electric field, what happens to the electrical potential energy associated with the charge? a. It increases. b. It decreases. c. It remains the same. d. It sharply increases, and then decreases. 39. Charge buildup between the plates of a capacitor stops when a. there is no net charge on the plates. b. unequal amounts of charge accumulate on the plates. c. the potential difference between the plates is equal to the applied potential difference. d. the charge on both plates is the same. 40. A 0.25 µf capacitor is connected to a 9.0 V battery. What is the charge on the capacitor? a C c C b C d C 41. A parallel-plate capacitor has a capacitance of C F. If the area of the plates is doubled while the distance between the plates is halved, the new capacitance will be a. 4C. c. C 2. b. 2C. d. C A wire carries a steady current of 0.1 A over a period of 20 s. What total charge moves through the wire in this time interval? a. 200 C c. 2 C b. 20 C d C 43. What is the potential difference across a 5.0 Ω resistor that carries a current of 5.0 A? a V c V b. 25 V d. 1.0 V 44. A flashlight bulb with a potential difference of 4.5 V across it has a resistance of 8.0 Ω. How much current is in the bulb filament? a. 36 A c. 1.8 A b. 9.4 A d A 5

6 Name: 45. If a 75 W lightbulb operates at a voltage of 120 V, what is the current in the bulb? a A c A b. 1.6 A d A 46. Tripling the current in a circuit with constant resistance has the effect of changing the power by what factor? a. 1 9 c. 3 b. 1 3 d If a 325 W heater has a current of 6.0 A, what is the resistance of the heating element? a. 88 Ω c. 9.0 Ω b. 54 Ω d. 4.5 Ω 48. What happens when the switch is closed in the circuit shown above? a. The lamp lights because current from the battery flows through the lamp. b. Current from the battery flows through the resistor. c. Current from the battery flows through both the lamp and the resistor. d. The lamp goes out, because the battery terminals connect to each other. 49. If the potential difference across the bulb in a camping lantern is 9.0 V, what is the potential difference across the battery used to power it? a. 1.0 V c. 9.0 V b. 3.0 V d. 18 V 50. Three resistors with values of 4.0 Ω, 6.0 Ω, and 8.0 Ω, respectively, are connected in series. What is their equivalent resistance? a. 18 Ω c. 6.0 Ω b. 8.0 Ω d. 1.8 Ω 51. Three resistors with values of 4.0 Ω, 6.0 Ω, and 10.0 Ω are connected in parallel. What is their equivalent resistance? a Ω c. 6.0 Ω b. 7.3 Ω d. 1.9 Ω 6

7 Name: 52. What is the equivalent resistance of the resistors in the figure shown above? a. 7.5 Ω c. 16 Ω b. 10 Ω d. 18 Ω 53. Two resistors with values of 6.0 Ω and 12 Ω are connected in parallel. This combination is connected in series with a 4.0 Ω resistor. What is the equivalent resistance of this combination? a Ω c. 8.0 Ω b. 2.0 Ω d. 22 Ω 54. Three resistors connected in parallel have individual values of 4.0 Ω, 6.0 Ω, and 10.0 Ω, as shown above. If this combination is connected in series with a 12.0 V battery and a 2.0 Ω resistor, what is the current in the 10.0 Ω resistor? a A c. 11 A b. 1.0 A d. 16 A 55. Where is the magnitude of the magnetic field around a permanent magnet greatest? a. The magnitude is greatest close to the poles. b. The magnitude is greatest far from the poles. c. The magnitude is equal at all points on the field. d. The magnitude is greatest halfway between poles. 7

8 Name: 56. Which compass needle orientation in the figure above might correctly describe the magnet s field at that point? a. a c. c b. b d. d 57. An electron moves north at a velocity of m/s and has a magnetic force of N exerted on it. If the magnetic field points upward, what is the magnitude of the magnetic field? a. 1.0 mt c. 3.6 mt b. 2.0 mt d. 4.8 mt 58. An electron that moves with a speed of m/s perpendicular to a uniform magnetic field of 0.40 T experiences a force of what magnitude? (q e = C) a N c N b N d. 0 N 59. The direction of the force on a current-carrying wire in an external magnetic field is a. perpendicular to the current only. b. perpendicular to the magnetic field only. c. perpendicular to both the current and the magnetic field. d. parallel to the current and to the magnetic field. 60. What is the path of an electron moving perpendicular to a uniform magnetic field? a. straight line c. ellipse b. circle d. parabola 61. What is the path of an electron moving parallel to a uniform magnetic field? a. straight line c. ellipse b. circle d. parabola 62. A current-carrying wire 0.50 m long is positioned perpendicular to a uniform magnetic field. If the current is 10.0 A and there is a resultant force of 3.0 N on the wire due to the interaction of the current and field, what is the magnetic field strength? a T c T b. 15 T d T 63. Consider two long, straight, parallel wires, each carrying a current I. If the currents move in opposite directions, a. the two wires will attract each other. b. the two wires will repel each other. c. the two wires will exert a torque on each other. d. neither wire will exert a force on the other. 8

9 Name: 64. A mass attached to a spring vibrates back and forth. At the equilibrium position, the a. acceleration reaches a maximum. c. net force reaches a maximum. b. velocity reaches a maximum. d. velocity reaches zero. 65. A simple pendulum swings in simple harmonic motion. At maximum displacement, a. the acceleration reaches a maximum. c. the acceleration reaches zero. b. the velocity reaches a maximum. d. the restoring force reaches zero. 66. For a system in simple harmonic motion, which of the following is the number of cycles or vibrations per unit of time? a. amplitude c. frequency b. period d. revolution 67. How are frequency and period related in simple harmonic motion? a. They are directly related. b. They are inversely related. c. Their sum is constant. d. Both measure the number of cycles per unit of time. 68. By what factor should the length of a simple pendulum be changed in order to triple the period of vibration? a. 3 c. 9 b. 6 d A wave travels through a medium. As the wave passes, the particles of the medium vibrate in a direction perpendicular to the direction of the wave s motion. The wave is a. longitudinal. c. electromagnetic. b. a pulse. d. transverse. 70. One end of a taut rope is fixed to a post. What type of wave is produced if the free end is quickly raised and lowered one time? a. pulse wave c. sine wave b. periodic wave d. longitudinal wave 71. Each compression in the waveform of the longitudinal wave shown above corresponds to what feature of the transverse wave below it? a. wavelength c. troughs b. crests d. amplitude 9

10 Name: 72. Each stretched region in the waveform of the longitudinal wave shown above corresponds to what feature of the transverse wave below it? a. wavelength c. troughs b. crests d. amplitude 73. When two mechanical waves coincide, the amplitude of the resultant wave is always the amplitudes of each wave alone. a. greater than c. the sum of b. less than d. the same as 74. Two mechanical waves that have positive displacements from the equilibrium position meet and coincide. What kind of interference occurs? a. constructive c. complete destructive b. destructive d. none 75. Two mechanical waves meet and coincide. One wave has a positive displacement from the equilibrium position, and the other wave has a negative displacement. What kind of interference occurs? a. constructive c. complete constructive b. destructive d. none 76. Which of the following types of interference will occur when the pulses in the figure above meet? a. no interference c. destructive interference b. constructive interference d. total interference 77. Waves arriving at a fixed boundary are a. neither reflected nor inverted. c. reflected and inverted. b. reflected but not inverted. d. inverted but not reflected. 78. Waves arriving at a free boundary are a. neither reflected nor inverted. c. reflected and inverted. b. reflected but not inverted. d. inverted but not reflected. 79. Which of the following wavelengths would produce standing waves on a string approximately 3.5 m long? a m c m b m d m 80. Which of the following wavelengths would not produce standing waves on a rope whose length is 1 m? a. 2/3 m c. 2 m b. 1 m d. 2 1/4 m 10

11 Name: 81. The standing wave shown in the diagram above would be produced on a string of length L by a wave having wavelength a. 1/2 L. c. 2 L. b. L. d. 4 L. 82. How many nodes and antinodes are shown in the standing wave above? a. two nodes and three antinodes c. one-third node and one antinode b. one node and two antinodes d. three nodes and two antinodes 83. How many nodes and antinodes are shown in the standing wave above? a. four nodes and four antinodes c. four nodes and five antinodes b. four nodes and three antinodes d. five nodes and four antinodes 84. Sound waves a. are a part of the electromagnetic spectrum. b. do not require a medium for transmission. c. are longitudinal waves. d. are transverse waves. 85. The trough of the sine curve used to represent a sound wave corresponds to a. a compression. c. the amplitude. b. the wavelength. d. a rarefaction. 86. Which of the following is the region of a sound wave in which the density and pressure are greater than normal? a. rarefaction c. amplitude b. compression d. wavelength 87. The highness or lowness of a sound is perceived as a. compression. c. ultrasound. b. wavelength. d. pitch. 11

12 Name: 88. Pitch depends on the of a sound wave. a. frequency c. power b. amplitude d. speed 89. In general, sound travels faster through a. solids than through gases. c. gases than through liquids. b. gases than through solids. d. empty space than through matter. 90. A train moves down the track toward an observer. The sound from the train, as heard by the observer, is the sound heard by a passenger on the train. a. the same as c. higher in pitch than b. a different timbre than d. lower in pitch than 91. The Doppler effect occurs with a. only sound waves. c. only water waves. b. only transverse waves. d. all waves. 92. At a distance of 3 m, the intensity of a sound will be the intensity it was at a distance of 1 m. a. one-ninth c. 3 times b. one-third d. 9 times 93. If a guitar string has a fundamental frequency of 500 Hz, what is the frequency of its second harmonic? a. 250 Hz c Hz b. 750 Hz d Hz 94. How many beats per second are heard when two vibrating tuning forks having frequencies of 342 Hz and 345 Hz are held side by side? a. 687 Hz c. 5 Hz b Hz d. 3 Hz 95. Which portion of the electromagnetic spectrum is used in a television? a. infrared waves c. radio waves b. X rays d. gamma waves 96. Which portion of the electromagnetic spectrum is used in a microscope? a. infrared waves c. visible light b. gamma rays d. ultraviolet light 97. Which portion of the electromagnetic spectrum is used to identify fluorescent minerals? a. ultraviolet light c. infrared waves b. X rays d. gamma rays 98. What is the wavelength of microwaves of Hz frequency? a m c m b m d m 99. What is the frequency of an electromagnetic wave with a wavelength of m? a Hz c Hz b Hz d Hz 100. In a vacuum, electromagnetic radiation of short wavelengths a. travels as fast as radiation of long wavelengths. b. travels slower than radiation of long wavelengths. c. travels faster than radiation of long wavelengths. d. can travel both faster and slower than radiation of long wavelengths. 12

13 Name: 101. When red light is compared with violet light, a. both have the same frequency. c. both travel at the same speed. b. both have the same wavelength. d. red light travels faster than violet light Snow reflects almost all of the light incident upon it. However, a single beam of light is not reflected in the form of parallel rays. This is an example of reflection off a surface. a. regular, rough c. diffuse, specular b. regular, specular d. diffuse, rough 103. When a straight line is drawn perpendicular to a flat mirror at the point where an incoming ray strikes the mirror s surface, the angles of incidence and reflection are measured from the normal and a. the angles of incidence and reflection are equal. b. the angle of incidence is greater than the angle of reflection. c. the angle of incidence is less than the angle of reflection. d. the angle of incidence can be greater than or less than the angle of reflection If a light ray strikes a flat mirror at an angle of 14 from the normal, the reflected ray will be a. 14 from the mirror s surface. c. 90 from the mirror s surface. b. 76 from the normal. d. 14 from the normal The image of an object in a flat mirror is always a. larger than the object. c. independent of the size of the object. b. smaller than the object. d. the same size as the object If you stand 3.0 m in front of a flat mirror, how far away from you would your image be in the mirror? a. 1.5 m c. 6.0 m b. 3.0 m d m 107. Which of the following best describes the image produced by a flat mirror? a. virtual, inverted, and magnification greater than one b. real, inverted, and magnification less than one c. virtual, upright, and magnification equal to one d. real, upright, and magnification equal to one 108. For a spherical mirror, the focal length is equal to the radius of curvature of the mirror. a. one-fourth c. one-half b. one-third d. the square of 109. A concave mirror with a focal length of 10.0 cm creates a real image 30.0 cm away on its principal axis. How far from the mirror is the corresponding object? a. 20 cm c. 7.5 cm b. 15 cm d. 5.0 cm 110. If a virtual image is formed 10.0 cm along the principal axis from a convex mirror with a focal length of 15.0 cm, what is the object s distance from the mirror? a. 30 cm c. 6.0 cm b. 12 cm d. 3.0 cm 111. A mirror has an object located on its principal axis 40.0 cm from the mirror s surface. A virtual image is formed 15.0 cm behind the mirror. What is the mirror s focal length? a cm c cm b cm d. 13 cm 13

14 Name: 112. When red light and green light shine on the same place on a piece of white paper, the spot appears to be a. yellow. c. white. b. brown. d. black Which of the following is not an additive primary color? a. yellow c. red b. blue d. green 114. Which of the following is not a primary subtractive color? a. yellow c. magenta b. cyan d. blue 115. Part of a pencil that is placed in a glass of water appears bent in relation to the part of the pencil that extends out of the water. What is this phenomenon called? a. interference c. diffraction b. refraction d. reflection 116. Refraction is the bending of a wave disturbance as it passes at an angle from one into another. a. glass c. area b. medium d. boundary 117. The of light can change when light is refracted because the medium changes. a. frequency c. wavelength b. medium d. transparency 118. When light passes at an angle to the normal from one material into another material in which its speed is higher, a. it is bent toward the normal to the surface. b. it always lies along the normal to the surface. c. it is unaffected. d. it is bent away from the normal to the surface When a light ray moves from air into glass, which has a higher index of refraction, its path is a. bent toward the normal. c. parallel to the normal. b. bent away from the normal. d. not bent A ray of light in air is incident on an air-to-glass boundary at an angle of exactly 30.0 with the normal. If the index of refraction of the glass is 1.65, what is the angle of the refracted ray within the glass with respect to the normal? a c b d The focal length for a converging lens is a. always positive. b. always negative. c. dependent on the location of the object. d. dependent on the location of the image A virtual image has a image distance (q) and is located in of the lens. a. positive, front c. negative, front b. positive, back d. negative, back 14

15 Name: 123. The focal length for a diverging lens is a. always positive. b. always negative. c. dependent on the location of the object. d. dependent on the location of the image An object is placed 20.0 cm from a thin converging lens along the axis of the lens. If a real image forms behind the lens at a distance of 8.00 cm from the lens, what is the focal length of the lens? a cm c cm b cm d cm 125. An object is placed 14.0 cm from a diverging lens. If a virtual image appears 10.0 cm from the lens on the same side as the object, what is the focal length of the lens? a. 50 cm c. 5.8 cm b. 34 cm d. 1.6 cm 126. An object that is 18 cm from a converging lens forms a real image 22.5 cm from the lens. What is the magnification of the image? a c b d Which is not correct when describing the formation of rainbows? a. A rainbow is really spherical in nature. b. Sunlight is spread into a spectrum when it enters a spherical raindrop. c. Sunlight is internally reflected on the back side of a raindrop. d. All wavelengths refract at the same angle. Problem 128. What is the electric force between an electron and a proton that are separated by a distance of m? Is the force attractive or repulsive? (e = C, k C = N m 2 /C 2 ) 129. Two equal charges are separated by m. The force between the charges has a magnitude of N. What is the magnitude of q on the charges? (k C = N m 2 /C 2 ) 130. If a force of 50 N stretches a spring 0.10 m, what is the spring constant? 131. How much displacement will a coil spring with a spring constant of 120 N/m achieve if it is stretched by a 60 N force? 132. What is the period of a 4.12 m long pendulum with a bob of mass 75.0 kg? 133. A periodic wave has a wavelength of 0.50 m and a speed of 20 m/s. What is the wave frequency? 134. What length of guitar string would vibrate at a fundamental frequency of 825 Hz if the string is stretched so that the velocity of waves on the string is 577 m/s? 135. A resonating glass tube closed at one end is 4.0 cm wide and 47.0 cm long. What are the frequencies of the first two harmonics for the resonating tube? The speed of sound in air at this temperature is 346 m/s. 15

16 Cp physics - Spring Final Review (second semester topics) Answer Section MULTIPLE CHOICE 1. B 2. A 3. B 4. C 5. D 6. D 7. A 8. A 9. B 10. C 11. C 12. B 13. A 14. B 15. B 16. C 17. B 18. A 19. D 20. A 21. D 22. B 23. D 24. C 25. A 26. D 27. B 28. A 29. B 30. C 31. B 32. D 33. A 34. D 35. D 36. B 37. A 38. B 1

17 39. C 40. B 41. A 42. C 43. B 44. D 45. A 46. D 47. C 48. D 49. C 50. A 51. D 52. B 53. C 54. A 55. A 56. A 57. A 58. B 59. C 60. B 61. A 62. A 63. B 64. B 65. A 66. C 67. B 68. C 69. D 70. A 71. B 72. C 73. C 74. A 75. B 76. B 77. C 78. B 79. A 80. D 81. B 2

18 82. D 83. D 84. C 85. D 86. B 87. D 88. A 89. A 90. C 91. D 92. A 93. C 94. D 95. C 96. C 97. A 98. C 99. B 100. A 101. C 102. D 103. A 104. D 105. D 106. C 107. C 108. C 109. B 110. A 111. A 112. A 113. A 114. D 115. B 116. B 117. C 118. D 119. A 120. D 121. A 122. C 123. B 124. A 3

19 125. B 126. A 127. D PROBLEM N; attractive Given q e = e = C q p = +e = C r = m k C = N m 2 /C 2 Solution Ê q e q p Ê F electric = k C = Nm 2 /C 2 ˆ r 2 Ë Á Ë Á F electric = N Ê ˆ C Ë Á Ê Ë Á C ˆ ˆ Ê ˆ m Ë Á C Given q 1 = q 2 F electric = N r = m k C = N m 2 /C 2 Solution F electric = k C q 1 q 2 r 2 q = q = F electric r 2 k C = = k q 2 C r 2 ( N)( m) Nm 2 C 2 ( N)( m 2 ) q = C Nm 2 /C 2 4

20 N/M Given F elastic = 50 N x = 0.10 m Solution F elastic = kx k = F elastic = 50 N x 0.10 m k = 500 N/m m Given k = 120 N/m F elastic = 60 N Solution F elastic = kx x = F elastic k x = 0.5 m s = 60 N 120 N/m Given L = 4.12 m m = 75.0 kg (This mass is not relevant to the problem.) Solution T = 2π L a g = 2π 4.12 m 9.81 m/s 2 = 4.07 s Hz Given v = 20 m/s λ = 0.50 m Solution v = fλ f = v = 20 m/s λ 0.50 m = 40 Hz 5

21 m Given ν = 577 m/s f = 825 Hz Solution f 1 = v 2L L = v 2f 1 = Hz, 552 Hz 577 m/s 2(825 Hz) = m Given v = 346 m/s L = 47 cm = 0.47 m The diameter of the tube is irrelevant to the problem. Solution For a resonating tube closed at one end, f n = n v 4L At the fundamental frequency (first harmonic), n = 1, so f 1 = v 4L = 346 m/s = 184 Hz 4(0.47 m) The next harmonic in a closed pipe is the third, where n = 3. f 3 = 3 v 4L = 3 Ê 346 m/s ˆ Ë Á 4(0.47 m) = 552 Hz 6

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