Spring 2014 213 labs:1. Graphical Analysis Revisited2. Vibrational Physics - Uniform String Under Tension3. Coulomb's Law4. Mapping Electric Fields5. Resistivity of Metals - Temperature Dependence6. Ohmic and Non-Ohmic Devices in Circuits7. Measurement of the Energy Gap in a Semiconductor8. Resistor-Capacitor Circuits9. Electrical Power - The Latent Heat of Vaporization of Liquid Nitrogen10 Geometrical Optics - Snell's Law and THin Lenses11 Interference and Diffraction of Light

Lab 2 - Vibrational Physics

1. A sinusoidal wave is traveling toward the right as shown. Which letter correctly labels the amplitude of the wave?

2. A sinusoidal wave is traveling toward the right as shown. Which letter correctly labels the wavelength of the wave?

3. The displacement of a string carrying a traveling sinusoidal wave is given by

y(x,t) = ymsin(kx – t – ).

At time t = 0 the point at x = 0 has a displacement of 0 and is moving in the positive y direction. What is the phase constant

4. The displacement of a string carrying a traveling sinusoidal wave is given by

y(x,t) = ymsin(kx – t – ).

At time t = 0 the point at x = 0 has a velocity of 0 and a positive displacement. What is the phase constant

5. Water waves in the sea are observed to have a wavelength of 300 m and a frequency of 0.07 Hz. What is the speed of these waves?

6. Sinusoidal water waves are generated in a large ripple tank. The waves travel at 20 cm/s and their adjacent crests are 5.0 cm apart. What is the time required for each new whole cycle to be generated?

7. The tension in a string with a linear density of 0.0010 kg/m is 0.40 N. What is a wavelength of a 100 Hz sinusoidal wave on this string?

8. When a 100-Hz oscillator is used to generate a sinusoidal wave on a certain string the wavelength is 10 cm. When the tension in the string is doubled what is the new wavelength of the wave the generator produces on the string?

9. A string carries a sinusoidal wave with an amplitude of 2.0 cm and a frequency of 100 Hz. What is the maximum speed of any point on the string?

10. A transverse traveling sinusoidal wave on a string has a frequency of 100 Hz, a wavelength of 0.040 m and an amplitude of 2.0 mm. What is the maximum velocity in m/s of any point on the string?

11. A transverse traveling sinusoidal wave on a string has a frequency of 100 Hz, a wavelength of 0.040 m and an amplitude of 2.0 mm. What is the maximum acceleration in m/s2 of any point on the string?

12. Two sinusoidal waves have the same angular frequency, the same amplitude ym, and travel in the same direction in the same medium. If they differ in phase by 50, what is the amplitude of the resultant wave?

13. When a certain string is clamped at both ends, the lowest four resonant frequencies are 50, 100, 150, and 200 Hz. When the string is also clamped at its midpoint, what are the lowest four resonant frequencies?

14. When a certain string is clamped at both ends, the lowest four resonant frequencies are measured to be 100, 150, 200, and 250 Hz. One of the resonant frequencies (below 200 Hz) is missing. What is it?

15. A standing wave pattern is established in a string as shown. What is the wavelength of one of the component traveling waves?

16. Standing waves are produced by the interference of two traveling sinusoidal waves, each of frequency 100 Hz. The distance from the 2nd node to the 5th node is 60 cm. What is the wavelength of each of the two original waves?

17. Two sinusoidal waves, each of wavelength 5 m and amplitude 10 cm, travel in opposite directions on a 20-m stretched string which is clamped at each end. Excluding the nodes at the ends of the string, how many nodes appear in the resulting standing wave?

18. A string, clamped at its ends, vibrates in three segments. The string is 100 cm long. What is the wavelength?

19. A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. What is the wavelength of the constituent traveling waves?

20. A 30-cm long string, with one end clamped and the other free to move transversely, is vibrating in its second harmonic. What is the wavelength of the constituent traveling waves?

21. A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. If the wave speed is 320 cm/s what is the frequency?

22. A sound wave has a wavelength of 3.0 m. What is the distance from a compression center to the adjacent rarefaction center?

23. A fire whistle emits a tone of 170 Hz. Take the speed of sound in air to be 340 m/s. What is the wavelength of this sound?

24. Two small identical speakers are connected (in phase) to the same source. The speakers are 3 m apart and at ear level. An observer stands at X, 4 m in front of one speaker as shown. If the amplitudes are not changed, what the wavelength of the sound should be so that the sound he hears is least intense?

25. Two small identical speakers are connected (in phase) to the same source. The speakers are 3 m apart and at ear level. An observer stands at X, 4 m in front of one speaker as shown. What the wavelength of the sound should be so that the sound he hears is most intense?

26. A piano wire has a length of 81 cm and a mass of 2.0 g. If its fundamental frequency is to be 394 Hz, what its tension must be?

27. A column of argon is open at one end and closed at the other. The shortest length of such a column that will resonate with a 200 Hz tuning fork is 42.5 cm. What is the speed of sound in argon?

28. A 1024 Hz tuning fork is used to obtain a series of resonance levels in a gas column of variable length, with one end closed and the other open. The length of the column changes by 20 cm from resonance to resonance. From this data, what is the speed of sound in this gas?

29. A vibrating tuning fork is held over a water column with one end closed and the other open. As the water level is allowed to fall, a loud sound is heard for water levels separated by 17 cm. If the speed of sound in air is 340 m/s, what is the frequency of the tuning fork?

30. If the speed of sound is 340 m/s, what are the two lowest frequencies of an 0.5 m organ pipe, closed at one end?

31. The lowest tone produced by a certain organ comes from a 3.0-m pipe with both ends open. If the speed of sound is 340 m/s, what is the frequency of this tone?

32. The speed of sound in air is 340 m/s. What is the shortest air column, closed at one end, which will respond to a 512 Hz tuning fork?

33. If the speed of sound is 340 m/s, what is the shortest closed pipe which resonates at 218 Hz?

34. An organ pipe with both ends open is 0.85 m long. Assuming that the speed of sound is 340 m/s, what is the frequency of the third harmonic of this pipe?

Lab 9 - Electrical Power - The Latent Heat of Vaporization of Liquid Nitrogen

35. A cube of aluminum has an edge length of 20 cm. Aluminum has a density 2.7 times that of water (1 g/cm3) and a specific heat 0.217 times that of water (1 cal/gC˚). When the internal energy of the cube increases by 47000 cal what is the increase of its temperature?

36. The energy given off by 300 grams of an alloy as it cools through 50C raises the temperature of 300 grams of water from 30C to 40C. What is the specific heat of the alloy (in cal/g C˚)?

37. The specific heat of lead is 0.030 cal/g C. 300 g of lead shot at 100C is mixed with 100 g of water at 70C in an insulated container. What is the final temperature of the mixture?

38. How many calories are required to change one gram of 0C ice to 100C steam? The latent heat of fusion is 80 cal/g and the latent heat of vaporization is 540 cal/g. The specific heat of water is 1.00 cal/g K.

39. Ten grams of ice at –20C is to be changed to steam at 130C. The specific heat of both ice and steam is 0.5 cal/g C. The heat of fusion is 80 cal/g and the heat of vaporization is 540 cal/g. How much energy the entire process requires?

40. A certain humidifier operates by raising water to the boiling point and then evaporating it. Every minute 30 g of water at 20C are added to replace the 30 g that are evaporated. The heat of fusion of water is333 kJ/kg, the heat of vaporization is 2256 kJ/kg, and the specific heat is 4190 J/kg How many joules of energy per minute does this humidifier require?

41. Fifty grams of ice at 0C is placed in a thermos bottle containing one hundred grams of water at 6C. How many grams of ice will melt? The heat of fusion of water is 333 kJ/kg and the specific heat is 4190 J/kg K.

Lab 3. Coulomb's Law

42. Two electrons (e1 and e2) and an proton (p) lie on a straight line, as shown. Show the directions of the force of e2 on e1, the force of p on e1, and the total force on e1.

43. Two protons (p1 and p2) and an electron (e) lie on a straight line, as shown. Show the directions of the force of p1 on e, the force of p2 on e, and the total force on e.

44. The magnitude of the total negative charge on the electrons in 1 kg of helium (atomic number 2, atomic mass 4)?

45. A wire contains a steady current of 2 A. What is the charge that passes a cross section in 2 s?

46. A wire contains a steady current of 2 A. What is the number of electrons that pass a cross section in 2 s?

47. A 5.0-C charge is 10 m from a –2.0-C charge. What is the electrostatic force on the positive charge?

48. Two identical charges, 2.0 m apart, exert forces of magnitude 4.0 N on each other. What is the value of either charge?

49. A particle with charge 2C charge is placed at the origin, an identical particle, with the same charge, is placed 2 m from the origin on the x axis, and a third identical particle, with the same charge, is placed 2 m from the origin on the y axis. What is the magnitude of the force on the particle at the origin?

50. A particle with a charge of 5 10–6 C and a mass of 20 g moves uniformly with a speed of 7 m/s in a circular orbit around a stationary particle with a charge of –5 10–6 C. What is the radius of the orbit?

Lab 4 - Mapping Electric Fields

51. The diagram shows the electric field lines in a region of space containing two small charged spheres (Y and Z). Which of them is charged positively?

52. What is the electric field at a distance of 10 cm from an isolated point particle with a charge of 2 10–9 C?

53. Two protons (p1 and p2) are on the x axis, as shown below. What are the directions of the electric field at points 1, 2, and 3?

54. The diagrams below depict four different charge distributions. The charged particles are all the same distance from the origin. For which of these configurations the electric field at the origin is zero?

55. The diagram shows a particle with positive charge Q and a particle with negative Q. What is the direction of the electric field at point P on the perpendicular bisector of the line joining them?

56. The diagram shows two identical particles, each with positive charge Q. What is the direction of the electric field at point P on the perpendicular bisector of the line joining them?

57. Two point particles, one with charge +8 10–9 C and the other with charge–2 10–9 C, are separated by 4 m. What is the electric field in N/C midway between them?

58. Positive charge Q is uniformly distributed on a semicircular rod. What is the direction of the electric field at point P, the center of the semicircle?

59. Positive charge +Q is uniformly distributed on the upper half of a semicircular rod and negative charge –Q is uniformly distributed on the lower half. What is the direction of the electric field at point P, the center of the semicircle?

60. Positive charge +Q is uniformly distributed on the upper half of a rod and a negative charge –Q is uniformly distributed on the lower half. What is the direction of the electric field at point P, on the perpendicular bisector of the rod?

61. What is the magnitude of the force of a 400-N/C electric field on a 0.02-C point charge?

62. A charged oil drop with a mass of 2 10–4 kg is held suspended by a downward electric field of 300 N/C. What is the charge on the drop?

63. If 500 J of work are required to carry a 40-C charge from one point to another, what is the

potential difference between these two points?

64. The potential difference between two points is 100 V. If a particle with a charge of 2 C is transported from one of these points to the other, what is the magnitude of the work done?

65. Two large parallel conducting plates are separated by a distance d = 0.01 m, placed in a vacuum, and connected to a source of potential difference V = 10 V. An oxygen ion, with charge 2e, starts from rest on the surface of one plate and accelerates to the other. If e denotes the magnitude of the electron charge, what is the final kinetic energy of this ion?

66. What is the work required to carry a particle with a charge of 6.0-C from a 5.0-V equipotential surface to a 6.0-V equipotential surface and back again to the 5.0-V surface?

67. An electron goes from one equipotential surface to another along one of the four paths shown below. Rank the paths according to the work done by the electric field, from least to greatest.

68. The diagram shows four pairs of large parallel conducting plates. The value of the electric potential is given for each plate. Rank the pairs according to the magnitude of the electric field between the plates, least to greatest.

69. The potential difference between its ends of a 2-meter stick that is parallel to a uniform electric field is 400 V. What is the magnitude of the electric field?

Lab 8 - Resistor-Capacitor Circuits

70. Each plate of a capacitor stores a charge of magnitude 1 mC when a 100-V potential difference is applied. What is the capacitance?

71. What potential difference is required to charge a 1-F capacitor with 2 C?

72. A parallel-plate capacitor has a plate area of 0.2 m2 and a plate separation of 0.1 mm. To obtain an electric field of 2.0 106 V/m between the plates, what the magnitude of the charge on each plate should be?

73. A parallel-plate capacitor has a plate area of 0.2 m2 and a plate separation of 0.1 mm. If the charge on each plate has a magnitude of 4 10–6 C what is the potential difference across the plates?

74. Capacitor C1 and C2 are connected in parallel. What is the equivalent capacitance if C1 = 10 nf and C2 = 20 nf?

75. Capacitor C1 and C2 are connected in series. What is the equivalent capacitance if C1 = 10 nf and C2 = 20 nf?

76. Two identical capacitors, each with capacitance C = 10 nf, are connected in parallel and the combination is connected in series to a third identical capacitor. What is the equivalent capacitance of this arrangement?

77. Capacitor C1 is connected alone to a battery and charged until the magnitude of the charge on each plate is 4.0 108 C. Then it is removed from the battery and connected to two other capacitors C2 and C3, as shown. The charge on the positive plate of C1 is then 1.0 108 C. What are the charges on the positive plates of C2 and C3?

78. Each of the four capacitors shown is 500 F. The voltmeter reads 1000V. What is the magnitude of the charge, in coulombs, on each capacitor plate?

79. The diagram shows six 6-F capacitors. What is the capacitance between points a and b?

80. Each of the three 25-F capacitors shown is initially uncharged. How many coulombs of charge pass through the ammeter A after the switch S is closed?

Lab 6 Ohmic and Non-Ohmic Devices in Circuits

81. A 60-watt light bulb carries a current of 0.5 ampere. What is the total charge passing through it in one hour?

82. A 10-ohm resistor has a constant current. If 1200 C of charge flow through it in 4 minutes what is the value of the current?

83. A nichrome wire is 1 m long and 1 10–6 m2 in cross-sectional area. When connected to a potential difference of 2 V, a current of 4 A exists in the wire. What is the resistivity of this nichrome?

84. A current of 0.5 ampere exists in a 60-ohm lamp. What is the applied potential difference?

85. Which of the following graphs best represents the current-voltage relationship for a device that obeys Ohm's law?

86. A certain sample carries a current of 4 A when the potential difference is 2 V and a current of 10 A when the potential difference is 4 V. Does this sample obey Ohm's law?

87. A flat iron is marked "120 volt, 600 watt". In normal use, What is the current in it?

88. An certain resistor dissipates 0.5 W when connected to a 3 V potential difference. When connected to a 1 V potential difference, what will this resistor dissipate?

89. An ordinary light bulb is marked "60 watt, 120 volt". What is its resistance?

90. The mechanical equivalent of heat is 1 cal = 4.18 J. The specific heat of water is 1 cal/g·K. How long will it take for an electric immersion water heater, rated at 400 W, to

heat a liter of water from 10C to 30C?

91. The mechanical equivalent of heat is 1 cal = 4.18 J. A heating coil, connected to a 120-V source, develops 60,000 calories in 10 minutes. What is the current in the coil?

92. A current of 0.3 A is passed through a lamp for 2 minutes using a 6 V power supply. What is the energy dissipated by this lamp during the 2 minutes?

93. In the diagram R1 > R2 > R3. Rank the three resistors according to the current in them, least to greatest.

94. Four 20- resistors are connected in series and the combination is connected to a 20-V emf device. What is the current in any one of the resistors?

95. Four 20- resistors are connected in series and the combination is connected to a 20-V emf device. What is the potential difference across any one of the resistors?

96. Resistances of 2.0 , 4.0 , and 6.0 and a 24-V emf device are all in series. What is the potential difference across the 2.0- resistor?

97. Resistances of 2.0 , 4.0 , and 6.0 and a 24-V battery are all in series. What is the current in the 2.0 resistor?

98. In the diagram, the current in the 3- resistor is 4 A. What is the potential difference between points 1 and 2?

99. What is the current in the 5.0- resistor in the circuit shown?

100. A portion of a circuit is shown, with the values of the currents given for some branches. What is the direction and value of the current i?

101. Four wires meet at a junction. The first carries 4A into the junction, the second carries 5A out of the junction, and the third carries 2A out of the junction. What is the current in the fourth?

102. What is the equivalent resistance between points 1 and 2 of the circuit shown?

103. Each of the resistors in the diagram is 12 . What is the resistance of the entire circuit?

104. A total resistance of 3.0 is to be produced by combining an unknown resistor R with a 12 resistor. What is the value of R and how is it to be connected to the 12 resistor?

105. By using only two resistors, R1 and R2 a student is able to obtain resistances of 3 , 4 , 12 , and 16 . What are the values of R1 and R2 (in ohms)?

106. A 3- and a 1.5- resistor are wired in parallel and the combination is wired in series to a 4- resistor and a 10-V emf device. What is the current in the 3- resistor?

107. A 3- and a 1.5- resistor are wired in parallel and the combination is wired in series to a 4- resistor and a 10-V emf device. What is the potential difference across the 3- resistor?

108. In an antique automobile, a 6-V battery supplies a total of 48 W to two identical headlights in parallel. What is the resistance (in ohms) of each bulb?

109. When switch S is open, the ammeter in the circuit shown reads 2.0 A. What is the ammeter when S is closed?

110. A certain voltmeter has an internal resistance of 10,000 and a range from 0 to 100 V. What one should connect and how in order to give it a range from 0 to 1000 V?

111. A certain ammeter has an internal resistance of 1 and a range from 0 to 50 mA. What one should connect and how in order to to make its range from 0 to 5 A?

112. A galvanometer has an internal resistance of 12 and requires 0.01 A for full scale deflection. What resistance connected in series one must use in order to convert it to a voltmeter reading 3 V full scale?

113. A certain voltmeter has an internal resistance of 10,000 and a range from 0 to 12 V. What resistance should be used in series in order to extend its range to 120 V?

114. Four circuits have the form shown in the diagram. The capacitor is initially uncharged and the switch S is open. The values of the emf , resistance and R, and capacitance C for each for the circuits are

circuit 1: = 18 V, R = 3 , C = 1 Fcircuit 2: = 18 V, R = 6 , C = 9 Fcircuit 3: = 12 V, R = 1 , C = 7 Fcircuit 4: = 10 V, R = 5 , C = 7 F

Rank the circuits according to the current just after switch S is closed least to greatest.

115. Four circuits have the form shown in the diagram. The capacitor is initially uncharged and the switch S is open.

The values of the emf , resistance R, and the capacitance C for each of the circuits arecircuit 1: = 18 V, R = 3 , C = 1 Fcircuit 2: = 18 V, R = 6 , C = 9 Fcircuit 3: = 12 V, R = 1 , C = 7 F

circuit 4: = 10 V, R = 5 , C = 7 FRank the circuits according to the time after switch S is closed for the capacitors to reach half their final charges, least to greatest.

116. In the circuit shown, the capacitor is initially uncharged. At time t = 0, switch S is closed. If denotes the time constant, what is the current through the 3 resistor when t = /10?

117. Suppose the current charging a capacitor is kept constant. Which graph below correctly gives the potential difference V across the capacitor as a function of time?

118. A charged capacitor is being discharged through a resistor. At the end of one time constant the charge has been reduced by (1 – 1/e) = 63% of its initial value. By what percent of its initial value the charge has been reduced at the end of two time constants?

119. A certain capacitor, in series with a resistor, is being charged. At the end of 10 ms its charge is half the final value. What is the time constant for the process?

120. A certain capacitor, in series with a 720- resistor, is being charged. At the end of 10 ms its charge is half the final value. What is the capacitance?

Magnetism Problems - unfortunately, no lab for this during this semester

121. An electron moves in the negative x direction, through a uniform magnetic field in the negative y direction. What is the direction of the magnetic force on the electron?

122. A beam of electrons is sent horizontally down the axis of a tube to strike a fluorescent screen at the end of the tube. On the way, the electrons encounter a magnetic field directed vertically downward. In what direction the spot on the screen will be deflected?

123. An electron (charge = –1.6 10–19 C) is moving at 3 105 m/s in the positive x direction. A magnetic field of 0.8 T is in the positive z direction. What is the magnetic force on the electron (magnitude and direction)?

124. Suppose this page is perpendicular to a uniform magnetic field and the magnetic flux through it is 5 Wb. If the page is turned by 30 around an edge what is the flux through it now?

125. A 2-T uniform magnetic field makes an angle of 30 with the z axis. What is the magnetic flux through a 3-m2 portion of the xy plane?

126. One hundred turns of insulated copper wire are wrapped around an iron core of cross-sectional area 0.100 m2. The circuit is completed by connecting the coil to a 10- resistor. As the magnetic field along the coil axis changes from 1.00 T in one direction to 1.00 T in the other direction, what is the total charge that flows through the resistor?

127. A car travels northward at 75 km/h along a straight road in a region where Earth's magnetic field has a vertical component of 0.50 10–4 T. What is the emf induced between the left and right side, separated by 1.7 m?

128. A rectangular loop of wire has area A= 0.1 m2. It is placed perpendicular to a uniform magnetic field B = 1 T and then spun around one of its sides at frequency f = 100 Hz. What is the maximum induced emf?

129. The circuit shown is in a uniform magnetic field that is into the page. The current in the circuit is 0.20 A. At what rate is the magnitude of the magnetic field changing? Is it increasing or decreasing?

130. A 10 turn conducting loop with a radius of 3.0 cm spins at 60 revolutions per second in a magnetic field of 0.50 T. What is the maximum generated emf?

131. A single loop of wire with a radius of 7.5 cm rotates about a diameter in a uniform magnetic field of 1.6 T. At what speed it should rotate in order to produce a maximum emf of 1.0 V?

132. A merry-go-round has an area of 300 m2 and spins at 2 rpm about a vertical axis at a place where the Earth's magnetic field is vertical and has a magnitude of 5 10–5 T. What is the emf around the rim?

133. As a loop of wire with a resistance of 10 moves in a constant non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5 mJ/s. What is the induced current in the loop?

134. As a loop of wire with a resistance of 10 moves in a non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5 mJ/s. What is the induced emf in the loop?

135. A rod with resistance R = 100 Ohms lies across frictionless conducting rails in a constant uniform magnetic field B = 1.2 T, as shown. Assume the rails have negligible resistance. What is the magnitude of the force that must be applied by a person to pull the rod to the right at constant speed v = 2.0 m/s?

136. A square loop of wire lies in the plane of the page. A decreasing magnetic field is directed into the page. What is the direction of the induced current in the loop?

137. A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries a constant current i, as shown. The wire is being moved toward the rectangle. What is the direction of the induced current in the rectangle?

138. A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries an increasing current in the direction shown. What is the direction of the induced current in the rectangle?

139. A long straight wire is in the plane of a rectangular conducting loop. The straight wire initially carries a constant current i in the direction shown. What is the direction of the induced current in the rectangle while the current i is being shut off?

140. The figure shows a bar moving to the right on two conducting rails. To make an induced current i in the direction indicated, a constant magnetic field in region A should be in what direction?

141. A rod lies across frictionless rails in a uniform magnetic field B, as shown. The rod moves to the right with speed v. How the magnetude of the magnetic field should change in order for the emf around the circuit to be zero?

Lab 10 Geometrical Optics - Snell's Law and Thin Lenses

142. The diagram shows the passage of a ray of light from air into a substance X. What is the index of refraction of X?

143. If nwater = 1.33, what is the angle of refraction for the ray shown?

144. Which diagram below illustrates the path of a light ray as it travels from a given point X in air to another given point Y in glass?

145. The index of refraction of benzene is 1.80. What is the critical angle for total internal reflection at a benzene-air interface?

146. The index of refraction of a certain glass is 1.50. What is the sine of the critical angle for total internal reflection at a glass-air interface?

147. The illustration shows total internal reflection taking place in a piece of glass. What is the index of refraction of this glass?