PHYF144 Tutorial Questions updated.doc

PHYF144 Tutorial Department of Engineering Sciences and Mathematics, COE

Chapter 1: Temperature

2. The temperature difference between the inside and outside of an automobile engine is 450°C. Express this temperature difference on (a) the Fahrenheit scale and (b) the Kelvin scale.

4. The melting point of gold is 1064 °C, and its boiling point is 2660 °C. (a) Express these temperatures in Kelvin. (b) Compute the difference between these temperatures in Celsius degrees and Kelvin.

7. A thin brass ring of inner diameter 10.00 cm at 20.0 °C is warmed and slipped over an aluminum rod of diameter 10.01 cm and at 20.0 °C. Assuming the average coefficient of linear expansion are constant, (a) to what temperature must this combination be cooled to separate the parts? Explain whether this separation is attainable. (b) What if? What if the aluminum rod were 10.02 cm in diameter?

11. A hollow aluminum cylinder 20.0 cm deep has an internal capacity of 2.000 L at 20.0°C. It is filled with turpentine and then slowly warmed to 80.0°C. (a) How much turpentine overflows? (b) If the cylinder is then cooled back to 20.0 °C, how far below the cylinder’s rim does the turpentine’s surface recede?

12. At 20.0°C, an aluminum ring has inner diameter of 5.0000 cm and a brass rod has a diameter of 5.0500 cm. (a) if only the ring is warmed, what temperature must it reach so that it will just slip over the rod? (b) What if? If both the ring and the rod are warmed together, what temperature must they both reached so that the ring barely slips over the rod? Would this latter process work? Explain.

13. A volumetric flask made of Pyrex is calibrated at 20.0°C. It is filled to the 100-mL mark with 35.0°C acetone. (a) What is the volume of the acetone when it cools to 20.0°C? (b) How significant is the change in volume of the flask?

30. The density of gasoline is 730 kg/m3 at 0°C. Its average coefficient of volume expansion is 9.60 × 10-4 (°C)-1. Assume 1.00 gal of gasoline occupies 0.00380 m3. How many extra kilograms of gasoline would you get if you bought 10.0 gal of gasoline at 0°C rather than a 20.0°C from a pump that is not temperature compensated?

31. A mercury thermometer is constructed as shown in Figure P19.31. The capillary tube

has a diameter of 0.00400 cm, and the bulb has a diameter of 0.250 cm. Ignoring the expansion of the glass, find the change in the height of the mercury column that occurs with a temperature change of 30.0°C.

Figure P19.31

43. Two concrete spans of a 250-m-long bridge are placed end to end so that no room is allowed for expansion (Fig. P19.43a). If a temperature increase of 20.0°C occurs, what is the height y to which the spans rise when they buckle (Fig. P19.43b)?

Figure P19.43

56. A steel wire and a copper wire, each of diameter 2.000 mm, are joined end to end. At 40.0°C, each has unstretched length of 2.000 m. The wires are connected between two fixed supports of 4.000 m apart on a tabletop. The steel wire extend from x=-2.000 m to x= 0, the copper wire extend from x= 0 to x= 2.000 m, and the tension is negligible. The temperature is then lowered to 20.0°C. At this lower temperature, find the tension in the wire and the x coordinate of the junction between the wires. (Refer to Table 12.1 and 19.1)

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Chapter 2: The First Law of Thermodynamics

24. (a) Determine the work done on a fluid that expands from i to f as indicated in Figure P20.24. (b) What If? How much work is performed on the fluid if it is compressed from f to i along the same path?

Figure P20.24

25. An ideal gas is enclosed in a cylinder with a movable piston on top of it. The piston has a mass of 8 000 g and an area of 5.00 cm2

and is free to slide up and down, keeping the pressure of the gas constant. How much work is done on the gas as the temperature of 0.200 mol of the gas is raised from 20.0°C to 300°C?

27. One mole of an ideal gas is heated slowly so that it goes from the PV state (P0, V0), to (3P0, 3V0), in such a way that the pressure is directly proportional to the volume. (a) How much work is done on the gas in the process? (b) How is the temperature of the gas related to its volume during this process?

28. A gas is compressed at a constant pressure of 0.800 atm from 9.00 L to 2.00 L. In the process, 400 J of energy leaves the gas by heat. (a) What is the work done on the gas? (b) What is the change in its internal energy?

30. A gas is taken through the cyclic process described in Figure P20.30. (a) Find the net energy transferred to the system by heat during one complete cycle. (b) What If? If the cycle is reversed—that is, the process follows the path ACBA—what is the net energy input per cycle by heat?

Figure P20.30

32. A sample of an ideal gas goes through the process shown in Figure P20.32. From A to B, the process is adiabatic; from B to C, it is isobaric with 100 kJ of energy entering the system by heat. From C to D, the process is isothermal; from D to A, it is isobaric with 150 kJ of energy leaving the system by heat. Determine the difference in internal energy Eint,B – Eint,A.

Figure P20.32

35. An ideal gas initially at 300 K undergoes an isobaric expansion at 2.50 kPa. If the volume increases from 1.00 m3 to 3.00 m3

and 12.5 kJ is transferred to the gas by heat, what are (a) the change in its internal energy and (b) its final temperature?

43. A bar of gold is in thermal contact with a bar of silver of the same length and area (Fig. P20.43). One end of the compound bar is maintained at 80.0°C while the opposite end is at 30.0°C. When the energy transfer reaches steady state, what is the temperature at the junction?

Figure P20.43

44. A thermal window with an area of 6.00 m2 is constructed of two layers of glass,

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each 4.00 mm thick, and separated from each other by an air space of 5.00 mm. If the inside surface is at 20.0°C and the outside is at –30.0°C, what is the rate of energy transfer by conduction through the window?

47. The surface of the Sun has a temperature of about 5 800 K. The radius of the Sun is 6.96 108 m. Calculate the total energy radiated by the Sun each second. Assume that the emissivity is 0.965.

Chapter 3: The Kinetic Theory of Gases

3. A sealed cubical container 20.0 cm on a side contains three times Avogadro's number of molecules at a temperature of 20.0°C. Find the force exerted by the gas on one of the walls of the container.

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7. (a) How many atoms of helium gas fill a balloon having a diameter of 30.0 cm at 20.0°C and 1.00 atm? (b) What is the average kinetic energy of the helium atoms? (c) What is the root-mean-square speed of the helium atoms?

9. A cylinder contains a mixture of helium and argon gas in equilibrium at 150°C. (a) What is the average kinetic energy for each type of gas molecule? (b) What is the root-mean-square speed of each type of molecule?

10. A 5.00-L vessel contains nitrogen gas at 27.0C and 3.00 atm. Find (a) the total translational kinetic energy of the gas molecules and (b) the average kinetic energy per molecule.

13. A 1.00-mol sample of hydrogen gas is heated at constant pressure from 300 K to 420 K. Calculate (a) the energy transferred to the gas by heat, (b) the increase in its internal energy, and (c) the work done on the gas.

18. A vertical cylinder with a heavy piston contains air at 300 K. The initial pressure is 200 kPa and the initial volume is 0.350 m3. Take the molar mass of air as 28.9 g/mol and assume that CV = 5R/2. (a) Find the specific heat of air at constant volume in units of J/kgC. (b) Calculate the mass of the air in the cylinder. (c) Suppose the piston is held fixed. Find the energy input required to raise the temperature of the air to 700 K. (d) What If? Assume again the conditions of the initial state and that the heavy piston is free to move. Find the energy input required to raise the temperature to 700 K.

21. A 1.00-mol sample of an ideal monatomic gas is at an initial temperature of 300 K. The gas undergoes an isovolumetric process acquiring 500 J of energy by heat. It then undergoes an isobaric process losing this same amount of energy by heat. Determine (a) the new temperature of the gas and (b) the work done on the gas.

24. During the compression stroke of a certain gasoline engine, the pressure increases from 1.00 atm to 20.0 atm. If the process is adiabatic and the fuel-air mixture behaves as a diatomic ideal gas, (a) by what factor does the volume change and (b) by what factor does the temperature change? (c) Assuming that the compression starts with 0.016 0 mol of gas at 27.0C, find the values of Q, W, and Eint that characterize the process.

29. A 4.00-L sample of a diatomic ideal gas with specific heat ratio 1.40, confined to a cylinder, is carried through a closed cycle. The gas is initially at 1.00 atm and at 300 K. First, its pressure is tripled under constant volume. Then, it expands adiabatically to its original pressure. Finally, the gas is compressed isobarically to its original volume. (a) Draw a PV diagram of this cycle. (b) Determine the volume of the gas at the end of the adiabatic expansion. (c) Find the temperature of the gas at the start of the adiabatic expansion. (d) Find the temperature at the end of the cycle. (e) What was the net work done on the gas for this cycle?

31. How much work is required to compress 5.00 mol of air at 20.0°C and 1.00 atm to one tenth of the original volume (a) by an isothermal process? (b) by an adiabatic process? (c) What is the final pressure in each of these two cases?

Chapter 4: Fluid Mechanics

3. A 50.0-kg woman balances on one heel of a pair of high-heeled shoes. If the heel is circular and has a radius of 0.500 cm, what pressure does she exert on the floor?

4. The four tires of an automobile are inflated to a gauge pressure of 200 kPa. Each tire has an area of 0.024 0 m2 in contact with the ground. Determine the weight of the automobile.

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6. (a) Calculate the absolute pressure at an ocean depth of 1 000 m. Assume the density of seawater is 1 024 kg/m3 and that the air above exerts a pressure of 101.3 kPa. (b) At this depth, what force must the frame around a circular submarine porthole having a diameter of 30.0 cm exert to counterbalance the force exerted by the water?

14. The tank in Figure P14.14 is filled with water 2.00 m deep. At the bottom of one side wall is a rectangular hatch 1.00 m high and 2.00 m wide, which is hinged at the top of the hatch. (a) Determine the force the water exerts on the hatch. (b) Find the torque exerted by the water about the hinges.

22. (a) A light balloon is filled with 400 m3 of helium. At 0C, the balloon can lift a payload of what mass? (b) What If? In Table 14.1, observe that the density of hydrogen is nearly one-half the density of helium. What load can the balloon lift if filled with hydrogen?

Figure P14.14

29.A cube of wood having an edge dimension of 20.0 cm and a density of 650 kg/m3

floats on water. (a) What is the distance from the horizontal top surface of the cube to the water level? (b) How much lead weight has to be placed on top of the cube so that its top is just level with the water?

30. A spherical aluminum ball of mass 1.26 kg contains an empty spherical cavity that is concentric with the ball. The ball just barely floats in water. Calculate (a) the outer radius of the ball and (b) the radius of the cavity.

35.A plastic sphere floats in water with 50.0 percent of its volume submerged. This same sphere floats in glycerin with 40.0 percent of its volume submerged. Determine the densities of the glycerin and the sphere.

39. A large storage tank, open at the top and filled with water, develops a small hole in its side at a point 16.0 m below the water level. If the rate of flow from the leak is 2.50 10–3 m3/min, determine (a) the speed at which the water leaves the hole and (b) the diameter of the hole.

40.A village maintains a large tank with an open top, containing water for emergencies. The water can drain from the tank through a hose of diameter 6.60 cm. The hose ends with a nozzle of diameter 2.20 cm. A rubber stopper is inserted into the nozzle. The water level in the tank is kept 7.50 m above the nozzle. (a) Calculate the friction force exerted on the stopper by the nozzle. (b) The stopper is removed. What mass of water flows from the nozzle in 2.00 h? (c) Calculate the gauge pressure of the flowing water in the hose just behind the nozzle.

Chapter 5: Oscillatory Motion

13. A 1.00-kg object is attached to a horizontal spring. The spring is initially stretched by 0.100 m, and the object is released from rest there. It proceeds to move without friction. The next time the speed of the object is zero is 0.500 s later. What is the maximum speed of the object?

19. A 50.0-g object connected to a spring with a force constant of 35.0 N/m oscillates on a horizontal, frictionless surface with amplitude of 4.00 cm. Find (a) the total energy of the system and (b) the speed of the object when the position is 1.00 cm. Find (c) the kinetic energy and

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(d) the potential energy when the position is 3.00 cm.

23. A particle executes simple harmonic motion with an amplitude of 3.00 cm. At what position does its speed equal one half of its maximum speed?

32. A simple pendulum is 5.00 m long. (a) What is the period of small oscillations for this pendulum if it is located in an elevator accelerating upward at 5.00 m/s2? (b) What is its period if the elevator is accelerating downward at 5.00 m/s2? (c) What is the period of this pendulum if it is placed in a truck that is accelerating horizontally at 5.00 m/s2?

53. A large block P executes horizontal simple harmonic motion as it slides across a frictionless surface with a frequency f = 1.50 Hz. Block B rests on it, as shown in Figure P15.53, and the coefficient of static friction between the two is s = 0.600. What maximum amplitude of oscillation can the system have if block B is not to slip?

Figure P15.53 Problems 53 and 54.

54. A large block P executes horizontal simple harmonic motion as it slides across a frictionless surface with a frequency f. Block B rests on it, as shown in Figure P15.53, and the coefficient of static friction between the two is s. What maximum amplitude of oscillation can the system have if the upper block is not to slip?

63. A simple pendulum with a length of 2.23 m and a mass of 6.74 kg is given an initial speed of 2.06 m/s at its equilibrium position. Assume it undergoes simple harmonic motion, and determine its (a) period, (b) total energy, and (c) maximum angular displacement.

66. A block of mass M is connected to a spring of mass m and oscillates in simple harmonic motion on a horizontal, frictionless track (Fig. P15.66). The force constant of the spring is k and the equilibrium length is . Assume that all portions of the spring oscillate in phase

and that the velocity of a segment dx is proportional to the distance x from the fixed end; that is, vx = (x/)v. Also, note that the mass of a segment of the spring is dm = (m/)dx. Find (a) the kinetic energy of the system when the block has a speed v, and (b) the period of oscillation.

Figure P15.66

67. A ball of mass m is connected to two rubber bands of length L, each under tension T, as in Figure P15.67. The ball is displaced by a small distance y perpendicular to the length of the rubber bands. Assuming that the tension does not change, show that (a) the restoring force is –(2T/L)y and (b) the system exhibits simple harmonic motion with an angular frequency 2T / mL.

Figure P15.67

71. A block of mass m is connected to two springs of force constants k1 and k2 as shown in Figures P15.71a and P15.71b. In each case, the block moves on a frictionless table after it is displaced from equilibrium and released. Show that in the two cases the block exhibits simple harmonic motion with periods

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(a) T 2 m k1 k2 k1k2

(b) T 2 mk1 k2


Figure P15.71

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Chapter 6: Wave Motion

2. Ocean waves with a crest-to-crest distance of 10.0 m can be described by the wave function y(x, t) = (0.800 m) sin[0.628(x - vt)], where v = 1.20 m/s. (a) Sketch y(x, t) at t = 0. (b) Sketch y(x, t) at t = 2.00 s. Note that the entire wave form has shifted 2.40 m in the positive x direction in this time interval.

7. A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along the rope in 10.0 s. What is the wavelength?

9. A wave is described by y = (2.00 cm) sin (kx - t), where k = 2.11 rad/m, = 3.62 rad/s, x is in meters, and t is in seconds. Determine the amplitude, wavelength, frequency, and speed of the wave.

15. (a) Write the expression for y as a function of x and t for a sinusoidal wave traveling along a rope in the negative x direction with the following characteristics: A = 8.00 cm, = 80.0 cm, f = 3.00 Hz, and y(0, t) = 0 at t = 0. (b) What If? Write the expression for y as a function of x and t for the wave in part (a) assuming that y(x, 0) = 0 at the point x = 10.0 cm.

18. A transverse sinusoidal wave on a string has a period T = 25.0 ms and travels in the negative x direction with a speed of 30.0 m/s. At t = 0, a particle on the string at x = 0 has a transverse position of 2.00 cm and is traveling downward with a speed of 2.00 m/s. (a) What is the amplitude of the wave? (b) What is the initial phase angle? (c) What is the maximum transverse speed of the string? (d) Write the wave function for the wave.

22. Transverse waves with a speed of 50.0 m/s are to be produced in a taut string. A 5.00-m length of string with a total mass of 0.060 0 kg is used. What is the required tension?

27. Transverse waves travel with a speed of 20.0 m/s in a string under a tension of 6.00N. What tension is required for a wave speed of 30.0 m/s in the same string?

31. A 30.0-m steel wire and a 20.0-m copper wire, both with 1.00-mm diameters, are connected end to end and stretched to a tension of 150 N. How long does it take a transverse wave to travel the entire length of the two wires?

39. A sinusoidal wave on a string is described by the equation y = (0.15 m) sin (0.80x - 50t) where x and y are in meters and t is in seconds. If the mass per unit length of this string is 12.0 g/m, determine (a) the speed of the wave, (b) the wavelength, (c) the frequency, and (d) the power transmitted to the wave

49. The wave function for a traveling wave on a taut string is (in SI units)

y(x,t) = (0.350 m) sin(10 t – 3 x + /4)

(a) What are the speed and direction of travel of the wave? (b) What is the vertical position of an element of the string at t = 0, x = 0.100 m? (c) What are the wavelength and frequency of the wave? (d) What is the maximum magnitude of the transverse speed of the string?

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Chapter 7: Standing wave

5. Two sinusoidal waves are described by the wave functions

y1 = (5.00 m) sin[(4.00x – 1 200t)] and y2 = (5.00 m) sin[(4.00x – 1 200t – 0.250)]

where x, y1, and y2 are in meters and t is in seconds. (a) What is the amplitude of the resultant wave? (b) What is the frequency of the resultant wave?

11. Two sinusoidal waves in a string are defined by the functions

y1 = (2.00 cm) sin(20.0x – 32.0t) andy2 = (2.00 cm) sin(25.0x – 40.0t)

where y and x are in centimeters and t is in seconds. (a) What is the phase difference between these two waves at the point x = 5.00 cm at t = 2.00 s? (b) What is the positive x value closest to the origin for which the two phases differ by at t = 2.00 s? (This is where the two waves add to zero.)

14. Two waves in a long string are given by

y1 0.0150m cos x

2 40t

and

y2 0.0150m cos x

2 40t

where y1, y2, and x are in meters and t is in seconds. (a) Determine the positions of the nodes of the resulting standing wave. (b) What is the maximum transverse position of an element of the string at the position x = 0.400 m?

17 Two sinusoidal waves combining in a medium are described by the wave functionsy1 = (3.0 cm) sin(x + 0.60t) andy2 = (3.0 cm) sin(x – 0.60t)

where x is in centimeters and t is in seconds. Determine the maximum transverse position of an element of the medium at (a) x = 0.250cm, (b) x = 0.500 cm, and (c) x = 1.50 cm. (d) Find the three smallest values of x corresponding to antinodes.

22. A vibrator, pulley, and hanging object are arranged as in Figure P18.21, with a compound string, consisting of two strings of different masses and lengths fastened together end-to-end. The first string, which has a mass of 1.56 g and a length of 65.8 cm, runs from the vibrator to the junction of the two strings. The second string runs from the junction over the pulley to the suspended 6.93-kg object. The mass and length of the string from the junction to the pulley are, respectively, 6.75 g and 95.0 cm. (a) Find the lowest frequency for which

standing waves are observed in both strings, with a node at the junction. The standing wave patterns in the two strings may have different numbers of nodes. (b) What is the total number of nodes observed along the compound string at this frequency, excluding the nodes at the vibrator and the pulley?

Figure P18.21 Problems 21 and 22.

27. A cello A-string vibrates in its first normal mode with a frequency of 220 Hz. The vibrating segment is 70.0 cm long and has a mass of 1.20 g. (a) Find the tension in the string. (b) Determine the frequency of vibration when the string vibrates in three segments.

31. A standing-wave pattern is observed in a thin wire with a length of 3.00 m. The equation of the wave is

y = (0.002 m) sin( x)cos(100 t)

where x is in meters and t is in seconds. (a) How many loops does this pattern exhibit? (b) What is the fundamental frequency of vibration of the wire? (c) What If? If the original frequency is held constant and the tension in the wire is increased by a factor of 9, how many loops are present in the new pattern?

63. Two wires are welded together end to end. The wires are made of the same material, but the diameter of one is twice that of the other. They are subjected to a tension of 4.60 N. The thin wire has a length of 40.0 cm and a linear mass density of 2.00 g/m. The combination is fixed at both ends and vibrated in such a way that two antinodes are present, with the node between them being right at the weld. (a) What is the frequency of vibration? (b) How long is the thick wire?

67. Two waves are described by the wave functionsy1(x, t) = 5.0 sin(2.0x – 10t) and y2(x, t) = 10 cos(2.0x – 10t)

where y1, y2, and x are in meters and t is in seconds. Show that the wave resulting

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from their superposition is also sinusoidal. Determine the amplitude and phase of this sinusoidal wave.

69. A 12.0-kg object hangs in equilibrium from a string with a total length of L = 5.00 m and a linear mass density of = 0.00100 kg/m. The string is wrapped around two light, frictionless pulleys that are separated by a distance of d = 2.00 m (Fig. P18.69a). (a) Determine the tension in the string. (b) At what frequency must the string between the pulleys vibrate in order to form the standing wave pattern shown in Figure P18.69b?

Figure P18.69

Chapter 8: The Nature of Light and the Laws of Geometric Optics

3. In an experiment to measure the speed of light using the apparatus of Fizeau (see Fig. 35.2), the distance between light source and mirror was 11.45 km and the wheel had 720 notches. The experimentally determined value of c was 2.998 × 108 m/s. Calculate

the minimum angular speed of the wheel for this experiment.

Figure 35.2

6. The two mirrors illustrated in Figure P35.6 meet at a right angle. The beam of light in the vertical plane P strikes mirror 1 as shown. (a) Determine the distance the reflected light beam travels before striking mirror 2. (b) In what direction does the light beam travel after being reflected from mirror 2?

Figure P35.6

12. The wavelength of red helium–neon laser light in air is 632.8 nm. (a) What is its frequency? (b) What is its wavelength in glass that has an index of refraction of 1.50? (c) What is its speed in the glass?

18. An opaque cylindrical tank with an open top has a diameter of 3.00 m and is completely filled with water. When the afternoon Sun reaches an angle of 28.0° above the horizon, sunlight ceases to illuminate any part of the bottom of the tank. How deep is the tank?

21. When the light illustrated in Figure P35.21 passes through the glass block, it is shifted laterally by the distance d. Taking n = 1.50, find the value of d.

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Figure P35.21

35. The index of refraction for violet light in silica flint glass is 1.66, and that for red light is 1.62. What is the angular dispersion of visible light passing through a prism of apex angle 60.0° if the angle of incidence is 50.0°? (See Fig. P35.35.)

Figure P35.35

38. Determine the maximum angle θ for which the light rays incident on the end of the pipe in Figure P35.38 are subject to total internal reflection along the walls of the pipe. Assume that the pipe has an index of refraction of 1.36 and the outside medium is air.

Figure P35.3849. A small underwater pool light is 1.00 m

below the surface. The light emerging from the water forms a circle on the water surface. What is the diameter of this circle?

59. The light beam in Figure P35.59 strikes surface 2 at the critical angle. Determine the angle of incidence θ1.

Figure P35.59

61. A light ray of wavelength 589 nm is incident at an angle θ on the top surface of a block of polystyrene, as shown in Figure P35.61. (a) Find the maximum value of θ for which the refracted ray undergoes total internal reflection at the left vertical face of the block. What If? Repeat the calculation for the case in which the polystyrene block is immersed in (b) water and (c) carbon disulfide.

Figure P35.61

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Chapter 9: Image Formation2. In a church choir loft, two parallel walls

are 5.30 m apart. The singers stand against the north wall. The organist faces the south wall, sitting 0.800 m away from it. To enable her to see the choir, a flat mirror 0.600 m wide is mounted on the south wall, straight in front of her. What width of the north wall can she see? Suggestion: Draw a topview diagram to justify your answer.

6. A periscope (Figure P36.6) is useful for viewing objects that cannot be seen directly. It finds use in submarines and in watching golf matches or parades from behind a crowd of people. Suppose that the object is a distance p1 from the upper mirror and that the two flat mirrors are separated by a distance h. (a) What is the distance of the final image from the lower mirror? (b) Is the final image real or virtual? (c) Is it upright or inverted? (d) What is its magnification? (e) Does it appear to be left–right reversed?

Figure P36.614. (a) A concave mirror forms an inverted

image four times larger than the object. Find the focal length of the mirror, assuming the distance between object and image is 0.600 m. (b) A convex mirror forms a virtual image half the size of the object. Assuming the distance between image and object is 20.0 cm, determine the radius of curvature of the mirror.

16. An object 10.0 cm tall is placed at the zero mark of a meter stick. A spherical mirror located at some point on the meter stick creates an image of the object that is upright, 4.00 cm tall, and located at the 42.0-cm mark of the meter stick. (a) Is the mirror convex or concave? (b) Where is the mirror? (c) What is the mirror’s focal length?

23. A glass sphere (n = 1.50) with a radius of 15.0 cm has a tiny air bubble 5.00 cm above its center. The sphere is viewed looking down along the extended radius containing the bubble. What is the apparent depth of the bubble below the surface of the sphere?

27. A goldfish is swimming at 2.00 cm/s toward the front wall of a rectangular aquarium. What is the apparent speed of the fish measured by an observer looking in from outside the front wall of the tank? The index of refraction of water is 1.33.

33. The nickel’s image in Figure P36.33 has twice the diameter of the nickel and is 2.84 cm from the lens. Determine the focal length of the lens.

Figure P36.33

36. The projection lens in a certain slide projector is a single thin lens. A slide 24.0 mm high is to be projected so that its image fills a screen 1.80 m high. The slide-to-screen distance is 3.00 m. (a) Determine the focal length of the projection lens. (b) How far from the slide should the lens of the projector be placed in order to form the image on the screen?

37. An object is located 20.0 cm to the left of a diverging lens having a focal length f = –32.0 cm. Determine (a) the location and (b) the magnification of the image. (c) Construct a ray diagram for this arrangement.

72. Figure P36.72 shows a thin converging lens for which the radii of curvature are R1 = 9.00 cm and R2 = –11.0 cm. The lens is in front of a concave spherical mirror with the radius of curvature R = 8.00 cm. (a) Assume its focal points F1 and F2 are 5.00 cm from the center of the lens. Determine its index of refraction. (b) The lens and mirror are 20.0 cm apart, and an object is placed 8.00 cm to the left of the lens. Determine the position of the final image and its magnification as seen by the eye in the figure. (c) Is the final image inverted or upright? Explain.

Figure P36.72

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Chapter 10: Interference of Light Waves

1. A laser beam ( = 632.8 nm) is incident on two slits 0.200 mm apart. How far apart are the bright interference fringes on a screen 5.00 m away from the double slits?

3. Two radio antennas separated by 300 m as shown in Figure P37.3 simultaneously broadcast identical signals at the same wavelength. A radio in a car traveling due north receives the signals. (a) If the car is at the position of the second maximum, what is the wavelength of the signals? (b) How much farther must the car travel to encounter the next minimum in reception? (Note: Do not use the small-angle approximation in this problem.)

4. In a location where the speed of sound is 354 m/s, a 2 000-Hz sound wave impinges on two slits 30.0 cm apart. (a) At what angle is the first maximum located? (b) What If ? If the sound wave is replaced by 3.00-cm microwaves, what slit separation gives the same angle for the first maximum? (c) What If ? If the slit separation is 1.00 m, what frequency of light gives the same first maximum angle?

7. Two narrow, parallel slits separated by 0.250 mm are illuminated by green light (= 546.1 nm). The interference pattern is observed on a screen 1.20 m away from the plane of the slits. Calculate the distance (a) from the central maximum to the first bright region on either side of the central maximum and (b) between the first and second dark bands.

8. Light with wavelength 442 nm passes through a double-slit system that has a slit separation d = 0.400 mm. Determine how far away a screen must be placed in order that a dark fringe appear directly opposite both slits, with just one bright fringe between them.

10. Two slits are separated by 0.320 mm. A beam of 500-nm light strikes the slits, producing an interference pattern. Determine the number of maxima observed in the angular range –30.0o < < 30.0o.

16. The intensity on the screen at a certain point in a doubleslit interference pattern is 64.0% of the maximum value. (a) What minimum phase difference (in radians) between sources produces this result? (b) Express this phase difference as a path difference for 486.1-nm light.

17. In Figure 37.5, let L = 120cm and d = 0.250cm. The slits are illuminated with coherent 600-nm light. Calculate the distance y above the central maximum for which the average intensity on the screen is 75.0% of the maximum.

Figure 37.5

19. Two narrow parallel slits separated by 0.850 mm are illuminated by 600-nm light, and the viewing screen is 2.80 m away from the slits. (a) What is the phase difference between the two interfering waves on a screen at a point 2.50 mm from the central bright fringe? (b) What is the ratio of the intensity at this point to the intensity at the center of a bright fringe?

55. Measurements are made of the intensity distribution in a Young’s interference pattern (see Fig. 37.7). At a particular value of y, it is found that I/Imax = 0.810 when 600-nm light is used. What wavelength of light should be used to reduce the relative intensity at the same location to 64.0% of the maximum intensity?

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Chapter 11 Modern Physics

Section 40.1, 40.2, 40.3: Introduction to Quantum Physics

6. A sodium-vapor lamp has a power output of 10.0 W. Using 589.3 nm as the average wavelength of this source, calculate the number of photons emitted per second.

7. Calculate the energy, in electron volts, of a photon whose frequency is (a) 620 THz, (b) 3.10 GHz, (c) 46.0 MHz. (d) Determine the corresponding wavelengths for these photons and state the classification of each on the electromagnetic spectrum.

9. An FM radio transmitter has a power output of 150 kW and operates at a frequency of 99.7 MHz. How many photons per second does the transmitter emit?

13. Molybdenum has a work function of 4.20 eV. (a) Find the cutoff wavelength and cutoff frequency for the photoelectric effect. (b) What is the stopping potential if the incident light has a wavelength of 180 nm?

14. Electrons are ejected from a metallic surface with speeds ranging up to 4.60 × 105 m/s when light with a wavelength of 625 nm is used. (a) What is the work function of the surface? (b) What is the cutoff frequency for this surface?

17. Two light sources are used in a photoelectric experiment to determine the work function for a particular metal surface. When green light from a mercury lamp (λ = 546.1 nm) is used, a stopping potential of 0.376 V reduces the photocurrent to zero. (a) Based on this measurement, what is the work function for this metal? (b) What stopping potential would be observed when using the yellow light from a helium discharge tube (λ = 587.5 nm)?

21. Calculate the energy and momentum of a photon of wavelength 700 nm.

22. X-rays having an energy of 300 keV undergo Compton scattering from a target. The scattered rays are detected at 37.0° relative to the incident rays. Find (a) the Compton shift at this angle, (b) the energy of the scattered x-ray, and (c) the energy of the recoiling electron.

Section 42.3: Bohr’s Model of the Hydrogen Atom

5. For a hydrogen atom in its ground state, use the Bohr model to compute (a) the

orbital speed of the electron, (b) the kinetic energy of the electron, and (c) the electric potential energy of the atom.

8. How much energy is required to ionize hydrogen (a) when it is in the ground state? (b) when it is in the state for which n = 3?

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