## Lecture Examples - Physics 111.6 (02) 2007-08

(Lecture Examples in pdf format)

1. A car is moving at constant speed v around a flat, circular track of radius R. It takes a time T for the car to complete one lap. The acceleration, a, of the car is given by:

The (constant) speed of the car is:
Calculate the speed v and the radius of the circular track, R, if a = 7.85 m/s2 and T = 15.9 s.

ANS: 19.9 m/s, 50.4 m

2. On a clear October day two students take a three-hour automobile trip to enjoy the fall foliage. In the first two hours they travel 100 km at a constant speed. In the third hour they travel another 80 km at a different constant speed. What is the average speed for each segment and for the entire trip?

ANS: 50 km/h, 80 km/h, 60 km/h

3. (Example 2.8) The spacecraft shown in Figure 2.14a is travelling with a velocity of +3250 m/s. Suddenly the retrorocket is fired, and the spacecraft begins to slow down with an acceleration whose magnitude is 10.0 m/s2. What is the velocity of the spacecraft when the displacement of the craft is +215 km, relative to the point where the retrorocket began firing?

ANS: ±2500 m/s

4. A motorcycle that is stopped at a traffic light accelerates at 4.20 m/s2 as soon as the light turns green. Just then, a car going 54.0 km/h passes the motorcycle. The car continues at that speed. How long after the light has changed will the motorcycle overtake the car and what is the speed of the motorcycle then, assuming it accelerated at 4.20 m/s2 throughout that time?

ANS: 7.14 s, 30.0 m/s

5. A stone is thrown vertically from the roof of a building. It passes a window 14.0 m below the roof with a speed of 22.0 m/s and hits the ground 2.80 s after it was thrown. Determine the initial velocity of the stone and the height of the building.

ANS: 14.5 m/s DOWN, 79.1 m

6. A person stands 12.0 m from a building whose roof is 60.0 m above the person's eyes.  (a) Calculate the distance from the person's eyes to the roof.  (b) Calculate the angle of the person's line of sight to the roof.

ANS:  (a) 61.2 m, (b) 78.7°

7. An airplane flies horizontally on a southwesterly heading a distance of 250 km.  It then flies 400 km due North.  Calculate the distance of the plane from its point of departure and the direction of its final destination from the point of departure.

ANS:  285 m @ 51.6° North of West

8. (Example 3.3) Figure 3.9 shows an airplane moving horizontally with a constant velocity of +115 m/s at an altitude of 1050 m. The directions to the right and upward have been chosen as the positive directions. The plane releases a 'care package' that falls to the ground along a curved trajectory. Ignoring air resistance, determine the time required for the package to hit the ground. (Example 3.4) Find the speed of the package and the direction of the velocity vector just before the package hits the ground. How far does the package travel horizontally during its fall?

ANS: 14.6 s, 184 m/s at 51.3° below horizontal, 1680 m

9. A boy wants to throw a ball over a fence that is 15.0 m high and 6.00 m away. At the instant when the ball leaves the boy's hand, it is 1.00 m aboveground. What must be the initial velocity of the ball so that it will be moving horizontally when it clears the fence? (i.e. Want minimum values for both launch angle and 0.)

ANS: 17.0 m/s at 78° above horizontal

10. How far will a stone travel over level ground if it is thrown upward at an angle of 30.0° with respect to the horizontal and with a speed of 12.0 m/s?

ANS: 12.7 m

11. (Example 4.1) Two people are pushing a stalled car, as Figure 4.5a indicates. The mass of the car is 1850 kg. One person applies a force of 275 N to the car, while the other applies a force of 395 N. Both forces act in the same direction. A third force of 560 N also acts on the car, but in a direction opposite to that in which the people are pushing. This force arises because of friction and the extent to which the pavement opposes the motion of the tires. Find the car's acceleration.

ANS: 0.059 m/s2

12. A furniture van has a smooth ramp for making deliveries. The ramp makes an angle with the horizontal. A large crate of mass m is placed at the top of the ramp. Assuming the ramp is a frictionless plane, what is the acceleration of the crate as it moves down the ramp?

ANS: -g sin

13. A 68.0 kg passenger rides in an elevator that is accelerating upward at 1.00 m/s2 because of external forces. What is the force exerted by the passenger on the floor of the elevator?

ANS: 740 N DOWN

14. (Example 4.10) A sled is travelling at 4.00 m/s along a horizontal stretch of snow, as Figure 4.24a illustrates. The coefficient of kinetic friction is µk = 0.0500. How far does the sled go before stopping? (Example 4.9) The coefficient of static friction is µs = 0.350. The sled and its rider have a total mass of 38.0 kg. Determine the horizontal force needed to get the sled barely moving again after it has stopped.

ANS: 16.3 m, 130 N

15. A 4.00 kg bag of potatoes is held by a string. If the tension in the string is 39.2 N, what is the state of motion of the bag? What should the tension in the string be so that the bag accelerates upward at 1.80 m/s2?

ANS: at rest, 46.4 N

16. Suppose that a block of mass M on an inclined plane is joined to a mass m by a cord over a pulley. The block slides on a frictionless surface and the effects of the pulley are negligible. What is the acceleration of the block if the surface is inclined at 20.0° and m = ½M.

ANS: 1.0 m/s2 up the plane

17. In the diagram, find the angle and the mass M.

ANS: 38.7°, 30.4 kg

18. At the Six Flags amusement park near Atlanta, the Wheelie carries passengers in a circular path with a radius of 7.70 m. The ride makes a complete rotation every 4.00 s. (a) What is a passenger's speed due to the circular motion? (b) What acceleration does a passenger experience?

ANS: 12.1 m/s, 19.0 m/s2

19. A student ties a 0.0600 kg lead fishing weight to the end of a piece of string and whirls it around in a horizontal circle. If the radius of the circle is 0.300 m and the object moves with a speed of 2.00 m/s, what is the horizontal component of force that directs the lead weight toward the centre of the circle? What is the tension in the string?

ANS: 0.80 N, 0.99 N

20. A satellite is placed into a circular equatorial orbit at a height of 6.37 × 106 m above the surface of the Earth. Calculate the period and orbital velocity of the satellite. What is the acceleration due to gravity experienced by the satellite?

ANS: 3.96 h, 5.60 × 103 m/s, 2.47 m/s2

21. (Example 5.11) What is the height above the Earth's surface at which all synchronous satellites (regardless of mass) must be placed in orbit?

ANS: 3.59 × 107 m

22. A mass of 5.00 kg is given a push along a horizontal plane so that its initial speed is 8.00 m/s. The coefficient of kinetic friction between the plane and mass is 0.400. How far will the mass slide before it comes to rest?

ANS: 8.16 m

23. A student accidentally knocks a plant off a window sill, and it falls from rest to the ground 5.27 m below. Use the principle of conservation of mechanical energy to determine its speed just before it strikes the ground. Ignore any effects due to air resistance.

ANS: 10.2 m/s

24. A 2.00 kg mass slides down a frictionless plane that makes an angle of 30.0° with the horizontal. The mass starts from rest. What is its speed after it has slipped a distance of 3.00 m along the plane?

ANS: 5.42 m/s

25. The heart may be regarded as an intermittent pump that forces about 70.0 cm3 of blood into the 1.00 cm radius aorta about 75 times a minute. Measurements show that the average force with which the blood is pushed into the aorta is about 5.00 N. What is the approximate power used in moving the blood to the aorta?

ANS: 1.39 W

26. Using the following data, determine the average force on a baseball hit by a bat. The baseball has a mass of 0.140 kg and an initial speed of 30.0 m/s. It rebounds from the bat with a speed of 40.0 m/s in the opposite direction and is in contact with the bat for 0.00200 s.

ANS: 4900 N

27. A 60.0 kg ice skater is standing at rest on a frozen lake. The friction between his skates and the surface of the ice is negligible. If he throws a 2.00 kg block of ice horizontally with a velocity of 12.0 m/s, what is his recoil velocity?

ANS: -0.40 m/s

28. In a safety test of automobile equipment, two cars of unequal mass undergo a head-on collision in which the stick together after the collision. A Buick Park Avenue with a mass of 1660 kg and an initial velocity of 8.00 km/h strikes an 830 kg Geo Metro with a velocity of 10.0 km/h toward the first. (a) What is the velocity of the combination immediately after the collision? (b) How do the accelerations of the two cars during collision compare?

ANS: +2.0 km/h, aGeo = -2 aBuick

29. The ballistic pendulum is a simple device used to measure the velocity of a bullet. A block of wood of mass 1.50 kg, suspended from group of light strings, is initially at rest when a bullet of mass 0.0100 kg is fired horizontally into the wood. The bullet embeds itself in the block, which then swings in the direction of the projectile's velocity, attaining a height of 0.350 m relative to its initial position. What was the bullet's initial speed?

ANS: 395 m/s

30. A railroad boxcar of mass m1 is initially in motion to the right along a straight track, which we denote as the x axis with the positive direction to the right. The boxcar collides with a stationary boxcar of mass m2 on the same track. The ratio of the masses of the two cars is m1/m2 = 1/2. After the collision, what is the velocity of each boxcar if the collision is elastic?

ANS: f1 = -o1/3, f2 = 2vo1/3

31. Two cars approach an intersection at right angles. Car A has a mass of 1000 kg and travels at 8.00 m/s North; car B has a mass of 600 kg and travels at 10.0 m/s East. Immediately following the collision car B is observed to move with a velocity of 6.00 m/s at 60.0° North of East. Find the velocity of car A just after the collision. Was the collision elastic?

ANS: 6.44 m/s at 49.3° N of E, inelastic since KEf = 31.5 kJ and KEo = 62 kJ

32. An electric motor accelerates from rest to 500 rpm in 4.00 s. The output shaft of the motor has a radius of 0.0100 m and a pulley radius of 0.0400 is fitted to the shaft.
(a) Calculate the angular acceleration of the motor shaft while the motor is accelerating.
(b) Calculate the angular acceleration of the pulley.
(c) Through how many revolutions does the pulley rotate while accelerating?
Once the motor has reached constant angular velocity:
(d) Calculate the speed of a point on the rim of the motor shaft.
(e) Calculate the speed of a point on the rim of the pulley.
(f) Calculate the acceleration of a point on the rim of the pulley.

ANS: 13.1 rad/s2, 13.1 rad/s2, 16.7 rev, 0.524 m/s, 2.10 m/s, 110 m/s2

33. A motorcycle whose wheels have a diameter of 60.0 cm approaches an intersection at a speed of 72.0 km/h. When the motorcycle is 50.0 m from the intersection, the traffic light turns red and the cyclist applies the brakes, decelerating uniformly. She comes to rest at the intersection. Find (a) the angular velocity of the wheels before the brakes are applied; (b) the angular acceleration of the wheels; (c) the angle through which each wheel turns during the time the cycle decelerates.

34. (Example 9.5) A bodybuilder holds a dumbbell of weight Wd as shown in Figure 9.8a. His arm is extended horizontally and weighs Wa = 31.0 N. The deltoid muscle is assumed to be the only muscle acting and is attached to the arm as shown. The maximum force M that the deltoid muscle can supply to keep the arm horizontal has a magnitude of 1840 N. Figure 9.8b shows the distances that locate where the various forces act on the arm. What is the heaviest dumbbell that can be held, and what are the horizontal and vertical force components, Sx and Sy that the shoulder joint applies to the arm?

ANS: Wd = 86.1 N, Sx = 1790 N, Sy = -297 N

35. A sign weighing 400 N is suspended at the end of a 350 N uniform rod that is hinged at the wall. What is the tension in a support cable that attaches the end of the rod to the wall, if the cable makes an angle of 35.0° with the rod?

ANS: T = 1000 N

36. A cylindrical winch of radius R and moment of inertia I is free to rotate without friction about an axis. A cord of negligible mass is wrapped around the winch and attached to bucket of mass m. When the bucket is released, it accelerates downward as the cord unwinds from the winch. Find the acceleration of the bucket.

ANS:

37. An ice skater starts spinning at a rate of 1.50 rev/s with arms extended. She then pulls her arms in close to her body, resulting in a decrease of her moment of inertia to three quarters of the initial value. What is the skater's final angular velocity?

ANS: 2.0 rev/s

38. Four children, each of mass m = 30.0 kg, are on the edge of a merry-go-round of radius R = 2.00 m and mass M = 200 kg that is initially rotating with an angular velocity of 2.08 rad/s. The 4 children now make their way toward the centre of the merry-go-round. Find the angular velocity of the system when the children are 0.750 m from the centre. What is the kinetic energy of the system when the children are at the periphery and when they are 0.750 m from the centre of the merry-go-round?

ANS: 3.92 rad/s, KEo = 1900 J, KEf = 3590 J

39. The position of an object relative to its equilibrium location is given by x = 0.40 cos(7.85 t), where x is in metres and t is in seconds. What are the amplitude of oscillation, the frequency, and the angular frequency? What is the velocity of the object at t = 0? What is the acceleration at t = 0?

ANS: 0.40 m, 1.25 Hz, 7.85 rad/s, 0, -24.7 m/s2

40. A metal block is hung from a spring that obeys Hooke's Law. When the block is pulled down 12.0 cm from the equilibrium position and released from rest, it oscillates with a period of 0.750 s, passing through the equilibrium position with a speed of 1.00 m/s.
(a) What is the displacement and (b) what is the speed of the block 0.280 s after it is released?

ANS: -0.084 m, -0.71 m/s

41. A mass is attached to a spring of spring constant 400 N/m. If this mass is displaced from equilibrium by 4.00 cm and released at t = 0, it oscillates at a frequency of 15.6 Hz. Write an expression for the displacement, velocity, and acceleration of this mass as a function of time and determine the value of the mass.

ANS: 0.0400 m cos(98.0 t), -3.92 m/s sin(98.0 t), -384 m/s2 cos (98.0 t), 0.042 kg

42. A mass of 200 g on a frictionless horizontal surface is connected to a horizontal ideal spring of spring constant 250 N/m. The mass is displaced 2.00 cm and released. Calculate the kinetic energy and speed of the mass when it passes through the equilibrium position.

ANS: 0.0500 J, 0.707 m/s

43. A 200 g object on a frictionless plane inclined at 30.0° with the horizontal is pushed against a 250 N/m spring until the spring is compressed 5.00 cm. Calculate the speed of the object when it has travelled a distance of 25.0 cm along the plane.

ANS: 0.822 m/s

44. A spring stretches by 0.150 m when a mass of 1.00 kg is suspended from its end. What mass should be attached to this spring so that the natural vibration frequency of the system will be 8.00 Hz?

ANS: 0.026 kg

45. A 0.500 kg mass is supported by a spring. The system is set in vibration at its natural frequency of 4.00 Hz with an amplitude of 5.00 cm. Find the spring constant of the spring, the maximum speed of the mass, and the energy of the system.

ANS: 316 N/m, 1.26 m/s, 0.40 J

46. A simple pendulum consists of a bob of mass 2.4 kg and a string of length L. What should the value of L be so that the period of the pendulum is 2.00 s at a location where g = 9.80 m/s2?

ANS: 0.993 m

47. The acceleration of gravity varies slightly over the surface of the Earth. If a pendulum has a period of 3.0000 s at a location where g = 9.803 m/s2 and a period of 3.0024 s at another location, what is g at this new location?

ANS: 9.787 m/s2

48. A nurse administers medication in a saline solution to a patient by infusion into a vein in the patient's arm. The density of the solution is 1.00 × 103 kg/m3 and the gauge pressure inside the vein is 2.40 × 103 Pa. How high above the insertion point must the container by hung so that there is sufficient pressure to force the fluid into the patient?

ANS: 24.5 cm

49. You can make a simple hydraulic lift by fitting a piston attached to a handle into a 3.00 cm diameter cylinder, which is connected to a larger cylinder of 24.0 cm diameter. If a 50.0 kg woman puts all her weight on the handle of the smaller piston, how much weight can be lifted by the larger one? Assume both pistons are at the same height.

ANS: 3.14 × 104 N

50. A block of Styrofoam floats on water with only 12% of its volume submerged. What is the average density of Styrofoam?

ANS: 120 kg/m3

51. An object of mass m and volume V is suspended from a string so that it is half-submerged in a fluid of density r.  Determine the expression for the tension in the string.

ANS: T = mg - rgV/2

52. An object has a weight of Wair in air (its true weight) and an apparent weight of Wsub when completely submerged in water.  Determine the expression for the density of the object in terms of Wair, Wsub, and the density of water, rwater.

ANS:  robject = rwater (Wair/(Wair - Wsub))

53. A horizontal pipe of 25.0 cm2 cross section carries water at a velocity of 3.00 m/s. The pipe feeds into a smaller pipe with a cross section of only 15.0 cm2. (a) What is the velocity of water in the smaller pipe? (b) Determine the pressure change that occurs on going from the larger diameter pipe to the smaller pipe.

ANS: 5.0 m/s, -8000 Pa

54. A patient is given sucrose intravenously. Her venous gauge pressure is 18.0 mm Hg and the elevation difference between the intravenous needle and sucrose bottle is 0.80 m. If the rate of sucrose flow is to be 2.00 mL/min, what should the diameter of the 4.00 cm long needle be? Assume the density and viscosity of sucrose to be 1.06 × 103 kg/m3 and 2.084 × 10–3 N.s/m2, respectively.

ANS: 0.372 mm

55. The diagram represents two snapshots of a wave on a rope. The snapshots were taken 0.100 s apart. We know that the wave was travelling to the right and that it moved by less than one wavelength between pictures. Find its (a) wavelength, (b) wave speed, and (c) frequency. (d) Write an expression for the rope's displacement from its equilibrium position as a function of position and time. The maximum displacement is 3.00 cm.

ANS: 2.00 m, 10.0 m/s, 5.00 Hz

56. Consider a constant-power source that is emitting sound uniformly in all directions.  At a distance r1 from the source the sound intensity is 1.25 × 10-4 W/m2.  Calculate the corresponding intensity level in dB.  At a distance r2 from the source the intensity level is 87.0 dB.  Calculate the corresponding sound intensity.  Calculate the ratio r2/r1.

ANS:  81.0 dB, 5.01 × 10-4 W/m2, 4.00

57. A train is approaching a grade crossing at 80.0 km/h and sounds its horn, whose frequency is 320 Hz. What is the frequency of sound heard by a stationary observer at the grade crossing (a) as the train approaches; (b) as the train recedes? The speed of sound in air is 343 m/s.

ANS: 342 Hz, 300 Hz

58. A ship transmits sonar pulses of 20.00 MHz at regular intervals while steaming due west. The sonar operator records a reflected signal from a stationary reef due west of the ship and notes that the frequency of the received signal is 20.15 MHz. The speed of sound in seawater is 5620 km/h (1560 m/s). Calculate the speed of the ship.

ANS: 21.0 km/h

59. One string of a bass fiddle is 1.80 m long and has a fundamental frequency of resonance of 81 Hz when it is under a tension of 120 N. If the total length of the string (including the part wound about the tuning peg) is 2.10 m, what is the mass of the string? If the tension is increased to 140 N, what will the new fundamental resonant frequency be?

ANS: 2.96 g, 87.5 Hz

60. You are asked to construct a pipe that will resonate at room temperature at the following frequencies: 180 Hz and 540 Hz, and no other frequencies between 0 and 600 Hz. Describe the pipe and give its length. (speed of sound = 343 m/s)

ANS: 0.47 m long with one end open and one end closed

61. Two point charges of +4.00 × 10–2 C and –6.00 × 10–2 C are 3.00 m apart. What is the magnitude and the nature of the electrostatic force between them?

ANS: 2.4 × 106 N, attractive

62. Three charges are located along a straight line as shown. What is the net electrostatic force on the +3 µC charge?

ANS: -1.42 N (to left)

63. Where should the +3 µC charge be placed in the following arrangement of charges so that it experiences no net electrostatic force?

ANS: x = 1.66 m

64. Three charges q1 = +3.70 µC, q2 = –3.70 µC, and q3 = +4.80 µC are fixed at the corners of an equilateral triangle 3.00 × 10–2 m on a side. Find the magnitude and direction of the net force on charge q3 due to the other charges.

ANS: 178 N in +x direction (q3 is at the apex of the triangle and q1 and q2 are on the x-axis

65. An electron is located in an electric field of 600 N/C. What is the force acting on the electron and what is its acceleration if it is free to move? If the field points in the positive x direction, what is the direction of the acceleration of the electron?

ANS: 9.61 × 10-17 N opposite to E, 1.05 × 1014 m/s2 in -x direction

66. A charge of 4.00 µC is placed at x = 0, y = 20.0 cm and a charge of –2.00 µC is placed at x = 20.0 cm, y = 0. Determine the electric field at the origin.

ANS: 10.1 × 105 N/C at -63.4° to +x axis

67. An alpha particle (helium nucleus) is accelerated in a cyclotron to an energy of 40.0 MeV (4.00 × 107 eV). Calculate the speed of this particle. What would be the speed of a proton whose energy is 40.0 MeV? (The mass of the alpha particle is approximately 6.64 × 10–27 kg and the mass of the proton is 1.673 × 10–27 kg.)

ANS: 4.39 × 107 m/s, 8.75 × 107 m/s

68. A proton is released from rest in a uniform electric field of 500 V/m. Calculate the speed of the proton after it has moved a distance of 0.500 m.

ANS: 2.19 × 105 m/s

69. Charges of 16.0 and 24.0 µC are separated by 0.800 m. What is the electric field and the electric potential midway between the two charges?

ANS: 4.5 × 105 N/C toward 16 µC charge, 9.0 × 105 V

70. What is the resistance of a resistor through which 8.00 × 104 C flow in one hour if the potential difference across it is 12.0 V?

ANS: 0.54

71. A piece of copper wire has a cross section of 4.00 mm2 and a length of 2.00 m. The resistivity of copper is 1.72 ´ 10–8 m at 20.0 °C and its temperature coefficient of resistivity is 0.00393/°C.
(a) What is the electric resistance of the wire at 20.0 °C?
(b) What is the potential difference across the wire when it carries a current of 10.0 A?
(c) Calculate the resistance at 40.0 °C.

ANS: 0.0086 , 0.086 V, 9.28 ´ 103 W

72. (Example 19.3) A 60.0 W headlight is connected across a 12.0 V battery.  Calculate the number of electrons that flow through the headlight filament in one hour.

ANS: 1.13 ´ 1023

73. An electric hair dryer provides a good example of electric resistance. A typical dryer designed to operate on a 120 V household circuit is rated at 1500 W. What is the resistance of the dryer?

ANS: 9.6

74. (Example 20.9) A 6.00 resistor and a 3.00 resistor are connected in series with a 12.0 V battery. Assuming that the battery contributes no resistance to the circuit, find
(a) the current
(b) the power dissipated in each resistor
(c) the total power delivered to the resistors by the battery.

ANS: 1.33 A, 10.6 W in 6 , 5.31 W in 3 , 15.9 W

75. To adjust the light intensity from a desk lamp with an incandescent bulb, a person places a variable resistor R in series with the desk lamp. The lamp's bulb is rated 100 W at 110 V. What should be the range over which R can be varied so that the bulb can be operated between 40.0 W and 80.0 W?

ANS: 15.0 < R < 70.0

76. A 10.0 V battery is connected to the parallel combination of an unknown resistance and a 5.00 resistor. The total power dissipated in the circuit is 45.0 W. Find the unknown resistance.

ANS: 4.00

77. A proton moving with a velocity of 6.00 × 106 m/s to the North enters a region where the magnetic field is 1.50 T and points directly up. Determine the required magnitude and direction of the electric field E that will allow the proton to move undeviated through this region.

ANS: 8.99 × 106 N/C West

78. Singly ionized ions that have been accelerated through a potential of 800 V describe a circular trajectory of 16.0 cm radius in a magnetic field of 0.200 T. What is the mass of these atoms?

ANS: 1.03 × 10-25 kg

79. A cylindrical container is 4.00 cm in diameter and 2.40 cm high. The container is initially empty. A woman looks into the container in such a way that she can just see the far edge of the bottom of the container. The container is now filled with an unknown transparent liquid. Without moving her head from her initial position, the woman can now see the middle of the bottom of the container. What is the refractive index of the unknown liquid? (Assume the refractive index of air to be 1.00.)

ANS: 1.34

80. (Example 26.2) A searchlight on a yacht is being used at night to illuminate a sunken chest. The chest is 3.30 m below the surface of the water and is a lateral distance of 2.00 m from the point at which the searchlight beam enters the water.
(a) At what angle of incidence should the searchlight be aimed?
(b) What is the apparent depth of the sunken chest?

ANS: 43.6°, 2.10 m

81. An optical fibre (light pipe) is made of material with n = 1.70 and is given a protective coating with another material of index of refraction 1.25. What is the critical angle for total internal reflection?

ANS: 47.3°

82. An object is located 9.00 cm in front of a converging lens (f = 6.00 cm). Determine the location of the image.

ANS: +18.0 cm

83. A lens forms an erect image of an object twice the size of the object. The image appears 60.0 cm from the lens. Determine the object distance and focal length of the lens.

ANS: do = +30.0 cm, f = +60.0 cm

84. A converging lens (f = 12.0 cm) is located 30.0 cm to the left of a diverging lens (f = –6.00 cm). A postage stamp is placed 36.0 cm to the left of the converging lens.
(a) Locate the final image of the stamp relative to the diverging lens.
(b) Calculate the overall magnification.
(c) Is the final image real or virtual, upright or inverted, larger or smaller?

ANS: -4.00 cm, -0.167, virtual, inverted, reduced

85. A person goes to the optometrist, who prescribes corrective contact lenses of –40.0 cm focal length. With the aid of these contacts, that person's far point is at infinity, and the near point is at 20.0 cm. What are the person's uncorrected far and near points?

ANS: 40.0 cm and 13.3 cm

86. A biology student wishes to use a 6.00 cm focal length lens as a magnifier. The student's near point is 25.0 cm.
(a) What is the magnification of the lens when used with a relaxed eye?
(b) What is the maximum magnification of the lens?

ANS: 4.17, 5.17

87. You are given a 180 mm long tube with an objective lens of focal length 2.00 mm at one end and an eyepiece lens of focal length 30.0 mm at the other end. Where should an object be placed to use the tube and lenses as a microscope with maximum magnification? Assume the user has a near point of 30.0 cm.

ANS: 2.03 mm from objective lens

88. The overall magnification of an astronomical telescope is desired to be -20.0×. If an objective of 80.0 cm focal length is used:
(a) What must be the focal length of the eyepiece?
(b) What is the refractive power of the eyepiece lens in diopters?
(c) What is the overall length of the telescope when adjusted for use by the relaxed eye?

ANS: 4.00 cm, 25.0, n/a, 84.0 cm

89. Two slits separated by 0.400 mm are illuminated with a monochromatic, coherent light source. The separation between the 0th and 1st order maxima of the interference pattern detected on a screen 2.50 m from the slits is 1.20 mm. Find the wavelength of the incident light.

ANS: 192 nm

90. The angle of deviation of light of 400 nm wavelength is 30.0° in second order.
(a) How many lines per centimetre are there on this grating?
(b) How many orders of the complete visible spectrum are produced by this grating?
(c) Are these visible spectra clearly separated in all orders?

ANS: 6250 /cm, 2

91. A light source emits 1018 photons per second. If the wavelength of the emitted light is 600 nm, what is the power radiated?

ANS: 0.331 W

92. The work function of sodium is 2.30 eV. What is the maximum wavelength of light that is able to release photoelectrons from a sodium surface?

ANS: 539 nm

93. A 17.2 keV x-ray from molybdenum is Compton-scattered through an angle of 90.0°. What is the energy of the x-ray after scattering?

ANS: 16.6 keV

94. What is the wavelength of the Balmer line that corresponds to the n = 5 to n = 2 transition?

ANS: 434 nm

95. What is the minimum voltage required in an x-ray tube to produce photons whose wavelength is 0.100 nm?

ANS: 1.24 × 104 V

96. Compute the binding energy per nucleon of 14C. (The atomic mass of 14C is 14.003242 u.)

ANS: 7.52 MeV/nucleon

97. A sample of 131I (half life of 8 days) has an activity of 0.0500 Ci.  (1Ci = 3.70 ´ 1010 Bq)
(a) How many radioactive iodine nuclei does this sample contain?
(b) What will the activity of the sample be after 16 days?
(c) How many days will elapse before the activity of the sample has diminished to 0.00200 Ci?

ANS: 1.85 × 1015 nuclei, 0.0125 Ci, 37.3 days

98. An archaeologist finds a bone that contains 5.00 g of carbon. The 14C counting rate from this 5.00 g of carbon is found to be 30.0 counts/min. If the 14C counting rate from natural carbon is 0.230 Bq per gram, how old is the bone? The half-life of 14C is 5730 years.

ANS: 7580 y

99. Calculate the energy released in the initial step of the neutron-induced fission of 235U that yields the unstable isotopes of 144Ba and 89Kr and three neutrons? Atomic masses: 235U = 235.043925 u; 144Ba = 143.922673 u;  89Kr = 88.917563 u.

ANS: 174 MeV

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