1 - Morgan Park High School



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AP® Physics B

1998 Multiple Choice Questions

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1. A solid metal ball and a hollow plastic ball of the same external radius are released from rest in a large vacuum chamber. When each has fallen 1m, they both have the same

(A) inertia (B) speed (C) momentum (D) kinetic energy (E) change in potential energy

2. A student weighing 700 N climbs at constant speed to the top of an 8 m vertical rope in 10 s. The average power expended by the student to overcome gravity is most nearly

(A) 1.1 W (B) 87.5 W (C) 560 W (D) 875 W (E) 5,600 W

3. A railroad car of mass m is moving at speed v when it collides with a second railroad car of mass M which is at rest. The two cars lock together instantaneously and move along the track. What is the speed of the cars immediately after the collision?

(A) v/2 (B) mv/M (C) Mv/m (D) (m + M )v/m (E) mv/(m+M)

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4. An open cart on a level surface is rolling without frictional loss through a vertical downpour of rain, as shown above. As the cart rolls, an appreciable amount of rainwater accumulates in the cart. The speed of the cart will

(A) increase because of conservation of momentum (B) increase because of conservation of mechanical energy

(C) decrease because of conservation of momentum (D) decrease because of conservation of mechanical energy

(E) remain the same because the raindrops are falling perpendicular to the direction of the cart's motion

5. Units of power include which of the following?

I. Watt

II. Joule per second

III. Kilowatt-hour

(A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III

6. A 2 kg object moves in a circle of radius 4 m at a constant speed of 3 m/s. A net force of 4.5 N acts on the object. What is the angular momentum of the object with respect to an axis perpendicular to the circle and through its center?

(A) 9 N m/kg (B) 12 m2/s (C) 13.5 kg m2/s2 (D) 18 N m/kg (E) 24 kg m2/s.

7. Three forces act on an object. If the object is in translational equilibrium, which of the following must be true?

I. The vector sum of the three forces must equal zero.

II. The magnitudes of the three forces must be equal.

III. All three forces must be parallel.

(A) I only (B) II only (C) I and III only (D) II and III only (E) I, II, and III

[pic]

8. The graph above represents the potential energy U as a function of displacement x for an object on the end of a spring oscillating in simple harmonic motion with amplitude x0. Which of the following graphs represents the kinetic energy K of the object as a function of displacement x ?

[pic][pic][pic]

9. A child pushes horizontally on a box of mass m which moves with constant speed v across a horizontal floor. The coefficient of friction between the box and the floor is (. At what rate does the child do work on the box?

(A) (mgv (B) mgv (C) (mg/v (D) (mg/v (E) (mv2

10. Quantum transitions that result in the characteristic sharp lines of the X-ray spectrum always involve

(A) the inner electron shells (B) electron energy levels that have the same principal quantum number

(C) emission of beta particles from the nucleus (D) neutrons within the nucleus

(E) protons within the nucleus

11. Which of the following experiments provided evidence that electrons exhibit wave properties?

I. Millikan oil-drop experiment

II. Davisson-Germer electron-diffraction experiment

III. J. J. Thomson's measurement of the charge-to-mass ratio of electrons

(A) I only (B) II only (C) I and III only (D) II and III only (E) I, II, and III

12. Quantities that are conserved in all nuclear reactions include which of the following?

I. Electric charge

II. Number of nuclei

III. Number of protons

(A) I only (B) II only (C) I and III only (D) II and III only (E) I, II, and III

13. Which of the following is true about the net force on an uncharged conducting sphere in a uniform electric field?

(A) It is zero.

(B) It is in the direction of the field.

(C) It is in the direction opposite to the field.

(D) It produces a torque on the sphere about the direction of the field.

(E) It causes the sphere to oscillate about an equilibrium position.

14. Two parallel conducting plates are connected to a constant voltage source. The magnitude of the electric field between the plates is 2,000 N/C. If the voltage is doubled and the distance between the plates is reduced to 1/5 the original distance, the magnitude of the new electric field is

(A) 800 N/C (B) 1,600 N/C (C) 2,400 N/C (D) 5,000 N/C (E) 20,000 N/C

Questions 15-16 refer to the following diagram that shows part of a closed electrical circuit.

[pic]

15. The electrical resistance of the part of the circuit shown between point X and point Y is

(A) 4/3 ( (B) 2 ( (C) 2.75 ( (D) 4 ( (E) 6 (

16. When there is a steady current in the circuit, the amount of charge passing a point per unit of time is

(A) the same everywhere in the circuit (B) greater at point X than at point Y

(C) greater in the 1 ( resistor than in the 2 ( resistor (D) greater in the 1 ( resistor than in the 3 ( resistor

(E) greater in the 2 ( resistor than in the 3 ( resistor

Questions 17-18

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The figure above shows two particles, each with a charge of +Q, that are located at the opposite corners of a square of side d.

17. What is the direction of the net electric field at point P ?

(A) [pic] (B) [pic] (C) [pic] (D) [pic] (E) [pic]

18. What is the potential energy of a particle of charge +q that is held at point P ?

(A) Zero (B) [pic] (C) [pic] (D) [pic] (E) [pic]

[pic]

19. A rectangular wire loop is at rest in a uniform magnetic field B of magnitude 2 T that is directed out of the page. The loop measures 5 cm by 8 cm, and the plane of the loop is perpendicular to the field, as shown above. The total magnetic flux through the loop is

(A) zero (B) 2 x 10-3 T-m2 (C) 8 x 10-3 T-m2 (D) 2 x 10-1 T-m2 (E) 8 x 10-1 T-m

20. A certain coffeepot draws 4.0 A of current when it is operated on 120 V household lines. If electrical energy costs 10 cents per kilowatt-hour, how much does it cost to operate the coffeepot for 2 hours?

(A) 2.4 cents (B) 4.8 cents (C) 8.0 cents (D) 9.6 cents (E) 16 cents

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21. An electron is in a uniform magnetic field B that is directed out of the plane of the page, as shown above. When the electron is moving in the plane of the page in the direction indicated by the arrow, the force on the electron is directed

(A) toward the right (B) out of the page (C) into the page (D) toward the top of the page

(E) toward the bottom of the page

Questions 22-23

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A certain quantity of an ideal gas initially at temperature T0, pressure p0, and volume V0 is compressed to one-half its initial volume. As shown above, the process may be adiabatic (process 1), isothermal (process 2), or isobaric (process 3).

22. Which of the following is true of the mechanical work done on the gas?

(A) It is greatest for process 1.

(B) It is greatest for process 3.

(C) It is the same for processes I and 2 and less for process 3.

(D) It is the same for processes 2 and 3 and less for process 1.

(E) It is the same for all three processes.

23. Which of the following is true of the final temperature of this gas?

(A) It is greatest for process 1. (B) It is greatest for process 2.

(C) It is greatest for process 3. (D) It is the same for processes 1 and 2.

(E) It is the same for processes 1 and 3.

24. In a certain process, 400 J of heat is added to a system and the system simultaneously does 100 J of work. The change in internal energy of the system is

(A) 500 J (B) 400 J (C) 300 J (D) -100 J (E) -300 J

25. An ice cube of mass m and specific heat ci is initially at temperature T1, where T1 < 273 K. If L is the latent heat of fusion of water, and the specific heat of water is cw, how much energy is required to convert the ice cube to water at temperature T2, where 273 K < T2 < 373 K?

(A) m[ci (273 - T1) + L + cw (373 - T2)] (B) m[ci (273 - T1) + L + cw (T2 - 273)]

(C) ci (273 - T1) + cw (T2 - 273) (D) mL + cw (T2 - T1 )

(E) mL + (cw + ci)( T2 - T1)

26. A concave mirror with a radius of curvature of 1.0 m is used to collect light from a distant star. The distance between the mirror and the image of the star is most nearly

(A) 0.25 m (B) 0.50 m (C) 0.75 m (D) 1.0 m (E) 2.0 m

27. When light passes from air into water, the frequency of the light remains the same. What happens to the speed and the wavelength of light as it crosses the boundary in going from air into water?

Speed Wavelength

(A) Increases Remains the same

(B) Remains the same Decreases

(C) Remains the same Remains the same

(D) Decreases Increases

(E) Decreases Decreases

28. A physics student places an object 6.0 cm from a converging lens of focal length 9.0 cm. What is the magnitude of the magnification of the image produced?

(A) 0.6 (B) 1.5 (C) 2.0 (D) 3.0 (E) 3.6

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29. One end of a horizontal string is fixed to a wall. A transverse wave pulse is generated at the other end, moves toward the wall as shown above. and is reflected at the wall. Properties of the reflected pulse include which of the following?

I. It has a greater speed than that of the incident pulse.

II. It has a greater amplitude than that of the incident pulse.

III. It is on the opposite side of the string from the incident pulse.

(A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III

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30. An object is placed at a distance of 1.5f from a converging lens of focal length f, as shown above. What type of image is formed and what is its size relative to the object?

Type Size

(A) Virtual Larger

(B) Virtual Same size

(C) Virtual Smaller

(D) Real Larger

(E) Real Smaller

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31. A light ray passes through substances 1, 2, and 3, as shown above. The indices of refraction for these three substances are n1, n2, and n3, respectively. Ray segments in 1 and in 3 are parallel. From the directions of the ray, one can conclude that

(A) n3 must be the same as n1 (B) n2 must be less than n1

(C) n2 must be less than n3 (D) n1 must be equal to 1.00

(E) all three indices must be the same

32. At noon a radioactive sample decays at a rate of 4,000 counts per minute. At 12:30 PM. the decay rate has decreased to 2,000 counts per minute. The predicted decay rate at 1:30 PM. is

(A) 0 counts per minute (B) 500 counts per minute (C) 667 counts per minute

(D) 1,000 counts per minute (E) 1,333 counts per minute

33. A negative beta particle and a gamma ray are emitted during the radioactive decay of a nucleus of[pic]. Which of the following is the resulting nucleus?

(A) [pic] (B) [pic] (C) [pic] (D) [pic] (E) [pic]

34. If the momentum of an electron doubles, its de Broglie wavelength is multiplied by a factor of

(A) 1/4 (B)1/2 (C) 1 (D) 2 (E) 4

35. Quantum concepts are critical in explaining all of the following EXCEPT

(A) Rutherford's scattering experiments (B) Bohr's theory of the hydrogen atom

(C) Compton scattering (D) the blackbody spectrum (E) the photoelectric effect

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36. The graph above shows the decay of a sample of carbon 14 that initially contained No atoms. Which of the lettered points on the time axis could represent the half-life of carbon 14 ?

(A) A (B) B (C) C (D) D (E) E

37. If photons of light of frequency f have momentum p, photons of light of frequency 2f will have a momentum of

(A) 2p (B) [pic] (C) p (D) [pic] (E) ½ p

[pic]

38. A block of mass 3.0 kg is hung from a spring, causing it to stretch 12 cm at equilibrium, as shown above. The 3.0 kg block is then replaced by a 4.0 kg block, and the new block is released from the position shown above, at which the spring is unstretched. How far will the 4.0 kg block fall before its direction is reversed?

(A) 9 cm (B) 18 cm (C) 24 cm (D) 32 cm (E) 48 cm

39. An object has a weight W when it is on the surface of a planet of radius R. What will be the gravitational force on the object after it has been moved to a distance of 4R from the center of the planet?

(A) 16W (B) 4W (C) W (D) 4 (E) 1/16 W

40. What is the kinetic energy of a satellite of mass m that orbits the Earth, of mass M, in a circular orbit of radius R?

(A) Zero (B) [pic] (C) [pic] (D) [pic] (E) [pic]

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41. Two objects of mass 0.2 kg and 0.1 kg, respectively, move parallel to the x-axis, as shown above. The 0.2 kg object overtakes and collides with the 0.1 kg object. Immediately after the collision, the y-component of the velocity of the 0.2 kg object is 1 m/s upward. What is the y-component of the velocity of the 0.1 kg object immediately after the collision'?

(A) 2 m/s downward (B) 0.5 m/s downward (C) 0 m/s

(D) 0.5 m/s upward (E) 2 m/s upward

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42. A beam of white light is incident on a triangular glass prism with an index of refraction of about 1.5 for visible light, producing a spectrum. Initially, the prism is in a glass aquarium filled with air, as shown above. If the aquarium is filled with water with an index of refraction of 1.3, which of the following is true?

(A) No spectrum is produced.

(B) A spectrum is produced, but the deviation of the beam is opposite to that in air.

(C) The positions of red and violet are reversed in the spectrum.

(D) The spectrum produced has greater separation between red and violet than that produced in air.

(E) The spectrum produced has less separation between red and violet than that produced in air.

Questions 43-44

Three objects can only move along a straight, level path. The graphs below show the position d of each of the objects plotted as a function of time t.

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43. The magnitude of the momentum of the object is increasing in which of the cases?

(A) II only (B) III only (C) I and II only (D) I and III only (E) I, II, and III

44. The sum of the forces on the object is zero in which of the cases?

(A) II only (B) III only (C) I and II only (D) I and III only (E) I, II, and III

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45. A metal spring has its ends attached so that if forms a circle. It is placed in a uniform magnetic field, as shown above. Which of the following will not cause a current to be induced in the spring?

(A) Changing the magnitude of the magnetic field

(B) Increasing the diameter of the circle by stretching the spring

(C) Rotating the spring about a diameter

(D) Moving the spring parallel to the magnetic field

(E) Moving the spring in and out of the magnetic field

Questions 46-47

A magnetic field of 0.1T forces a proton beam of 1.5 mA to move in a circle of radius 0.1 m. The plane of the circle is perpendicular to the magnetic field.

46. Of the following, which is the best estimate of the work done by the magnetic field on the protons during one complete orbit of the circle?

(A) 0 J (B) 10-22 J (C) 10-5 J (D) 102 J (E) 1020 J

47. Of the following, which is the best estimate of the speed of a proton in the beam as it moves in the circle?

(A) 10-2 m/s (B) 103 m/s (C) 106 m/s (D) 108 m/s (E) 1015 m/s

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48. A single circular loop of wire in the plane of the page is perpendicular to a uniform magnetic field B directed out of the page, as shown above. If the magnitude of the magnetic field is decreasing, then the induced current in the wire is

(A) directed upward out of the paper (B) directed downward into the paper

(C) clockwise around the loop (D) counterclockwise around the loop

(E) zero (no current is induced)

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49. A small vibrating object on the surface of a ripple tank is the source of waves of frequency 20 Hz and speed 60 cm/s. If the source S is moving to the right, as shown above, with speed 20 cm/s, at which of the labeled points will the frequency measured by a stationary observer be greatest?

(A) A (B) B (C) C (D) D (E) It will be the same at all four points.

[pic]

50. An object, slanted at an angle of 45°, is placed in front of a vertical plane mirror, as shown above. Which of the following shows the apparent position and orientation of the object's image?

[pic] [pic] [pic] [pic] [pic]

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51. Plane sound waves of wavelength 0.12 m are incident on two narrow slits in a box with nonreflecting walls, as shown above. At a distance of 5.0 m from the center of the slits, a first-order maximum occurs at point P, which is 3.0 m from the central maximum. The distance between the slits is most nearly

(A) 0.07 m (B) 0.09 m (C) 0.16 m (D) 0.20 m (E) 0.24 m

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52. An ideal gas is initially in a state that corresponds to point 1 on the graph above, where it has pressure p1, volume V1, and temperature T1. The gas undergoes an isothermal process represented by the curve shown, which takes it to a final state 3 at temperature T3. If T2 and T4 are the temperatures the gas would have at points 2 and 4, respectively, which of the following relationships is true?

(A) T1 < T3 (B) T1 < T2 (C) T1 < T4 (D) T1 = T2 (E) T1 = T4

53. The absolute temperature of a sample of monatomic ideal gas is doubled at constant volume. What effect, if any, does this have on the pressure and density of the sample of gas?

Pressure Density

(A) Remains the same Remains the same

(B) Remains the same Doubles

(C) Doubles Remains the same

(D) Doubles Is multiplied by a factor of 4

(E) Is multiplied by a factor of 4 Doubles

54. The disk-shaped head of a pin is 1.0 mm in diameter. Which of the following is the best estimate of the number of atoms in the layer of atoms on the top surface of the pinhead?

(A) 104 (B) 1014 (C) 1024 (D) 1034 (E) 1050

55. In an experiment, light of a particular wavelength is incident on a metal surface, and electrons are emitted from the surface as a result. To produce more electrons per unit time but with less kinetic energy per electron, the experimenter should do which of the following?

(A) Increase the intensity and decrease the wavelength of the light.

(B) Increase the intensity and the wavelength of the light.

(C) Decrease the intensity and the wavelength of the light.

(D) Decrease the intensity and increase the wavelength of the light.

(E) None of the above would produce the desired result.

56. An object moves up and down the y-axis with an acceleration given as a function of time t by the expression

a = A sin (t, where A and ( are constants. What is the period of this motion?

(A) ( (B) 2(( (C) (2A (D) 2(/( (E) (/2(

57. A ball of mass 0.4 kg is initially at rest on the ground. It is kicked and leaves the kicker's foot with a speed of 5.0 m/s in a direction 60° above the horizontal. The magnitude of the impulse imparted by the ball to the foot is most nearly

(A) 1 N s (B) [pic] N s (C) 2 N s (D) [pic] N s (E) 4 N s

[pic]

58. A wheel of radius R and negligible mass is mounted on a horizontal frictionless axle so that the wheel is in a vertical plane. Three small objects having masses m, M, and 2M, respectively, are mounted on the rim of the wheel, as shown above. If the system is in static equilibrium, what is the value of m in terms of M ?

(A) M/2 (B) M (C) 3M/2 (D) 2M (E) 5M/2

Questions 59-60

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A rock of mass m is thrown horizontally off a building from a height h, as shown above. The speed of the rock as it leaves the thrower’s hand at the edge of the building is v0.

59. How much time does it take the rock to travel from the edge of the building to the ground?

(A) [pic] (B) [pic] (C) [pic] (D) [pic] (E) [pic]

60. What is the kinetic energy of the rock just before it hits the ground?

(A) mgh (B) ½ mv02 (C) ½ mv02 - mgh (D) ½ mv02+mgh (E) mgh-½ mv02

61. Which of the following statements is NOT a correct assumption of the classical model of an ideal gas?

(A) The molecules are in random motion.

(B) The volume of the molecules is negligible compared with the volume occupied by the gas.

(C) The molecules obey Newton's laws of motion.

(D) The collisions between molecules are inelastic.

(E) The only appreciable forces on the molecules are those that occur during collisions.

62. A sample of an ideal gas is in a tank of constant volume. The sample absorbs heat energy so that its temperature changes from 300 K to 600 K. If v1 is the average speed of the gas molecules before the absorption of heat and v2 is their average speed after the absorption of heat, what is the ratio v2/ v1 ?

(A) 1/2 (B) 1 (C) [pic] (D) 2 (E) 4

63. Two people of unequal mass are initially standing still on ice with negligible friction. They then simultaneously push each other horizontally. Afterward, which of the following is true?

(A) The kinetic energies of the two people are equal.

(B) The speeds of the two people are equal.

(C) The momenta of the two people are of equal magnitude.

(D) The center of mass of the two-person system moves in the direction of the less massive person.

(E) The less massive person has a smaller initial acceleration than the more massive person.

64. Two parallel conducting plates, separated by a distance d, are connected to a battery of emf (. Which of the following is correct if the plate separation is doubled while the battery remains connected?

(A) The electric charge on the plates is doubled.

(B) The electric charge on the plates is halved.

(C) The potential difference between the plates is doubled.

(D) The potential difference between the plates is halved

(E) The capacitance is unchanged.

Questions 65-66

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Two concentric circular loops of radii b and 2b, made of the same type of wire, lie in the plane of the page, as shown above.

65. The total resistance of the wire loop of radius b is R. What is the resistance of the wire loop of radius 2b ?

(A) R/4 (B) R/2 (C) R (D) 2R (E) 4R

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66. A uniform magnetic field B that is perpendicular to the plane of the page now passes through the loops, as shown above. The field is confined to a region of radius a, where a < b, and is changing at a constant rate. The induced emf in the wire loop of radius b is (. What is the induced emf in the wire loop of radius 2b ?

(A) Zero (B) (/2 (C) ( (D) 2( (E) 4(

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67. A stationary object explodes, breaking into three pieces of masses m, m, and 3m. The two pieces of mass m move off at right angles to each other with the same magnitude of momentum mV, as shown in the diagram above. What are the magnitude and direction of the velocity of the piece having mass 3m ?

Magnitude Direction

(A) [pic] [pic]

(B) [pic] [pic]

(C) [pic] [pic]

(D) [pic] [pic]

(E) [pic] [pic]

[pic]

68. A rod on a horizontal tabletop is pivoted at one end and is free to rotate without friction about a vertical axis, as shown above. A force F is applied at the other end, at an angle ( to the rod. If F were to be applied perpendicular to the rod, at what distance from the axis should it be applied in order to produce the same torque?

(A) L sin ( (B) L cos ( (C) L (D) L tan ( (E) [pic] L

69. Which of the following imposes a limit on the number of electrons in an energy state of an atom?

(A) The Heisenberg uncertainty principle (B) The Pauli exclusion principle

(C) The Bohr model of the hydrogen atom (D) The theory of relativity

(E) The law of conservation of energy

70. A 4 (F capacitor is charged to a potential difference of 100 V. The electrical energy stored in the capacitor is

(A) 2 x 10-10 J (B) 2 x 10-8 J (C) 2 x 10-6 J (D) 2x 10-4 J (E) 2 x 10-2 J

Free Response Lab-Based Questions from Past AP Exams

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1996B2 (15 points) A spring that can be assumed to be ideal hangs from a stand, as shown above.

a. You wish to determine experimentally the spring constant k of the spring.

i. What additional, commonly available equipment would you need?

ii. What measurements would you make?

iii. How would k be determined from these measurements?

b. Assume that the spring constant is determined to be 500 N/m. A 2.0-kg mass is attached to the lower end of the spring and released from rest. Determine the frequency of oscillation of the mass.

c. Suppose that the spring is now used in a spring scale that is limited to a maximum value of 25 N, but you would like to weigh an object of mass M that weighs more than 25 N. You must use commonly available equipment and the spring scale to determine the weight of the object without breaking the scale.

i. Draw a clear diagram that shows one way that the equipment you choose could be used with the spring scale to determine the weight of the object,

ii. Explain how you would make the determination.

[pic]

1996M1. A thin, flexible metal plate attached at one end to a platform, as shown above, can be used to measure mass. When the free end of the plate is pulled down and released, it vibrates in simple harmonic motion with a period that depends on the mass attached to the plate. To calibrate the force constant, objects of known mass are attached to the plate and the plate is vibrated, obtaining the data shown below.

a. Fill in the blanks in the data table.

[pic]

b. On the graph below, plot T2 versus mass. Draw on the graph the line that is your estimate of the best straight-line fit to the data points.

[pic]

c. An object whose mass is not known is vibrated on the plate, and the average time for ten vibrations is measured to be 16.1 s. From your graph, determine the mass of the object. Write your answer with a reasonable number of significant digits.

d. Explain how one could determine the force constant of the metal plate.

e. Can this device be used to measure mass aboard the space shuttle Columbia as it orbits the Earth? Explain briefly.

f. If Columbia is orbiting at 0.3 x 106 m above the Earth's surface, what is the acceleration of Columbia due to the Earth's gravity? (Radius of Earth = 6.4 x 106 m, mass of Earth = 6.0 x 1024 kg)

g. Since the answer to part (f) is not zero, briefly explain why objects aboard the orbiting Columbia seem weightless.

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1997B2. To study circular motion, two students use the hand-held device shown above, which consists of a rod on which a spring scale is attached. A polished glass tube attached at the top serves as a guide for a light cord attached the spring scale. A ball of mass 0.200 kg is attached to the other end of the cord. One student swings the teal around at constant speed in a horizontal circle with a radius of 0.500 m. Assume friction and air resistance al negligible.

a. Explain how the students, by using a timer and the information given above, can determine the speed of the ball as it is revolving.

b. How much work is done by the cord in one revolution? Explain how you arrived at your answer.

c. The speed of the ball is determined to be 3.7 m/s. Assuming that the cord is horizontal as it swings, calculate the expected tension in the cord.

d. The actual tension in the cord as measured by the spring scale is 5.8 N. What is the percent difference between this measured value of the tension and the value calculated in part c. ?

e. The students find that, despite their best efforts, they cannot swing the ball so that the cord remains exactly horizontal.

i. On the picture of the ball below, draw vectors to represent the forces acting on the ball and identify

the force that each vector represents.

[pic]

ii. Explain why it is not possible for the ball to swing so that the cord remains exactly horizontal.

iii. Calculate the angle that the cord makes with the horizontal.

[pic]

1998B3 (10 points) Students are designing an experiment to demonstrate the conversion of mechanical energy into thermal energy. They have designed the apparatus shown in the figure above. Small lead beads of total mass M and specific heat c fill the lower hollow sphere. The valves between the spheres and the hollow tube can be opened or closed to control the flow of the lead beads. Initially both valves are open.

a. The lower valve is closed and a student turns the apparatus 180° about a horizontal axis, so that the filled sphere is now on top. This elevates the center of mass of the lead beads by a vertical distance h. What minimum amount of work must the student do to accomplish this?

b. The valve is now opened and the lead beads tumble down the hollow tube into the other hollow sphere. If all of the gravitational potential energy is converted into thermal energy in the lead beads, what is the temperature increase of the lead?

c. The values of M, h, and c for the students' apparatus are M = 3.0 kg, h = 2.00 m, and c = 128 J/(kg · K). The students measure the initial temperature of the lead beads and then conduct 100 repetitions of the "elevate-and-drain" process. Again, assume that all of the gravitational potential energy is converted into thermal energy in the lead beads. Calculate the theoretical cumulative temperature increase after the 100 repetitions.

d. Suppose that the experiment were conducted using smaller reservoirs, so that M was one-tenth as large (but h was unchanged). Would your answers to parts (b) and (c) be changed? If so, in what way, and why? If not, why not?

e. When the experiment is actually done, the temperature increase is less than calculated in part (c). Identify a physical effect that might account for this discrepancy and explain why it lowers the temperature.

[pic]

1998B4 (10 points) In the circuit shown above, A, B. C, and D are identical lightbulbs. Assume that the battery maintains a constant potential difference between its terminals (i.e., the internal resistance of the battery is assumed to be negligible) and the resistance of each lightbulb remains constant.

a. Draw a diagram of the circuit in the box below, using the following symbols to represent the components in your diagram. Label the resistors A, B. C, and D to refer to the corresponding lightbulbs.

[pic]

b. List the bulbs in order of their brightnesses, from brightest to least bright. If any two or more bulbs have the same brightness, state which ones. Justify your answer.

c. Bulb D is then removed from its socket.

i. Describe the change in the brightness, if any, of bulb A when bulb D is removed from its socket. Justify your answer.

ii. Describe the change in the brightness, if any, of bulb B when bulb D is removed from its socket. Justify your answer.

[pic]

1998M1. Two gliders move freely on an air track with negligible friction, as shown above. Glider A has a mass of 0.90 kg and glider B has a mass of 0.60 kg. Initially, glider A moves toward glider B, which is at rest. A spring of negligible mass is attached to the right side of glider A. Strobe photography is used to record successive positions of glider A at 0.10 s intervals over a total time of 2.00 s, during which time it collides with glider B.

The following diagram represents the data for the motion of glider A. Positions of glider A at the end of each 0.10s interval are indicated by the symbol A against a metric ruler. The total elapsed time t after each 0.50 s is also indicated.

a. Determine the average speed of glider A for the following time intervals.

[pic]

i. 0.L0 s to 0.30 s ii. 0.90 s to 1.10 s iii. 1.70 s to 1.90 s

b. On the axes below, sketch a graph, consistent with the data above, of the speed of glider A as a function of time t for the 2.00 s interval.

[pic]

c. i. Use the data to calculate the speed of glider B immediately after it separates from the spring.

ii. On the axes below, sketch a graph of the speed of glider B as a function of time t.

[pic]

A graph of the total kinetic energy K for the two-glider system over the 2.00 s interval has the following shape. Ko is the total kinetic energy of the system at time t = 0.

[pic]

d. i. Is the collision elastic? Justify your answer.

ii. Briefly explain why there is a minimum in the kinetic energy curve at t = 1.00 s.

1999B6 (10 points) You are given the following equipment for use in the optics experiments in parts (a) and (b).

A solid rectangular block made of transparent plastic

A laser that produces a narrow, bright, monochromatic ray of light

A protractor

A meterstick

A diffraction grating of known slit spacing

A white opaque screen

a. Briefly describe the procedure you would use to determine the index of refraction of the plastic. Include a labeled diagram to show the experimental setup. Write down the corresponding equation you would use in your calculation and make sure all the variables in this equation are labeled on your diagram.

b. Since the index of refraction depends on wavelength, you decide you also want to determine the wavelength of your light source. Draw and label a diagram showing the experimental setup. Show the equation(s) you would use in your calculation and identify all the variables in the equation(s). State and justify any assumptions you make.

[pic]

1999M1 In a laboratory experiment, you wish to determine the initial speed of a dart just after it leaves a dart gun. The dart, of mass m, is fired with the gun very close to a wooden block of mass M0 which hangs from a cord of length l and negligible mass, as shown above. Assume the size of the block is negligible compared to l, and the dart is moving horizontally when it hits the left side of the block at its center and becomes embedded in it. The block swings up to a maximum angle from the vertical. Express your answers to the following in terms of m, M0, l, (max, and g.

a. Determine the speed v0 of the dart immediately before it strikes the block.

b. The dart and block subsequently swing as a pendulum. Determine the tension in the cord when it returns to the lowest point of the swing.

c. At your lab table you have only the following additional equipment.

Meter stick Stopwatch Set of known masses

Protractor 5 m of string Five more blocks of mass M0

Spring

Without destroying or disassembling any of this equipment, design another practical method for determining the speed of the dart just after it leaves the gun. Indicate the measurements you would take, and how the speed could be determined from these measurements.

d. The dart is now shot into a block of wood that is fixed in place. The block exerts a force F on the dart that is proportional to the dart's velocity v and in the opposite direction, that is F = -bv, where b is a constant. Derive an expression for the distance L that the dart penetrates into the block, in terms of m, v0, and b.

2000B6 (10 points) You are to design a procedure to determine experimentally the specific heat of an unknown liquid. You may not damage or destroy any equipment you use, and your method must be feasible and practical.

a. List the equipment you would need. Include a labeled diagram.

b. Describe the measurements you would make. Assign each measurement a symbol (such as time = t).

c. Show explicitly using equations how the measured quantities would be used to determine the specific heat of the unknown liquid.

d. Indicate one possible source of experimental error and discuss how it would affect your value for the specific heat. Justify your answer.

[pic]

(2000 M1) You are conducting an experiment to measure the acceleration due to gravity gu at an unknown location. In the measurement apparatus, a simple pendulum swings past a photogate located at the pendulum's lowest point, which records the time t10 for the pendulum to undergo 10 full oscillations. The pendulum consists of a sphere of mass m at the end of a string and has a length l. There are four versions of this apparatus, each with a different length. All four are at the unknown location, and the data shown below are sent to you during the experiment.

|[pic] |t10 |T |T2 |

|(cm) |(s) |(s) |(s2) |

|12 |7.62 | | |

|18 |8.89 | | |

|32 |12.08 | | |

a. For each pendulum, calculate the period T and the square of the period. Use a reasonable number of significant figures. Enter these results in the table above.

b. On the axes below, plot the square of the period versus the length of the pendulum. Draw a best-fit straight line for this data.

[pic]

c. Assuming that each pendulum undergoes small amplitude oscillations, from your fit determine the experimental value gexp of the acceleration due to gravity at this unknown location. Justify your answer.

d. If the measurement apparatus allows a determination of gu that is accurate to within 4%, is your experimental value in agreement with the value 9.80 m/s2 ? Justify your answer.

e. Someone informs you that the experimental apparatus is in fact near Earth's surface, but that the experiment has been conducted inside an elevator with a constant acceleration a. Assuming that your experimental value g is exact, determine the magnitude and direction of the elevator's acceleration.

2001B5 (10 points) A platinum resistor has a resistance that changes with temperature. Values of the resistance were obtained experimentally for several temperatures from 5°C to 30°C only and plotted on the graph above. Design a procedure in which this resistor can be used as a thermometer to measure the temperature of a liquid that is in the 50°C to 75°C range. The resistor can be safely immersed in liquids. Along with the resistor and the container of the liquid of unknown temperature, the following equipment and materials may be used.

Power supply

Ammeter (Note: The ammeter and the voltmeter cannot

Voltmeter be used directly as an ohmmeter.)

Connecting wires

Ice-water bath

Boiling-water bath

a. Sketch a diagram (with labels) to show how equipment is to be connected to make the necessary measurements, and briefly outline the steps to be followed.

b. Discuss what measurements will be taken to determine the temperature of the unknown liquid.

c. Discuss one assumption that must be made regarding equipment or procedure in order to use the method you have described.

[pic]

[pic]

2000M1. A motion sensor and a force sensor record the motion of a cart along a track, as shown above. The cart is given a push so that it moves toward the force sensor and then collides with it. The two sensors record the values shown in the following graphs.

a. Determine the cart's average acceleration between t = 0.33 s and t = 0.37 s.

b. Determine the magnitude of the change in the cart's momentum during the collision.

c. Determine the mass of the cart.

d. Determine the energy lost in the collision between the force sensor and the cart

2002B6. (10 points) In the laboratory, you are given a cylindrical beaker containing a fluid and you are asked to determine the density ρ of the fluid. You are to use a spring of negligible mass and unknown spring constant k attached to a stand. An irregularly shaped object of known mass m and density D >> ρ) hangs from the spring. You may also choose from among the following items to complete the task.

• A metric ruler

• A stopwatch

• String

(a) Explain how you could experimentally determine the spring constant k.

[pic]

(b) The spring-object system is now arranged so that the object (but none of the spring) is immersed in the unknown fluid, as shown above. Describe any changes that are observed in the spring-object system and explain why they occur.

(c) Explain how you could experimentally determine the density of the fluid.

(d) Show explicitly, using equations, how you will use your measurements to calculate the fluid density ρ. Start by identifying any symbols you use in your equations.

2002M3. An object of mass 0.5 kg experiences a force that is associated with the potential energy function

U(x) = [pic], where U is in joules and x is in meters.

a. On the axes below, sketch the graph of U(x) versus x.

[pic]

b. Determine the force associated with the potential energy function

given above.

c. Suppose that the object is released from rest at the origin. Determine the speed of the particle at x = 2 m.

In the laboratory, you are given a glider of mass 0.50 kg on an air track. The glider is acted on by the force determined in part (b). Your goal is to determine experimentally the validity of your theoretical calculation in part c.

d. From the list below, select the additional equipment you will need from the laboratory to do your experiment by checking the line to the left of each item. If you need more than one of an item, place the number you need on the line.

Meterstick _____ Stopwatch Photogate timer String Spring

Balance Wood block Set of objects of different masses

e. Briefly outline the procedure you will use, being explicit about what measurements you need to make in order to determine the speed. You may include a labeled diagram of your setup if it will clarify your procedure.

[pic]

AP® Physics B

2007 Free-Response Questions

Form B

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Permission to use copyrighted College Board materials may be requested online at:

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PHYSICS B

SECTION II

Time-90 minutes

7 Questions

Directions: Answer all seven questions, which are weighted according to the points indicated. The suggested times are about 17 minutes for answering each of Questions 1 and 3 and about 11 minutes for answering each of Questions 2 and 4-7. The parts within a question may not have equal weight. Show all your work in the goldenrod booklet in the spaces provided after each part, NOT in this lavender insert.

[pic]

B2007b1. (15 points) A child pulls a 15 kg sled containing a 5.0 kg dog along a straight path on a horizontal surface. He exerts a force of 55 N on the sled at an angle of 20° above the horizontal, as shown in the figure above. The coefficient of friction between the sled and the surface is 0.22.

(a) On the dot below that represents the sled-dog system, draw and label a free-body diagram for the system as it is pulled along the surface.

[pic]

(b) Calculate the normal force of the surface on the system.

(c) Calculate the acceleration of the system.

(d) Calculate the work done by the child's pulling force as the system moves a distance of 7.0 m.

(e) At some later time, the dog rolls off the side of the sled. The child continues to pull with the same force. On the axes below, sketch a graph of speed v versus time t for the sled. Include both the sled's travel with and without the dog on the sled. Clearly indicate with the symbol tr the time at which the dog rolls off.

[pic]

[pic]

B2007b2. (10 points) A beam of particles of charge q = +3.2 x 10-19 C and mass m = 6.68 x 10-26 kg enters Region I with a range of velocities all in the direction shown in the diagram above. There is a magnetic field in Region I directed into the page with magnitude B = 0.12 T. Charged metal plates are placed in appropriate locations to create a uniform electric field of magnitude E = 4800 N/C in Region I. As a result, some of the charged particles pass straight through Region I undeflected. Gravitational effects are negligible.

(a) i. On the diagram above, sketch electric field lines in Region I.

ii. Calculate the speed of the particles that pass straight through Region I.

The particles that pass straight through enter Region II in which there is no electric field and the magnetic field has the same magnitude and direction as in Region I. The path of the particles in Region II is a circular arc of radius R.

(b) Calculate the radius R.

(c) Within the beam there are particles moving slower than the speed you calculated in (a)ii. In what direction is the net initial force on these particles as they enter Region I?

_____To the left _____Toward the top of the page _____Out of the plane of the page

_____To the right _____Toward the bottom of the page _____Into the plane of the page

Justify your answer.

(d)A particle of the same mass and the same speed as in (a)ii but with charge q = –3.2 x 10-19 C enters Region I. On the following diagram, sketch the complete resulting path of the particle.

[pic]

[pic]

B2007b3. (15 points) In the circuit above, a 12.0 V battery is connected to two resistors, one of resistance 1000 Ω and the other of resistance 500 Ω . A capacitor with a capacitance of 30 x 10-6 F is connected in parallel with the 500 Ω resistor. The circuit has been connected for a long time, and all currents have reached their steady states.

(a) Calculate the current in the 500 Ω resistor.

(b)

(i) Draw an ammeter in the circuit above in a location such that it could measure the current in the 500 Ω resistor. Use the symbol [pic] to indicate the ammeter.

(ii) Draw a voltmeter in the circuit above in a location such that it could measure the voltage across the 1000 S2, resistor. Use the symbol [pic] to indicate the voltmeter.

(c) Calculate the charge stored on the capacitor.

(d) Calculate the power dissipated in the 1000 Ω resistor.

(e) The capacitor is now discharged, and the 500 Ω resistor is removed and replaced by a resistor of greater resistance. The circuit is reconnected, and currents are again allowed to come to their steady-state values. Is the charge now stored on the capacitor larger, smaller, or the same as it was in part (c)?

______Larger ______Smaller ______The same as

Justify your answer.

[pic]

B2007b4. (10 points) A cylindrical tank containing water of density 1000 kg/m3 is filled to a height of 0.70 m and placed on a stand as shown in the cross section above. A hole of radius 0.0010 m in the bottom of the tank is opened. Water then flows through the hole and through an opening in the stand and is collected in a tray 0.30 m below the hole. At the same time, water is added to the tank at an appropriate rate so that the water level in the tank remains constant.

(a) Calculate the speed at which the water flows out from the hole.

(b) Calculate the volume rate at which water flows out from the hole.

(c) Calculate the volume of water collected in the tray in t = 2.0 minutes.

(d) Calculate the time it takes for a given droplet of water to fall 0.25 m from the hole.

[pic]

B2007b5 (10 points) The cylinder above contains an ideal gas and has a movable, frictionless piston of diameter D and mass M. The cylinder is in a laboratory with atmospheric pressure Patm . Express all algebraic answers in terms of the given quantities and fundamental constants.

(a) Initially, the piston is free to move but remains in equilibrium. Determine each of the following.

(i) The force that the confined gas exerts on the piston

(ii) The absolute pressure of the confined gas

(b) If a net amount of heat is transferred to the confined gas when the piston is fixed, what happens to the pressure of the gas?

_______Pressure goes up. _______Pressure goes down. _______Pressure stays the same.

Explain your reasoning.

(c) In a certain process the absolute pressure of the confined gas remains constant as the piston moves up a distance xo . Calculate the work done by the confined gas during the process.

B2007b6 (10 points) A student is asked to determine the index of refraction of a glass slab. She conducts several trials for measurement of angle of incidence θa in the air versus angle of refraction θg in the glass at the surface of the slab. She records her data in the following table. The index of refraction in air is 1.0.

|Trial # |θg (degrees) |θa (degrees) |Sin θg |Sin θa |

|1 |5.0 |8.0 |0.09 |0.14 |

|2 |15 |21 |0.26 |0.36 |

|3 |25 |39 |0.42 |0.63 |

|4 |35 |56 |0.57 |0.83 |

(a) Plot the data points on the axes below and draw a best-fit line through the points.

[pic]

(b) Calculate the index of refraction of the glass slab from your best-fit line.

(c) Describe how you could use the graph to determine the critical angle for the glass-air interface. Do not use the answer to the part (b) for this purpose.

(d) On the graph in (a), sketch and label a line for a material of higher index of refraction.

B2007b7. (10 points) In the vicinity of a heavy nucleus, a high-energy photon can be converted into two particles: an electron and a positron. A positron has the same mass as the electron and equal but opposite charge. This process is called pair production.

(a) Calculate the rest energy of an electron, in eV.

(b) Determine the minimum energy, in eV, that a photon must have to give rise to pair production.

(c) Calculate the wavelength corresponding to the photon energy found in part (b).

(d) Calculate the momentum of the photon.

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