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Pre-AP Physics Review Problems

SECTION ONE: MULTIPLE-CHOICE QUESTIONS (50x2=100 points)

1. The graph above shows the velocity versus time for an object moving in a straight line. At what time aftert = 0 does the object again pass through its initial position?

(A) 1 s (B) Between 1 and 2 s (C) 2 s (D) Between 2 and 3 s

Questions 2-3The following TWO questions refer to the following information. An ideal elastic rubber ball is dropped from aheight of about 2 meters, hits the floor and rebounds to its original height.

2. Which of the following graphs would best represent the distance above the floor versus time for the abovebouncing ball?

3. Which of the following graphs would best represent acceleration versus time for the bouncing ball?

Questions 4–5

A 2-kg block slides down a 30° incline as shown above with an acceleration of 2 m/s2.

4. Which of the following diagrams best represents the gravitational force W. the frictional force f, and the normalforce N that act on the block?

5. Which of the following correctly indicates the magnitudes of the forces acting up and down the incline?(A) 20 N down the plane, 16 N up the plane(B) 4 N down the plane, 4 N up the plane(C) 0 N down the plane, 4 N up the plane(D) 10 N down the plane, 6 N up the plane

(D)

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8.

9.

6. A rope of negligible mass supports a block that weighs 30 N, as shown above. The breaking strength of therope is 50 N. The largest acceleration that can be given to the block by pulling up on it with the rope withoutbreaking the rope is most nearly(A) 6.7 m/s2 (B) 10 m/s2 (C) 16.7 m/s2 (D) 26.7 m/s2

7. Given the three masses as shown in the diagram above, if the coefficient of kinetic friction between the largemass (m2) and the table is μ, what would be the upward acceleration of the small mass (m3)? The mass andfriction of the cords and pulleys are small enough to produce a negligible effect on the system.(A) g(m1 + m2)/(m1 + m2 + m3) (B) g(m1 + m2 + m3)/ (m1 – m2 – m3)(C) g(m1 – m2 – m3)/ (m1 + m2 + m3) (D) g(m1 – m2 – m3)/ (m1 + m2 + m3)

Three blocks of masses 3m, 2m, ands are connected to strings A, B, and C as shown above. The blocks are pulled along a rough surface by a force of magnitude F exerted by string C. The coefficient of friction between each block and the surface is the same. Which string must be the strongest in order not to break?(A) A (B) B (C) C (D) They must all be the same strength.

A ball of mass m is attached to the end of a string of length Q as shown above. The ball is released from restfrom position P. where the string is horizontal. It swings through position Q. where the string is vertical, andthen to position R. where the string is again horizontal. What are the directions of the acceleration vectors of theball at positions Q and R?

Position RDownwardTo the rightDownward

Position Q(A) Downward(B) Downward(C) Upward(D) Upward To the left

10. A car is traveling on a road in hilly terrain, see figure to the right. Assume the car has speed vand the topsand bottoms of the hills have radius of curvature R. The driver of the car is most likely to feel weightless:

(A) at the top of a hill when v gR

(C) going down a hill when v gR

(B) at the bottom of a hill when v gR

(D) at the top of a hill when v gR

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11. The net force on a rocket with a weight of 1.5 x 104 N is 2.4 x 104 N. How much time is needed to increase therockets speed from 12 m/s to 36 m/s near the surface of the Earth at takeoff?(A) 0.78 s (B) 1.5 s (C) 3.8 s (D) 15 s

Questions 12-13: A block oscillates without friction on the end of a spring as shown. The minimum and maximum lengths of the spring as it oscillates are,respectively, xmin and xmax. The graphs below can represent quantitiesassociated with the oscillation as functions of the length x of the spring.

12. Which graph can represent the total mechanical energy of the block-spring system as a function of x ?(A) A (B) B (C) C (D) D (E) E

13. Which graph can represent the kinetic energy of the block as a function of x ?(A) A (B) B (C) C (D) D (E) EA force F at an angle θ above the horizontal is used to pull a heavy suitcase of weight mg a distance d along alevel floor at constant velocity. The coefficient of friction between the floor and the suitcase is µ. The workdone by the frictional force is:(A) –Fd cos θ (B) – µ Fd cos θ (C) -µmgd (D) -µ mgd cos θ

14.

15. A 500-kg car is moving at 28 m/s. The driver sees a barrier ahead. If the car takes 95 meters to come to rest,what is the magnitude of the minimum average net force necessary to stop?(A) 47.5 N (B) 1400 N (C) 2060 N (D) 19600 N

16. A person pushes a block of mass M = 6.0 kg with a constant speed of 5.0 m/s straight up a flat surface inclined30.0° above the horizontal. The coefficient of kinetic friction between the block and the surface is ȝ� �0.40.What is the net force acting on the block?(A) 0 N (B) 21 N (C) 30 N (D) 51 N

17. A block of mass M on a horizontal surface is connected to the end of amassless spring of spring constant k . The block is pulled a distance xfrom equilibrium and when released from rest, the block moves towardequilibrium. What coefficient of kinetic friction between the surface andthe block would allow the block to return to equilibrium and stop?

kxMg)(D

MgkxC

MgkxB

Mgkx)(A

22)()(

2

2

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18. A person pushes a box across a horizontal surface at a constant speed of 0.5 meter per second. The box has amass of 40 kilograms, and the coefficient of sliding friction is 0.25. The power supplied to the box by theperson is (A) 0.2 W (B) 5 W (C) 50 W (D) 100 W (E) 200 W

19. Two balls are on a frictionless horizontal tabletop. Ball X initially moves at 10 meters per second, as shown inFigure I above. It then collides elastically with identical ball Y which is initially at rest. After the collision, ballX moves at 6 meters per second along a path at 53° to its original direction, as shown in Figure II above. Whichof the following diagrams best represents the motion of ball Y after the collision?

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

From the top of a high cliff, a ball is thrown horizontally with initial speed vo. Which of the following graphs best represents the ball's kinetic energy K as a function of time t ?

20.

A system of two wheels fixed to each other is free to rotate about a frictionless axis through the common center of the wheels and perpendicular to the page. Four forces are exerted tangentially to the rims of the wheels, as shown. The magnitude of the net torque on the system about the axis is(A) zero (B) 2FR (C) 5FR (D) 14FR

21.

22. A uniform rigid bar of weight W is supported in a horizontal orientation as shown by a rope that makes a30°angle with the horizontal. The force exerted on the bar at point O, where it is pivoted, is bestrepresented by a vector whose direction is which of the following?

23. A rod of length L and of negligible mass is pivoted at a point that is off-center with lengths shown in thefigure below. The figures show two cases in which masses are suspended from the ends of the rod. Ineach case the unknown mass m is balanced by a known mass, M1 or M2, so that the rod remainshorizontal. What is the value of m in terms of the known masses?

(A) M1M2 (B) ½(Ml + M2) (C) Ml M2 (D) ½M1M2

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24. A turntable that is initially at rest is set in motion with a constant angular acceleration . What is theangular velocity of the turntable after it has made one complete revolution?

Questions 25-26

A solid cylinder of mass m and radius R has a string wound around it. A person holding the string pulls itvertically upward, as shown above, such that the cylinder is suspended in midair for a brief time interval t andits center of mass does not move. The tension in the string is T, and the rotational inertia of the cylinder about

its axis is 12MR2

25. the net force on the cylinder during the time interval t is(A) mg (B) T – mgR (C) mgR - Τ (D) zero

26. The linear acceleration of the person's hand during the time interval t is

(A) (T-mg)/m (B) 2g (C) g/2 (D) T/m27.When an object oscillating in simple harmonic motion is at its maximum displacement from the equilibrium

position. Which of the following is true of the values of its speed and the magnitude of the restoring force?Restoring ForceSpeed

(A) Zero(B) Zero

MaximumZero

(C) Maximum ½ maximum(D) Maximum Zero

Questions 28-29

A sphere of mass m1, which is attached to a spring, is displaced downward from its equilibrium position as shownabove left and released from rest. A sphere of mass m2, which is suspended from a string of length L, is displaced tothe right as shown above right and released from rest so that it swings as a simple pendulum with small amplitude.Assume that both spheres undergo simple harmonic motion

28. Which of the following is true for both spheres?(A) The maximum kinetic energy is attained as the sphere passes through its equilibrium position(B) The maximum kinetic energy is attained as the sphere reaches its point of release.(C) The minimum gravitational potential energy is attained as the sphere passes through its equilibrium position.(D) The maximum gravitational potential energy is attained when the sphere reaches its point of release.

29. If both spheres have the same period of oscillation, which of the following is an expression for the spring constant

(A) L / m1g (B) g / m2L (C) m2g / L (D) m1g / L

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30. A particle oscillates up and down in simple harmonic motion.Its height y as a function of time t is shown in the diagram.At what time t does the particle achieve its maximumpositive acceleration?(A) 1 s (B) 2 s (C) 3 s (D) 4 s

31. A simple pendulum consists of a l.0 kilogram brass bob on a string about 1.0 meter long. It has a period of 2.0seconds. The pendulum would have a period of 1.0 second if the(A) string were replaced by one about 0.25 meter long(B) string were replaced by one about 2.0 meters long(C) bob were replaced by a 0.25 kg brass sphere(D) bob were replaced by a 4.0 kg brass sphere

32. A string is firmly attached at both ends. When a frequency of60 Hz is applied, the string vibrates in the standing wave patternshown. Assume the tension in the string and its mass per unitlength do not change. Which of the following frequencies couldNOT also produce a standing wave pattern in the string?(A)30 Hz (B) 40 Hz (C) 80 Hz (D) 180 Hz

33. If the speed of sound in air is 340 m/s, the length of the organ pipe, open at both ends, that can resonate at thefundamental frequency of 136 Hz, would be:

(A)0.40 m (B) 0.80 m (C) 1.25 m (D) 2.5 m34. For a standing wave mode on a string fixed at both ends, adjacent antinodes are separated by a distance of 20

cm. Waves travel on this string at a speed of 1200 cm/s. At what frequency is the string vibrated to produce thisstanding wave?(A) 120 Hz (B) 60 Hz (C) 40 Hz (D) 30 Hz

35. A vibrating tuning fork sends sound waves into the air surrounding it. During the time in which the tuning forkmakes one complete vibration, the emitted wave travels(A) one wavelength(B) about 340 meters(C) a distance directly proportional to the square root of the air density(D) a distance inversely proportional to the square root of the pressure

36. The figure above shows two wave pulses that are approaching each other. Which of the following best showsthe shape of the resultant pulse when the centers of the pulses, points P and Q coincide?

(A)

37. Two blocks of steel, the first of mass 1 kg and the second of mass 2 kg, are in thermal equilibrium with athird block of aluminum of mass 2 kg that has a temperature of 400 K. What are the respectivetemperatures of the first and second steel blocks?(A)400 K and 200 K (B)200 K and 400 K (C)400 K and 400 K (D)800 K and 400 K

38. An ideal gas confined in a box initially has pressure p. If the absolute temperature of the gas is doubled and thevolume of the box is quadrupled, the pressure is(A) p/8 (B) p/4 (C) p/2 (D) 2p

39. A mass m of helium gas is in a container of constant volume V. It is initially at pressure p and absolute (Kelvin)temperature T. Additional helium is added, bringing the total mass of helium gas to 3m. After this addition, thetemperature is found to be 2T. What is the gas pressure?(A) 2/3 p (B) 3/2 p (C) 3 p (D) 6 p

40. In a certain process, 400 J of heat is transferred 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) 300 J (C) –100 J (D) –300 J

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41. A monatomic ideal gas at pressure P = 105 Pa is in a container of volume V = 12 m3 while at temperature T =50ºC. How many molecules of gas are in the container?(A) 1.74 × 1027 (B) 2.69 × 1026 (C) 2888 (D) 447

42. Two small spheres have equal charges q and are separated by a distance d. The force exerted on each sphereby the other has magnitude F. If the charge on each sphere is doubled and d is halved, the force on each spherehas magnitude(A) F (B) 4F (C) 8F (D) 16F

43. The diagram above shows an isolated, positive charge Q. Point (B) is twice as far away from Q as point A. Theratio of the electric field strength at point A to the electric field strength at point B is(A) 8 to 1 (B) 4 to 1 (C) 2 to 1 (D) 1 to 2

44. An electron e and a proton p are simultaneously released from rest in a uniform electric field E, as shown above.Assume that the particles are sufficiently far apart so that the only force acting on each particle after it isreleased is that due to the electric field. At a later time when the particles are still in the field, the electron andthe proton will have the same(A) direction of motion (B) speed (C) magnitude of acceleration(D) magnitude of force acting on them

45. A positive charge of 3.0 × 10–8 coulomb is placed in an upward directed uniform electric field of 4.0 × 104 N/C.When the charge is moved 0.5 meter upward, the work done by the electric force on the charge is(A) 6 × 10–4 J (B) 12 × 10–4 J (C) 2 × 104 J (D) 8 × 104 J

The following configurations of electric charges are located at the vertices of an equilateral triangle. Point P isequidistant from the charges.

46.

In which configuration is the electric field at P equal to zero?(A) A (B) B (C) C (D) D

47. From the electric field vector at a point, one can determine which of the following?I. The direction of the electrostatic force on a test charge of known sign at that pointII. The magnitude of the electrostatic force exerted per unit charge on a test charge at that pointIII. The electrostatic charge at that point

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

48. Two metal spheres that are initially uncharged are mounted on insulating stands, as shown above. A negativelycharged rubber rod is brought close to, but does not make contact with, sphere X. Sphere Y is then broughtclose to X on the side opposite to the rubber rod. Y is allowed to touch X and then is removed some distanceaway. The rubber rod is then moved far away from X and Y. What are the final charges on the spheres?

Sphere X Sphere YA) Zero ZeroB) Negative PositiveC) Positive NegativeD) Positive Positive

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Questions 49-50

Particles of charge Q and –4Q are located on the x–axis as shown in the figure above. Assume the particles areisolated from all other charges.

49. Which of the following describes the direction of the electric field at point P?(A) +y (B)–y (C) Components in both the –x and +y directions(D) Components in both the +x and –y directions

50. At which of the labeled points on the x–axis is the electric field zero?(A) A (B) B (C) C (D) E

SECTION TWO FREE-RESPONSE QUESTIONS

1. A 3-meter long rope is attached to a support at point C. A 60 kg person sits on a ledge at position A holding the other end of therope so that it is horizontal and taut. The person then drops off the ledge and swings down on the rope toward position B on a lower ledge where a rock of mass 5 kg is at rest. At position B the person grabs hold of the rock and simultaneously lets go of the rope. The person and the rock then land together in the lake at point D, which is a vertical distance 10 m below position B. Air resistance and the mass of the rope are negligible.

(a) What is the speed of the person just before the collision with the rock?(b) What is the tension in the rope just before the collision with the rock?(c) Determine the total horizontal displacement of the person from position A until the person and object land in the water at point D.

2. A hollow tube of length 0.5 m open at both ends as shown, is held in midair. A tuningfork with a frequency 400 Hz vibrates at one end of the tube and causes the air in the tube to vibrate at its fundamental frequency.

(a) Determine the wavelength of the sound.(b) Determine the speed of sound in the air inside the tube.(c) Determine the next higher frequency at which this air column would resonate.

(a) Determine the magnitude and sign of charge Q2.(b) Determine the magnitude and direction of the net force on charge Q1(c) Determine the potential energy of the entire system.

3. Two point charges, Q1 and Q2, are located a distance 0.20 meter apart, as shown above. Charge Q1 = +8.0 C. The net electric field iszero at point P, located 0.40 meter from Q1 and 0.20 meter from Q2.