2011-12 AP Physics b Exam Information

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2011‐12 AP Physics B 1st Semester Exam Information

• 30 multiple choice questions (60% of exam grade)

• 3 free response questions (40% of exam grade)

• Each student will be given the following choices for how they may take the exam……

o Choice “A”:

AP

Testing

Style

o No cheat sheet

o No calculator on the multiple choice section

o No equation sheet on the multiple choice section (Constant Sheet is allowed)

o 10% will be added to the student’s exam grade

o Choice “B”: Non AP Testing Style

o Cheat sheet allowed (Front and back side of 8½ x 11 paper, handwritten)

o Calculator allowed

o Equation sheet will be provided and may be used on both sections of test

o 0% will be added to the student’s exam grade

• Exam content

o Kinematics

o Position, displacement, speed, velocity, acceleration, graphs, free fall, projectile

motion, kinematics equations.

o Newton’s Laws

o Inertia, Net Force, action‐reaction force pairs, weight, free‐body diagrams,

normal force, friction, pulleys, inclined planes.

o Work, Energy, and Power

o Work, kinetic energy, work‐energy theorem, potential energy, conservation of

mechanical energy, power.

o Linear Momentum

o Impulse, conservation of linear momentum, collisions.

o Uniform Circular Motion and Newton’s Laws of Gravitation

o Uniform circular motion, torque, equilibrium, Newton’s law of gravitation.

o Oscillations

o Simple harmonic motion and energy conversion, kinematics of SHM, spring‐

block oscillator (vertical and horizontal), pendulums.

o Fluid Mechanics

o Density, pressure, hydrostatic pressure, buoyancy, flow rate and the continuity

equation, Bernoulli’s equation.

o Thermal Physics

o Heat transfer and temperature change, heat transfer and phase change, thermal

expansion, kinetic theory of gases, ideal gas law, pressure vs. volume graphs.

o Electrostatics

o Electric charge, coulomb’s law, electric field, conductors and insulators,

electrical potential energy, electric potential



Example Questions:

Kinematics

1. The displacement x of an object moving along the x‐axis is shown above as a function of time t. The

acceleration of this object must be

(A) zero (B) constant but not zero (C) increasing (D) decreasing (E) equal to g

2. An object is released from rest on a planet that has no atmosphere. The object falls freely for 3.0 meters in the

first second. What is the magnitude of the acceleration due to gravity on the planet?

(A) 1.5 m s2 (B) 3.0 m/s

2 (C) 6.0 m/s

2 (D) 10.0 m/s

2 (E) 12.0 m/s

2

A ball is thrown and follows the parabolic path shown above. Air friction is negligible. Point Q is the highest

point on the path. Points P and R are the same height above the ground.

3. How do the speeds of the ball at the three points compare?

(A) vp < vQ < vR (B) vR < vQ < vP (C) vQ < vR < vP (D) vQ < vP = vR (E) vP = vR < vQ

4. Which of the following diagrams best shows the direction of the acceleration of the ball at point P ?

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

5. Shown below is the velocity vs. time graph for a toy car moving along a straight line. What is the maximum

displacement from start for the toy car?

(A) 3 m (B) 5 m (C) 6.5 m (D) 7 m (E) 7.5 m



Questions 6‐7

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 .

6. The magnitude of the displacement 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

7. The acceleration of 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

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 v 0.

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

(A) hvo (B) h

v0

(C) hv

g

0 (D)

2h

g (E) 2h g

9. A body moving in the positive x direction passes the origin at time t = 0. Between t = 0 and t = 1 second, the

body has a constant speed of 24 meters per second. At t = 1 second, the body is given a constant acceleration

of 6 meters per second squared in the negative x direction. The position x of the body at t = 11 seconds is

(A) +99m (B) +36m (C) ‐ 36 m (D) ‐ 75 m (E) ‐ 99 m

10. A 500‐kilogram sports car accelerates uniformly from rest, reaching a speed of 30 meters per second in 6

seconds. During the 6 seconds, the car has traveled a distance of

(A) 15 m (B) 30 m (C) 60 m (D) 90 m (E) 180 m

Newton’s Laws



Example Questions: Linear Momentum

1. The graph shows the force on an object of mass M as a

l

(A) 40 kg m/s (B) 20 kg m/s

(E) indeterminable unless the mass M of the object is known

2. As shown in the top view, a disc of mass m is moving horizontally

a

v/3 (B) v/2 (C) 2v/3 (D) 3v/2 (E) 2v

uestions 3‐4

function of time. For the time interval 0 to 4 s, the tota

change in the momentum of the object is

(C) 0 kg m/s (D) – 20 kg m/s

to the

right with speed v on a table with negligible friction when it collides with

second disc of mass 2m The second disc is moving horizontally to the right

with speed v/2 at the moment of impact The two discs stick together upon

impact. The speed of the composite body immediately after the collision is

(A)

Q

ing on a frictionless air table are about to collide,

as shown. The 1.5 kg puck is moving directly east at 2.0 m/s.

3. W m before

the collision?

5.0 J (C) 7.0 J (D) 10 J (E) 11 J

4. W e two‐puck system after the collision?

5. A ude F in the direction of

of the object

(D) 4.0 m/s (E) 6.0 m/s

. with another disk that was initially stationary. The figures below show a top view of the initial path I of the sliding disk and a hypothetical path H

Two pucks mov

The 4.0 kg puck is moving directly north at 1.0 m/s.

hat is the total kinetic energy of the two‐puck syste

(A) √13 J (B)

hat is the magnitude of the total momentum of th

(A) 1.0 kg∙m/s (B) 3.5 kg∙m/s (C) 5.0 kg∙m/s (D) 7.0 kg∙m/s (E) 5.5√5 kg∙m/s

2 kg object initially moving with a constant velocity is subjected to a force of magnit

motion. A graph of F as a function of time t is shown. What is the increase, if any, in the velocity

during the time the force is applied?

(A) 0 m/s (B) 2.0 m/s (C) 3.0 m/s

6 A disk slides to the right on a horizontal, frictionless air table and collides

for each disk after the collision. Which figure shows an impossible situation?



Example Questions: Uniform Circular Motion and Newton’s Laws of Gravitation

ss M. What is the

radius of the satellite's orbit?

1. A satellite of mass m and speed v moves in a stable, circular orbit around a planet of ma

(A) mv

GM

(B) mM

Gv

(D) v

GmM

(C) 2v

GM

(E) 2v

GmM

2. The mass of Planet X is one‐tenth that of the Earth, and its diameter is one‐half that of the Earth. The

acceleration due to gravity at the surface of Planet X is most nearly

2(A) 2 m/s

2 (B) 4 m/s

2 (C) 5 m/s

2 (D) 7 m/s

2 (E) 10 m/s

3. Two artificial satellites, 1 and 2, orbit the Earth in circular orbits having radii R1 and R2, respectively, as shown

above. If R = 2R , the accelerations a and a of the two satellites are related by which of the following?

4.

. 23

kilograms and radius 3.4 × 106 meters. The acceleration of an object in

free‐fall near the surface of Mars is most nearly

6. 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?

. mark. Where should one hang a mass of 0.50 kg

to balance the stick?

2 1 2 1

(A) a2 = 4a1 (B) a2 = 2a1 (C) a2 = a1 (D) a2 = a1/2 (E) a2 = a1/4

Astronauts in an orbiting space shuttle are “weightless” because

(A) of their extreme distance from the earth

(B) the net gravitational force on them is zero

(C) there is no atmosphere in space

D) the space shuttle does not rotate

E) they are in a state of free fall

5 The planet Mars has mass 6.4 × 10

(A) zero (B) 1.0 m/s2 (C) 1.9 m/s

2 (D) 3.7 m/s

2 (E) 9.8 m/s

2

An object has a weight W when it is on the surface of a planet of radius R.

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

7 A uniform meterstick of mass 0.20 kg is pivoted at the 40 cm

(A) 16 cm (B) 36 cm (C) 44 cm (D) 46 cm (E) 54 cm



8. A uniform meterstick is balanced at its midpoint with several forces applied as shown below. If the stick is in

equilibrium, the magnitude of the force X in newtons (N) is

ple Questions: Oscillations

(A) 50 N (B) 100 N (C) 200 N (D) 300 N (E) impossible to determine without the weight of the stick

Exam

Questions 1‐2

block is attached to an initially unstretched spring of force constant k = 40 newtons per meter as

shown above. The block is released from rest at time t = 0.

harmonic motion of the block?

(A)

A 0.l ‐kilogram

1. What is the amplitude, in meters, of the resulting simple

m40

1 (B) m

20

1 (C) m

4

1 m2

1 (D) (E) 1m

2. What will the resulting period of oscillation be?

(A)

π π π π

40s

(B) 20s

(C) 10s (D) 5

s (E)

π

4s



Questions 3‐4. A block on a horizontal frictionless plane is attached to a spring, as shown above. The block

oscillates along the x‐axis with simple harmonic motion of amplitude A.

3. Which of the following statements about the block is correct?

(A) At x = 0, its velocity is zero. (B) At x = 0, its acceleration is at a maximum.

(C) At x = A, its displacement is at a maximum. (D) At x = A, its velocity is at a maximum.

(E) At x = A, its acceleration is zero.

4. Which of the following statements about energy is correct?

(A) The potential energy of the spring is at a minimum at x = 0.

(B) The potential energy of the spring is at a minimum at x = A.

(C) The kinetic energy of the block is at a minimum at x =0.

(D) The kinetic energy of the block is at a maximum at x = A.

(E) The kinetic energy of the block is always equal to the potential energy of the spring.

5. A mass m, attached to a horizontal massless spring with spring constant k, is set into simple harmonic motion.

Its maximum displacement from its equilibrium position is A. What is the mass’s speed as it passes through its equilibrium position?

k

m

A E

m

k

A D

k

m AC

m

k A B A

1)(

1)()()(0)(

6. A mass on the end of a spring oscillates with the displacement vs.

time graph shown. Which of the following statements about its

motion is INCORRECT?

(A) The amplitude of the oscillation is 0.08 m.

(B) The frequency of oscillation is 0.5 Hz.

(C) The mass achieves a maximum in speed at 1 sec. (D) The period of oscillation is 2 sec.

(E) The mass experiences a maximum in the size of the

acceleration at t=1.5 sec



Example Questions: Fluids

1. A cork has weight mg and density 25% of water density. A string is tied around the

cork and attached to the bottom of a water‐filled container. The cork is totally

immersed. Express in terms of the cork weight mg, the tension in the string

A) 0

B) mg

C) 2mg

D) 3mg

E) 4mg

2. An ideal fluid flows through a long horizontal circular pipe. In one region of the pipe, it has radius R. The pipe

then widens to radius 2R. What is the ratio of the fluids speed in the region of radius R to the speed of the

fluid in region with radius 2R

A) ¼ B) ½ C) 1 D) 2 E) 4

3. A fluid is forced through a pipe of changing cross section as shown. In which section would the pressure of the

fluid be a minimum

A) I B) II C) III D) IV E) all section have the same pressure.

4. As a rock sinks deeper and deeper into water of constant density, what happens to the buoyant force on it?

A) It increases.

B) It remains constant.

C) It decreases.

D) It may increase or decrease, depending on the shape of the rock.

5. Water flows through a pipe. The diameter of the pipe at point B is larger than at point A. Where is the water

pressure greater?

A) Point A

B) Point B

C) Same at both A and B

D) Cannot be determined from the information given.

6. Liquid flows through a 4 cm diameter pipe at 1.0 m/s. There is a 2 cm diameter restriction in the line. What is

the velocity in this restriction?

A) 0.25 m/s B) 0.50 m/s C) 2 m/s D) 4 m/s



Example Questions: Thermodynamics

1. In time t , an amount of heat Q flows through the solid door of area A and thickness d represented above. The

temperatures on each side of the door are T 2 and T 1, respectively. Which of the following changes would be

certain to decrease Q?

(A) Increasing A only (B) Decreasing d only (C) Increasing d and T 2

– T 1 only

(D) Decreasing A and T 2 – T 1 only (E) Increasing d, A, and T 2 – T 1

2. A gas with a fixed number of molecules does 32 J of work on its surroundings, and 16 J of heat are transferred

from the gas to the surroundings. What happens to the internal energy of the gas?

(A) It decreases by 48 J. (B) It decreases by 16 J. (C) It remains the same. (D) It increases by 16 J.

(E) It increases by 48 J.

3. A gas can be taken from state a to c by two different reversible processes, ac or abc. During the direct

process ac, 20.0 J of work are done by the system and 30.0 J of heat are added to the system. During the

process abc, 25.0 J of heat are added to the system. How much work is done by the system during

abc?

(A) 5.0 J (B) 10.0 J (C) 15.0 J (D) 20.0 J (E) 25.0 J

4. A heat engine takes in 200 J of thermal energy and performs 50 J of work in each cycle. What is its efficiency?

(A) 50 % (B) 40 % (C) 25 % (D) 20 % (E) 12 %

5. According to the kinetic theory of gases, when the absolute temperature of an ideal gas doubles, the averagekinetic energy of the molecules of the gas

(A) quadruples (B) doubles (C) stays the same (D) is cut in half (E) is quartered



Example Questions: Electrostatics

1. A solid conducting sphere is given a positive charge Q. How is the charge Q distributed in or on the sphere?

(A) It is concentrated at the center of the sphere.

(B) It is uniformly distributed throughout the sphere.

(C) Its density decreases radially outward from the center.

(D) Its density increases radially outward from the center.

(E) It is uniformly distributed on the surface of the sphere only.

2. The diagram above shows an isolated, positive charge Q. Point (B) is twice as far away from Q as point A. The

ratio 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 1 (E) 1 to 2

Questions 3‐4

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 .

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

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

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

(A) Zero (B) 2

4 0πε

qQ

d (C)

1

4 0πε

qQ

d (D)

2

4 0πε

qQ

d (E)

2 2

4 0πε

qQ

d



Free Response Examples:

A 10‐kilogram block rests initially on a table as shown in cases I and II above. The coefficient of sliding

friction between the block and the table is 0.2. The block is connected to a cord of negligible mass,

which hangs over a massless frictionless pulley. In case I a force of 50 newtons is applied to the cord.

In case II an object of mass 5 kilograms is hung on the bottom of the cord. Use g = 10 meters per

second squared.

a. Calculate the acceleration of the 10‐kilogram block in case I.

b. On the diagrams below, draw and label all the forces acting on each block in case II

10 kg

5 kg

c. Calculate the acceleration of the 10‐kilogram block in case II.



The horizontal uniform rod shown above has length 0.60 m and mass 2.0 kg. The left end of the rod is attached to

a vertical support by a frictionless hinge that allows the rod to swing up or down. The right end of the rod is

supported by a cord that makes an angle of 30° with the rod. A spring scale of negligible mass measures the

tension in the cord. A 0.50 kg block is also attached to the right end of the rod.

(a) On the diagram below, draw and label vectors to represent all the forces acting on the rod. Show each force

vector originating at its point of application.

(b) Calculate the reading on the spring scale.

(c) Calculate the magnitude of the force exerted by the hinge on the rod



A 2‐kilogram block is attached to an ideal spring (for which k = 200 N/m) and initially at rest on a horizontal

frictionless surface, as shown in the diagram above.

In an initial experiment, a 100‐gram (0.1 kg) ball of clay is thrown at the 2‐kilogram block. The clay is moving

horizontally with speed v when it hits and sticks to the block. The spring is attached to a wall as shown. As a result, the spring compresses a maximum distance of 0.4 meters.

a. Calculate the energy stored in the spring at maximum compression.

b. Calculate the speed of the clay ball and 2‐kilogram block immediately after the clay sticks to the block but

before the spring compresses significantly.

c. Calculate the initial speed v of the clay.



A pump, submerged at the bottom of a well that is 35 m deep, is used to pump water uphill to a house that is 50 m

above the top of the well, as shown above. The density of water is 1,000 kg/m3

. Neglect the effects of friction,

turbulence, and viscosity.

(a) Residents of the house use 0.35 m3 of water per day. The day’s pumping is completed in 2 hours during

the day.

i. Calculate the minimum work required to pump the water used per day

ii. Calculate the minimum power rating of the pump.

(b) In the well, the water flows at 0.50 m/s and the pipe has a diameter of 3.0 cm. At the house the diameter of the

pipe is 1.25 cm.

i.Calculate the flow velocity at the house when a faucet in the house is open.

ii. Calculate the pressure at the well when the faucet in the house is open.



A cylinder contains 2 moles of an ideal monatomic gas that is initially at state A with a volume of 1.0 × 10 –2

m3 and

a pressure of 4.0 × 105 Pa. The gas is brought isobarically to state B. where the volume is 2.0 × 10

–2 m

3. The gas

is then brought at constant volume to state C, where its temperature is the same as at state A. The gas is then

brought isothermally back to state A.

a. Determine the pressure of the gas at state C.

b. On the axes below, state B is represented by the point B. Sketch a graph of the complete cycle. Label points A

and C to represent states A and C, respectively.

2011-12 AP Physics b Exam Information

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