Practice Test 1
PRACTICE TESTS
PHYSICS B
You must take the entire B exam as follows:
First 90 minutes
Section I – Multiple Choice
70 Questions
No calculators allowed
Percent of Total Grade – 50
2-minute interval
Second 90 minutes
Section II – Free Response
7 Questions
Any battery-operated, hand-held calculator allowed
Percent of Total Grade – 50
Each multiple-choice question has equal weight. Rulers or straight-edges may be used in
both sections. However, calculators and the formula sheet provided may be used in
Section II only, NOT in Section I.
Show all work in answering the free response questions in Section II. Each question is
worth either 10 or 15 points, and the suggested time for answering the question is about 1
minute per scoreable point. The parts within a question may not have equal weight.
Calculators may not be shared. A table of information that may be helpful is on the
following page.
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Practice Test 1
TABLE OF INFORMATION
CONSTANTS AND CONVERSION FACTORS
1 unified atomic mass unit u = 1.66x10-27 kg
= 931 MeV/c2
Proton mass
mp = 1.67x10-27 kg
Neutron mass
mn = 1.67x10-27 kg
Electron mass
me = 9.11x10-31 kg
Electron charge
e = 1.6x10-19 C
Avogadro’s number
No = 6.02x1023 mol-1
Universal gas constant
R = 8.31 J/(mol K)
Boltzmann’s constant
kB = 1.38x10-23 J/K
Speed of light
c = 3x108 m/s
Planck’s constant
h = 6.63x10-34 J s
= 4.14x10-15 eV s
hc = 1.99x10-25 J m
= 1.24x103 eV nm
Vacuum permittivity
εo = 8.85x10-12 C2/Nm2
Coulomb’s law constant K = 9.0x109 Nm2/C2
Vacuum permeability
μo = 4πx10-7 T m/A
Univ. gravitational constant G = 6.67x10-11 m3/kgs2
Acceleration due to gravity g = 9.8 m/s2
1 atmosphere pressure 1 atm = 1.0x10 5 Pa
1 electron volt
1eV = 1.6x10-19 J
1 angstrom
1 Å = 1x10 -10 m
UNITS
Name
Symbol
meter
m
kilogram
kg
second
s
ampere
A
Kelvin
K
mole
mol
hertz
Hz
newton
N
Pascal
Pa
Joule
J
watt
W
coulomb
C
volt
V
ohm
Ω
henry
H
farad
F
tesla
T
Celsius
ºC
electron-volt eV
PREFIXES
Factor
Prefix
109
106
103
10-2
10-3
10-6
10-9
10-12
giga
mega
kilo
centi
milli
micro
nano
pico
Symbol
G
M
K
c
m
μ
n
p
VALUES OF
TRIGONOMETRIC
FUNCTIONS FOR
COMMON ANGLES
θ
sin
cos
tan
θ
θ
θ
0º
0
1
0
30º ½
√3/2 √3/3
37º 3/5
4/5
¾
45º √2/2 √2/2 1
53º 4/5
3/5
4/3
60º √3/2 ½
√3
90º 1
0
∞
The following conventions are used on this examination.
I. Unless otherwise stated, the frame of reference of any problem is assumed to be
inertial.
II. The direction of any electric current is the direction of flow of positive charge
(conventional current)
III. For any isolated electric charge, the electric potential is defined as zero at an infinite
distance from the charge.
IV. The work done ON a thermodynamic system is defined as a positive quantity.
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Practice Test 1
PHYSICS B
SECTION I
Time – 90 minutes
70 Questions
Directions: Each of the questions or incomplete statements below is followed by five suggested answers or
completions. Select the one that is best in each case and then fill in the corresponding oval on the answer
sheet.
Note: To simplify calculations, you may use g = 10 m/s2 in all problems.
1. The water in a river is running due west with a
speed of 4 m/s. A boy in a boat tries to cross the
river by rowing due south at 3 m/s. The velocity
of the boat relative to the shore is
(A) 12 m/s SW
(B) 7 m/s SW
(C) 5 m/s SW
(D) 4/3 m/s SW
(E) 1 m/s SW
4. Consider the following graphs of displacement
x vs. time t and velocity v vs. time t.
In which of the graphs does the moving object
reverse its direction?
x
(A)
(D)
x
t
Questions 2 - 3.
A child on a skateboard crosses a line on the
sidewalk traveling with a speed of 2 m/s when he
begins accelerating at a constant rate of 2 m/s2.
(B)
2. What will be the child’s speed after 3 s?
(A) 8 m/s
(B) 9 m/s
(C) 12 m/s
(D) 15 m/s
(E) 18 m/s
t
v
t
(C)
(E)
x
v
t
t
3. How far past the line on the sidewalk will the
child be after 3 s?
(A) 8 m
(B) 9 m
(C) 12 m
(D) 15 m
(E) 18 m
Y
X
5. Consider the figure above which shows a ball
that is projected and follows a parabolic path.
Point Y is the highest point on the path, and air
resistance is negligible. Which of the following
best shows the direction of the acceleration of
the ball at point X?
(A)
(D)
(B)
(E)
(C)
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Practice Test 1
Questions 6 - 8 relate to a ball thrown straight
up, reaching its maximum height in 3 s.
Air resistance may be neglected.
6. The initial velocity of the ball is most nearly
(A) 10 m/s
(B) 15 m/s
(C) 30 m/s
(D) 45 m/s
(E) 60 m/s
A
B
10. Two blocks A and B are attached to a string
that passes over a pulley of negligible mass and
friction as shown. The two blocks do not have
equal mass. Which of the following statements is
true?
(A) Block A is more massive than block B.
(B) Block B is more massive than block A.
(C) Both blocks will move with the same
constant velocity.
(D) Both blocks will move with the same
constant acceleration.
(E) Block A must have a greater acceleration
than block B.
7. The magnitude of the acceleration of the ball
at the instant it reaches its maximum height is
most nearly
(A) zero
(B) 5 m/s2
(C) 10 m/s2
(D) 12 m/s2
(E) 20 m/s2
8. The maximum height of the ball is most nearly
(A) 10 m
(B) 15 m
(C) 30 m
(D) 45 m
(E) 60 m
Questions 11 – 12:
A boat in still water of mass 1000 kg is being
pulled by ropes tied to two cars, causing the boat
to move along the dashed horizontal line as
shown above. The ropes make an angle of 45 to
the horizontal. The net force acting on the boat is
500 N. (sin 45 = cos 45 = 0.70, tan 45 = 1)
9. A block of mass m is at rest on a rough
inclined plane. Which of the following diagrams
best represents the correct directions for the
normal, weight, and friction forces acting on the
block?
N
(A)
N
(D)
f
11. What is the tension in each rope?
(A) 1000 N
(A) 500 N
(B) 350 N
(C) 250 N
(D) 100 N
W
f
W
(B)
(E)
f
N
12. What is the acceleration of the boat?
(A) 5 m/s2
(B) 3.5 m/s2
(C) 2.5 m/s2
(D) 2.0 m/s2
(E) 0.5 m/s2
f
N
W
W
(C)
f
W
N
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Practice Test 1
(A) The tension in the string is greater at point
III than at point I.
(B) The tension in the string is greater at point I
than at point III.
(C) The tension at point I is equal to the tension
at point III.
(D) The tension in the string is greatest at point
II.
(E) The tension in the string is the same at
points I, II, and III.
Questions 13 – 14: A 15 kg block rests on a
surface of negligible friction and is pulled by a
string which is passed over a pulley of negligible
mass and connected to a hanging 5 kg block.
13. The net force acting on the 15 kg block is
equal to
(A) the weight of the 5 kg block.
(B) the tension in the string.
(C) the difference between the weight of the 15
kg block and the 5 kg block.
(D) the sum of the weight of the 15 kg block
and the 5 kg block.
(E) the weight of the 15 kg block.
16. If the string were to break at point II, what
would be the initial path of the ball?
(A)
(D)
(B)
(E)
(C)
20N
14. In terms of the acceleration due to gravity g,
the acceleration of the system is
g
(A)
5
g
(B)
4
g
(C)
3
(D) g
(E) 3g
B
A
17. A board of negligible mass supports a mass
weighing 20 N at a distance of 2 m from the
support at point A. How much weight must be
placed at point B which is 5 m from point A in
order for the rod to remain horizontal?
(A) 4 N
(B) 8 N
(C) 10 N
(D) 40 N
(E) 60 N
Questions 15 – 16 A ball on the end of a string
is being swung in a vertical circle as shown
below. Points I, II, and III are labeled on the
circle.
I
Questions 18 – 19.
A ball of mass m is thrown horizontally at a
vertical wall with a speed v and bounces off
elastically and horizontally.
II
18. What is the magnitude of the change in
momentum of the ball?
mv
(A) 2mv
(D)
4
(B) mv
mv
(C) zero
(E)
2
III
15. Which of the following statements is true?
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Practice Test 1
19. Which of the following force vs. time graphs
below best represents the force acting on the ball
while it is in contact with the wall?
(A)
(D)
(B)
22. The change in the kinetic energy of the block
is
(A) Fd
F
(B)
d
(C) Ft
F
(D)
t
d
(E)
t
(E)
Questions 23 - 24: A red car and a blue car have
the same mass and are moving on the highway.
The red car is traveling at 60 miles per hour and
the blue car is traveling at 30 miles per hour.
(C)
23. The ratio of the red car’s momentum to the
blue car’s momentum is
(A) 4
(B) 2
(C) 1
(D) ½
(E) ¼
Questions 20 – 22: A horizontal force F acts on a
block of mass m which is initially at rest on a
floor of negligible friction. The force acts for a
time t and moves the block a horizontal
displacement d.
24. The ratio of the red car’s kinetic energy to
the blue car’s kinetic energy is
(A) 4
(B) 2
(C) 1
(D) ½
(E) ¼
20. The acceleration of the block is
(A) Ft
(B) Fd
F
(C)
m
m
(D)
F
d
(E)
t
25. A toy railroad car of mass 3 kg moving east
collides with a 6 kg railroad car at rest, and the
two cars lock together on impact and move away
together toward the east at 2 m/s. The speed of
the first car before the collision is
(A) 2 m/s
(B) 3 m/s
(C) 4 m/s
(D) 6 m/s
(E) 9 m/s
21. The change in momentum of the block is
(A)
F
t
m
t
(C) Fd
(D) Ft
(E) mt
(B)
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Practice Test 1
4m
29. An ideal fluid passes from a narrow tube to a
large tube as shown above. Which of the
following statements is true?
(A) The mass of the fluid passing through the
tube is greater in the narrow portion than in
the wide portion.
(B) The mass of the fluid passing through the
tube is greater in the wide portion than in the
narrow portion.
(C) The volume of the fluid passing through the
tube is greater in the narrow portion than in
the wide portion
(D) The speed of the fluid is greater in the
narrow portion than in the wide portion.
(E) The pressure of the fluid is greater in the
narrow portion than in the wide portion
26. A pendulum is dropped from a height of 4 m
as shown above. The speed of the pendulum at
the lowest point in the swing is most nearly
(A) 6 m/s
(B) 7 m/s
(C) 8 m/s
(D) 9 m/s
(E) 10 m/s
27. The second law of thermodynamics (law of
entropy) explains which of the following?
(A) The heat lost by one object must be gained
by another object.
(B) Heat flows naturally from a hotter body to a
cooler body.
(C) Celsius degrees and Kelvin degrees are
equivalent.
(D) Heat can be transformed into work.
(E) The average kinetic energy of molecules is
proportional to temperature.
Questions 30 – 31
A candle burns inside the metal container shown
above. The base of the candle is insulated from
the container. Three types of heat transfer are
listed below.
28. A satellite is orbiting the Earth in an
elliptical orbit. Which of the following must be
true if the satellite’s speed is increasing?
(A) The satellite’s distance from the Earth is
increasing.
(B) The satellite’s distance from the Earth is
decreasing.
(C) The kinetic energy of the satellite is
decreasing.
(D) The momentum of the satellite is
decreasing.
(E) The gravitational force acting on the
satellite is decreasing.
I.
II.
III.
Radiation
Conduction
Convection
30. Heat can be transferred to the inside surface
of the walls of the container by which of the
above?
(A) I only
(B) I and II only
(C) I and III only
(D) II only
(E) I, II, and III only
31. If you touch the outside surface of the metal
container, your hand will become warmer
directly by which of the above choices?
(A) I only
(B) I and II only
(C) I and III only
(D) II only
(E) III only
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Practice Test 1
32. If the average speed of the molecules of an
ideal gas is doubled, the temperature of the gas
(A) remains the same.
(B) is doubled.
(C) is halved.
(D) is quadrupled.
(E) is quartered.
c
p
a
b
Questions 33 – 34 relate to a heat engine which
uses heat to do 50 J of work, and then exhausts
100 J of energy into a cold reservoir.
36. Consider the graph of pressure vs. volume
above. The gas represented by the graph begins
at state a, and follows the arrows around the
cycle, returning to state a. Which of the
following statements is true?
(A) Work is done by the gas in process ab.
(B) Work is done on the gas in process ca.
(C) No work is done on the gas during process
bc
(D) Heat is removed from the gas during process
ca.
(E) Process abc is adiabatic.
33. The heat added to the heat engine is
(A) 150 J
(B) 100 J
(C) 50 J
(D) 2 J
(E) zero
34. The efficiency of the heat engine is
(A) 25%
(B) 33%
(C) 50%
(D) 75%
(E) 100%
Questions 37 – 39 relate to the two masses M1
and M2, which have a charge Q1 and Q2,
respectively. The masses are initially separated
by a distance r.
35. An ideal gas is enclosed in a container which
has a fixed volume. If the temperature of the gas
is increased, which of the following will also
increase?
I.
The pressure against the walls of the
container.
II.
The average kinetic energy of the gas
molecules.
III.
The number of moles of gas in the
container.
(A)
(B)
(C)
(D)
(E)
V
M1
M2
r
Q1
Q2
37. If the distance between the masses is
doubled, which of the following is true?
(A) the gravitational force will increase.
(B) the electric force will increase.
(C) the gravitational force will decrease but the
electric force will remain the same.
(D) the electric force will decrease, but the
gravitational force will remain the same.
(E) both the gravitational and electric forces
will decrease.
I only
I and II only
II and III only
II only
III only
38. If both masses are doubled, but the charge on
each remains the same, which of the following is
true?
(A) the gravitational force will decrease.
(B) the electric force will increase.
(C) the gravitational force will increase but the
electric force will remain the same.
(D) the electric force will increase, but the
gravitational force will remain the same.
(E) both the gravitational and electric forces will
decrease.
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Practice Test 1
39. If the two charged masses above are placed
in space so that no other forces affect them, and
they remain at a distance r apart indefinitely,
which of the following is true?
(A) both charges are positive.
(B) Q1 is positive and Q2 is negative.
(C) Q1 is negative and Q1 is positive.
(D) Q1 = Q2
(E) M1 = M2
A1
O
41. Which graph(s) can represent the potential
energy of the spring and mass as a function of
displacement x?
(A) I only
(B) I and II only
(C) II only
(D) III only
(E) II and III only
42. Which graph(s) can represent the net force
acting on the mass as a function of displacement
x?
(A) I only
(B) I and II only
(C) II only
(D) III only
(E) II and III only
A2
Questions 40 – 42 refer to the diagram of a mass
on a spring above. The mass is oscillating about
point O on a surface of negligible friction, and
the maximum displacements on either side of
point O are labeled A1 and A2. The graphs below
can represent quantities associated with the
oscillation as a function of length x of the spring.
I.
+1
+2
43. Three charges of + 1 microcoulomb, + 2
microcoulombs, and – 2 microcoulombs are
fixed at the vertices of an equilateral triangle as
shown. The net force acting on the + 1
microcoulomb charge is directed in which
direction?
O
II.
-2
(A)
(D)
(B)
(E)
(C)
O
III.
O
40. Which graph(s) can represent the kinetic
energy of the spring and mass as a function of
displacement x?
(A) I only
(B) I and II only
(C) II only
(D) III only
(E) II and III only
369
Practice Test 1
+
+
+
+
+
R
+
44. A neutral electroscope consists of a metal
sphere, a conducting rod, and two thin gold
leaves, as shown above. If a positively charged
rod is brought near the knob of the electroscope,
which of the following statements is true?
(A) The electroscope can be charged negatively
without the positively charged rod touching
the knob and using a only grounding wire.
(B) The electroscope can be charged positively
without the positively charged rod touching
the knob and using only a grounding wire.
(C) The leaves of the electroscope are
negatively charged.
(D) The knob of the electroscope is positively
charged.
(E) The electroscope has a net positive charge.
Q
+
+
+
+
+
+
+
+
Questions 46 – 47
An isolated conducting sphere of radius R is
positively charged. Consider the following
graphs:
(A)
(D)
(B)
(E)
I
II
45. An electron is placed in the center of the
space between plates I and II above. The
subsequent motion of the electron is described
by which of the following?
(A) The electron accelerates toward plate I.
(B) The electron accelerates toward plate II.
(C) The electron moves with constant velocity
toward plate I.
(D) The electron moves with constant velocity
toward plate II.
(E) The electron remains at rest halfway
between the plates.
(C)
46. Which of the graphs above best represents
the electric field as a function of distance from
the center of the sphere?
47. Which of the graphs above best represents
the electric potential as a function of distance
from the center of the sphere?
370
Practice Test 1
rA
rB = 2rA
rC = 2rB
1
48. Three resistors A, B, and C are made from
the same material and have equal lengths but
different radii. Which of the following is the
relationship between the resistance of C
compared to the resistance of A?
(A) RC  R A
2
Questions 52 – 53 refer to the circuit shown
above. A 50-volt battery supplies 100 watts of
power to each of the two identical light bulbs.
The current passing through bulb 1 is 4 A.
RC  4 R A
(C) RC  16R A
1
(D) RC  R A
4
1
RA
(E) RC 
16
(B)
52. The voltmeter across bulb 1 will read
(A) 100 V
(B) 50 V
(C) 25 V
(D) 4 V
(E) zero
53. The current through bulb 2 is
(A) 2 A
(B) 4 A
(C) 8 A
(D) 100 A
(E) zero
2
1
4V
3
54. The resistance of each bulb is most nearly
(A) 25 
(B) 20 
(C) 6 
(D) 4 
(E) 2 
4
Questions 49 – 51 Consider the capacitors in the
circuit above. Each capacitor has a capacitance
of 2 μF.
49. The total capacitance of the circuit is
(A) 8 μF
(B) 4 μF
(C) 2/3 μF
(D) 4/3 μF
(E) 8/3 μF
50. The charge on capacitor 1 is
(A) 8 μC
(B) 4 μC
(C) 2/3 μC
(D) 4/3 μC
(E) 8/3 μC
Questions 55 – 56
A circuit consists of a fully-charged capacitor
and a resistor as shown. The switch is initially
open.
51. The charge on capacitor 2 is
(A) 8 μC
(B) 4 μC
(C) 2/3 μC
(D) 4/3 μC
(E) 8/3 μC
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Practice Test 1
55. Which of the graphs below represents the
current I in the circuit as a function of time after
the switch is closed?
(A)
(D)
(B)
(E)
I
P
59. A wire on the y – axis of a coordinate
system has a current I in the +y direction as
shown above. What is the direction of the
magnetic field due to the wire at point P?
(A) to the left
(B) to the right
(C) down into the page and perpendicular to
the page
(D) up out of the page and perpendicular to the
page
(E) toward the bottom of the page
(C)
d
I (in)
56. Which of the graphs above represents the
voltage V across the capacitor as a function of
time after the switch is closed?
I (out)
60. Two long parallel wires are separated by a
distance d as shown above. One wire carries a
steady current I into the plane of the page and
the other wire carries an equal steady current I
which is out of the page. The net magnetic field
at a point halfway between the wires points in
which of the following directions?
B
(A)

(B)

(C) 
(D) 
(E) zero
Questions 61 – 62 relate to the standing wave in
a string shown below.
57. A small particle enters a magnetic field B
which is directed out of the page as shown.
Which of the following particles would follow
the path shown above while moving through the
magnetic field?
(A) proton
(B) electron
(C) neutron
(D) x-ray
(E) photon of red light
L
58. A positive charge moves through a magnetic
field of magnitude 10-2 T with a speed of 106 m/s
when it experiences a force of 10-14 N. The
magnitude of the charge is
(A) 10-22 C
(B) 10-18 C
(C) 10-10 C
(D) 10-6 C
(E) 10-2 C
A standing wave is produced in a string when a
periodic wave is passed through the string and is
reflected off the fixed end. The wavelength of
the wave in the string shown above is 0.5 m, and
the frequency of vibration is 120 Hz.
61. The speed of the wave is
(A) 240 m/s
(B) 120 m/s
(C) 60 m/s
(D) 30 m/s
(E) 20 m/s
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Practice Test 1
62. The length of the string is
(A) 1.50 m
(B) 0.75 m
(C) 0.50 m
(D) 0.25 m
(E) 0.10 m
Energy above
ground state
E4 = 8eV
E3 = 7eV
E2 = 5eV
63. Green light is passed through two narrow
slits and forms a pattern of bright and dark lines
on a screen. The phenomena primarily
responsible for this pattern is
(A) refraction
(B) reflection
(C) polarization
(D) interference
(E) intensity
E1 = 0
Questions 67 – 68 refer to the energy level
diagram for a hypothetical atom above. The
energy for each level is given above ground
state.
67. Which of the following photon energies
could NOT be emitted from this atom after it has
been excited to the 4th energy level?
(A) 1 eV
(B) 2 eV
(C) 3 eV
(D) 4 eV
(E) 7 eV
64. Which of the graphs below represent the
energy of a photon vs. its frequency?
(A)
(D)
(B)
68. Which of the following transitions will
produce the photon with the highest frequency?
(A) n = 2 to n = 1
(B) n = 3 to n = 1
(C) n = 3 to n = 2
(D) n = 4 to n = 1
(E) n = 4 to n = 3
(E)
(C)
69. In a radioactive decay process, the parent
atom undergoes the following radioactive
decays: alpha, alpha, beta. The atomic number of
the final daughter element is how many atomic
mass units less than the parent atom?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 7
Questions 65 – 66 relate to the converging lens
and principal axis shown and the choices that
follow. The focal length f and twice the focal
length 2f are marked on one side of the lens.
1
3f
2
2f
3
4
5
70. Which of the following statements is true?
(A) The binding energy of the nucleus is equal to
the mass of the nucleus in atomic mass units.
(B) The binding energy of the nucleus is equal to
the mass of the nucleus in MeV
(C) The atomic mass of a nucleus is greater than
the sum of the masses of the individual
nucleons.
(D) The atomic mass of a nucleus is less than the
sum of the masses of the individual nucleons
(E) The mass defect of the nucleus is equal to the
number of neutrons in the nucleus.
f
(A) Position 1
(B) Position 2
(C) Position 3
(D) Position 4
(E) Position 5
65. At which position could a candle be placed
so that a virtual image would be formed?
66. At which position could a candle be placed
so that an image smaller than the candle would
be formed?
373
Practice Test 1
W  F  s  F cos  s
1
KE  mv 2
2
1
1
2
2
W  KE f  KE0  mv f  mv0
2
2
PE  mgh
NEWTONIAN MECHANICS
v  vo
t
v  v o  at
a
W g  PE g  mg h0  h f
1
(v o  v)t
2
1
x  v o t  at 2
2
2
2
v  v o  2 a x
x 
PE0  KE0  PE f  KE f
W
t
P  F  v  F cos  v
P
F  Fnet  ma
p = mv
W  mg
f s max   s FN ( static)
J = Ft = p = mv f  mv 0
f k   k FN (kinetic)
xcm 
FG 
Gm1 m2
r2
m1 x1  m2 x2
m1  m2
  F
x cg 
2r
T
v2
ac 
r
mv 2
Fc 
r
GM E
v
r
v
W1 x1  W2 x 2
W1  W2
Fs  kx
1 2
kx
2
x  A cos t
2

 2f
T
m
TS  2
k
PEelastic 
TP  2
T
374
1
f
l
g

Practice Test 1
WAVES AND OPTICS
1
f 
T

v   f
T
FLUIDS AND THERMAL PHYSICS
F
A
m

V
Pdepth  P0  gh
P
sin  
D
 v 
f n  n
 n  1,2,3,4,.. (vibrating string and open tube)
 2L 
 v 
f n  n
 n  1,3,5,... (closed tube)
 4L 
FB  W fluid  gV fluid
1 A1v1   2 A2 v 2 (mass flow rate)
A1v1  A2 v 2 (volume flow rate)
P1 

1
1
v1 2  gy1  P2  v 2 2  gy 2
2
2
r  i
1
R
2
ho
d
 o
 hi d i
f 
TK  TC  273.15
L  Lo T
1
1
1


do di
f
m
PV  nRT
di
do
PiVi  Pf V f (constant temperatur e)
c  f
c
n
v
n1 sin 1  n 2 sin  2
Vi Vf

(constant pressure)
Ti Tf
KE avg 
v rms 
1
3
2
mvrms  k B T
2
2
v avg 2

3k B T
3RT

M

sin  c 
ho
d
 o
 hi d i
U  U f  U i  Q  W
W   PV  P(V f  Vi )
e
n2
n1
1
1
1


do di
f
W
QH
m
T  TC
T
e H
 1 C
TH
TH
375
di
do
Practice Test 1
q
t
V
R
I
L
R
A
P  IV
Rs  R1  R2  R3  ...
I
m
sin  
, m  0,1,2,3,...
d
y
tan  
L
 film 
t
vacuum
n
m film
, m  0,1,2,3,..
2
(destructiv e interferen ce)
1
1
1
1



 ...
R p R1 R2 R3
1

 m   film
2
t
, m  0,1,2,3,..
2
(constructi ve interferen ce)
m
sin  
, m  0,1,2,3,..
W
C P  C1  C 2  C 3  ...
1
1
1
1



 ...
C s C1 C 2 C 3
q  CV
1
1
1 Q2
CV 2  QV 
2
2
2 C
  RC
UE 
ELECTRICITY AND MAGNETISM
F
kq1 q 2
1 q1 q 2

2
40 r 2
r
B
F kq
1 q
E
 2 
q0 r
40 r 2
FB
q 0 v sin 
mv
qB
FB  ILB sin 
r
EPE 
V AB
kq1 q 2
1 q1 q 2

r
4 0 r
B
W
EPE B  EPE A
 AB 
q0
q0
Vr  
kq
1

r
4 0
q
r
V
s
q  CV
E
C
0A
d
1
1
1 Q2
U E  CV 2  QV 
2
2
2 C
376
0 I
2r
Practice Test 1
  vBL

E  hf 
I
hc

c  f
E photon  E f  Ei
R
  BA cos 

  N
t
VS
N
 S
VP N P
E  mc 2
1u  1.6726 x10 27 kg  931.5 MeV
A
Z X
IS NP

IP NS
P  IV
GEOMETRY AND
TRIGONOMETRY
Rectangle A  bh
1
Triangle A  bh
2
2
Circle A  r and C  2r
Parallelep iped V  lwh
ATOMIC AND NUCLEAR PHYSICS
E  hf
c  f
Wo  hf o
h
Cylinder V  r 2 l and S  2rl  2r 2
4
Sphere V  r 3 and S  4r 2
3
Right Triangle

ho  ha  h 2
KEmax  hf  Wo  eVstop
   
p
h
1  cos 
mc
2
h
mv
E  pc

2
h
sin   o
h
ha
cos  
h
h
tan   o
ha
377
h
ho
θ
ha
Practice Test 1
60˚
25˚
1. (15 points)
A ball of mass 0.50 kg hangs from two strings at the angles shown. The longer string is
0.50 m long.
(a) Determine the tension in each string.
The shorter string is cut, and the longer string swings from a height h above the lowest
point of the swing.
25˚
L=0.50 m
Blade
h
(b) Determine
i. the height h from which the ball is dropped.
ii. the potential energy at the height h.
iii. the speed of the ball as it passes through its lowest point.
At the instant the ball passes through its lowest point, the string is cut by a razor blade at
a height of 1.20 m above the floor.
(c) Determine
i. the time the ball is in the air.
ii. the horizontal distance the ball travels before striking the floor.
iii. the kinetic energy of the ball just before striking the floor.
378
Practice Test 1
2. (15 points)
A cart of mass 1.0 kg can roll freely on small wheels on a curved track as shown above.
The cart starts at a height of 0.80 m and rolls toward a cart of 3.0 kg attached to an
uncompressed spring of negligible mass at the bottom of the ramp. The two blocks stick
together on impact. A graph of Force F vs. displacement x for the spring is shown at the
left.
(a) Find the speed of the 1.0 kg cart at the bottom of the ramp.
(b) Determine the speed of the two blocks immediately after the collision.
(c) Using the graph at the left, determine the spring constant k.
(d) Determine the maximum compression of the spring after the collision.
(e) If the 3.0 kg block were removed and replaced with a plate of negligible mass, would
the maximum compression of the spring increase, decrease, or remain the same as in
part (d)? Justify your answer.
379
Practice Test 1
+
+
+
3. (15 points)
A metal ball is fixed to a wall and charged to Q = +4 nC. An uncharged metal ball of
mass m = 0.10 kg is hung by an insulating thread at a horizontal distance of d = 0.02 m
from center of the fixed ball.
(a) Assuming the hanging ball remains at a distance of 0.02 cm from the fixed ball, find
i. the magnitude and direction of the electric field at the location of the hanging ball.
ii. the electric potential at the location of the hanging ball.
There is now a charge of q = +4 nC placed on the hanging ball.
(b) If the force between the two charged balls is 1.60 x 10-4 N, determine the new
horizontal separation distance x between the balls as a result of both of them having a
charge. Neglect the small change in height of the hanging ball.
(c) Determine the work required to separate the charge the additional distance Δx when
the charge is placed on the hanging ball.
The hanging ball is discharged, and it swings like a pendulum toward the fixed ball,
touches it, and the balls are again separated to an equilibrium position.
(d) Would the new equilibrium separation distance of the two balls be greater than, less
than, or equal to the equilibrium separation distance determined in part (b)? Explain your
answer.
380
Practice Test 1
cm
5
20
35
50
65
80
95
100
4. (10 points)
A light bulb on a stand can be mounted on a 1.0-m long optical bench as shown above. A
convex lens and a concave mirror, each of focal length 15 cm, and a screen can also be
mounted on the bench. The convex lens is placed at the 50-cm mark of the bench, and the
light bulb is placed at the 5-cm mark.
(a) As the bulb is slowly moved toward the lens, describe the image formed by the lens.
Be sure to discuss the characteristics and changes in the image in terms of size,
whether the image is real or virtual, and its orientation. Note any significant object
distances as the candle moves toward the lens.
(b) On the diagram below, draw a sketch of the ray diagram for the bulb and lens when
the bulb is placed 15-cm from the lens. Briefly describe the image formed by the lens.
cm
5
20
35
65
80
95
50
The convex lens is removed, and the concave mirror is now placed at the 50-cm mark of
the bench, and the light bulb is placed at the 5-cm mark.
(c) As the bulb is slowly moved toward the mirror, describe the image formed by the
mirror. Be sure to discuss the characteristics and changes in the image in terms of size,
whether the image is real or virtual, and its orientation. Note any significant object
distances as the candle moves toward the mirror.
(d) The bulb is placed at an object distance which produces a real image on a screen. An
opaque card is then placed over the top half of the mirror. Describe the changes in the
real image, if any.
381
Practice Test 1
5. (10 points)
A ball of mass 0.01 kg and radius 0.01 m is placed on the surface of a liquid with a
density ρL = 1200 kg/m3. Determine
(a) the density of the ball.
(b) the buoyant force acting on the ball.
(c) the acceleration of the ball as it descends through the liquid.
382
Practice Test 1
P
B
a
b
I
6. (10 points)
A square loop of wire carries a current I = 0.20 A as it sits at rest in a uniform magnetic
field B = 0.40 T directed into the page. The square is 0.15 m on each side.
(a) Determine the magnitude and direction of the force acting on the side of the wire
labeled ab.
(b) Determine the magnitude and direction of the magnetic field Bw due to the current in
the wire at point P, which is a perpendicular distance d = 0.05 m away from the wire.
(c) Will this loop of wire tend to expand, contract, or remain the same size in this
magnetic field? Explain.
P
v
B
I
(d) An electron traveling at a speed of 3.0 x 104 m/s passes through the magnetic field
through point P as shown above.
i. Find the magnitude and direction of the magnetic force acting on the electron as it
passes point P.
ii. Draw arrows indicating the electric field that would need to be applied in order to
keep the electron moving in a straight line.
383
Practice Test 1
7. (15 points)
The electron energy levels for a mercury atom are shown below.
E=0
E4 = - 4.95
eV
E3 = -5.52 eV
E2 = -5.74 eV
E1 = - 10.38 eV
An electron in the ground state absorbs a photon which causes the electron to be raised to
the second energy level.
(a) Determine the following for the absorbed photon.
i. wavelength
ii. frequency
(b) State whether or not the absorbed photon is in the visible range. Explain your answer.
The electron absorbs a second photon of energy 10.00 eV while it is in the second energy
level of the atom.
(c) Find the following for the electron after it absorbs the 10.00 eV photon.
i. kinetic energy
ii. speed
iii. de Broglie wavelength
384
Practice Test 1
ANSWERS TO PRACTICE TEST 1
1. C
2. A
3. D
4. C
5. B
6. C
7. C
8. D
9. A
10. D
11. B
12. E
13. B
14. B
15. A
16. D
17. B
18. A
19. A
20. C
21. D
22. A
23. B
24. A
25. D
26. D
27. B
28. B
29. D
30. C
31. D
32. D
33. A
34. B
35. B
36. D
37. E
38. C
39. A
40. C
41. A
42. D
43. C
44. A
45. A
46. E
47. C
48. E
49. E
50. A
51. E
52. C
53. B
54. C
55. A
56. A
57. A
58. B
59. C
60. D
Free Response Questions Solutions for Practice Test 1
1. (a) 5 points
Drawing a free-body diagram for the ball:
FT1
FT2
60º
25º
W
F
x
0
FT 1x  FT 2 x
FT 1 cos 60  FT 2 cos 25
F
y
0
FT 1 y  FT 2 y  W
FT 1 sin 60  FT 2 sin 25  mg
385
61. C
62. B
63. D
64. D
65. E
66. A
67. D
68. A
69. B
70. D
Practice Test 1
Solving these two equations simultaneously for the tension forces gives
FT1 = 4.5 N and FT2 = 2.5 N
(b) 5 points
i. h  L  L sin 25  0.50m  0.50m sin 25  0.29m
ii. U  mgh  0.50kg 10m / s 2 0.29m  1.44 J
iii. Conservation of energy
U top  K bottom

mgh 
1 2
mv
2



v  2 gh  2 10m / s 2 0.29m   2.4 m / s
(c) 5 points
2y
21.2m 

 0.49 s
i. t 
g
10m / s 2
ii. x  vt  2.4 m / s 0.49s   1.18 m
iii.
1
K floor  U top  K top  mgy  mv 2
2
1
2
 0.50kg 10m / s 2 1.2m   0.50kg 2.4 m / s   7.44 J
2
2. (a) 3 points
Conservation of energy
1
mgh  mv 2
2


v  2 gh  2 10m / s 2 0.80m   4 m / s
(b) 2 points
Conservation of momentum
mv  m  M v 
1.0kg 4m / s   1.0 m / s
v 
4.0kg
(c) 3 points
The spring constant k is the slope of the F vs. x graph: k = 5 N/m
(d) 4 points
Conservation of energy
386
Practice Test 1
K   U spring
1
m  M v 2  1 kx2
2
2
x
m  M v 2
4kg 1m / s 2

 0.89m
k
5N /m
(e) 3 points
If the 3.0 kg mass were removed and replaced with a plate of negligible mass, then the
potential energy of the 1.0 kg block at maximum height would equal the potential energy
in the spring at maximum compression:
1
mgh  kx 2
2
2mgh
21kg 0.80m 
x

 0.57 m
k
5N /m
The compression of the spring would be smaller.
3. (a) 5 points

Nm 2 
 9.0 x10 9
4 x10 9 C 
2 
C 
KQ
 9 x10 4 N / C
i. E  2  
2
d
0.02m 

Nm2 
 9.0 x109 2  4 x10 9 C
C 
KQ 
ii. V 

 1.8 x103V
0.02m
d


(b) 4 points
KQq
F 2
x
KQq
x

F
(c) 4 points

Nm 2 
 9.0 x10 9
 4 x10 9 C 4 x10 9 C
2 
C 

 0.03m
1.60 x10  4 N






Nm 2 
Nm 2 
  9.0 x10 9 2 4 x10 9 C   9.0 x10 9 2 4 x10 9 C  




C 
C 
 KQ KQ 


9
W  qV  q 


  4 x10 C 

0.02m
0.03m
d2 
 d1






6
W  2.4 x10 J
(d) 2 points
Less than the original separation distance, since each charge would be +2 nC.
387
Practice Test 1
4. (a) 3 points
The bulb begins at an object distance of 3 focal lengths, and the image begins as real,
inverted, and smaller than the object. When the bulb is at 2f, the image is real, inverted,
and the same size as the object. As the bulb moves toward f it becomes larger than the
object and is real and inverted. The image disappears, and there is no image when the
object distance is equal to the focal length. As the bulb moves inside the focal length, the
image becomes upright, larger than the object, and virtual.
(b) 3 points
The bulb is placed at do = 15 cm = f :
cm
5
20
35
65
80
95
The rays emerge from the lens parallel, and thus no image is formed.
(c) 2 points
As the bulb is moved toward the concave mirror, the images formed are exactly the same
at the same locations as the convex lens in part (a).
(d) 2 points
A real image will still be formed as it would be if half the mirror were not blocked, but
the image would be dimmer.
5. (a) 3 points
0.01 kg
m
m
b  

 2387.3 kg / m 3
4
4
V
r 3
 0.01m3
3
3
(b) 3 points
Fbuoy   liquid gVdisplaced fluid  1200 kg / m3 10m / s 2 4.19 x10 6 m3  0.05 N



(c) 4 points
W  Fbuoy 0.10 N  0.05 N
F
a  net 

 5.0 m / s 2 downward.
m
m
0.01 kg
388

Practice Test 1
6. (a) 3 points
F  ILB  0.20 A0.15m0.40T   1.2 x10 2 N directed down to the bottom of the page
by the right-hand rule.
(b) 2 points
 I
4x10 7 Tm / A 0.20 A
B o 
 8x10 7 T
2d
2 0.05m


(c) 2 points
By the right-hand rule, the forces are inward on all sides of the loop, so the loop will tend
to contract.
(d) 3 points
i. The electron experiences a force from the magnetic field of 0.40 T and the magnetic
field due to the current in the wire, which is negligible.
F  evB  1.6 x10 19 C 3.0 x10 4 0.40T   1.9 x10 15 N
ii. The magnetic force on the electron is downward by the left-hand rule, so the electric
force to keep the electron moving in a straight line would point upward. Since the electric
field points in the direction a positive charge would experience a force, the electric field
should point downward in order to apply an upward force to the electron.



7. (a) 6 points
i.
E  E 2  E1  5.74eV   10.38eV   4.64eV
hc 1240 eV nm


 267.24nm  2.67 x10 7 m
E
4.64 eV
3.00 x10 8 m / s
 1.12 x1015 Hz
ii. f  
7

2.67 x10 m
c
(b) 2 points
This photon is not in the visible range of wavelengths, which is 400 nm to 700 nm.
(c) 7 points
i. K  10.00eV  5.74eV  4.26 eV  6.82 x10 19 J
ii. v 
2K

m


2 6.82 x10 19 J
 1.22 x10 6 m / s
9.11x10 31 kg
6.62 x10 34 J s
h

 5.94 x10 10 m
31
6
mv 9.11x10 kg 1.22 x10 m / s
This wavelength is in the x-ray range.
iii.  



389
Practice Test 1
Practice Test 1 Scoring Worksheet – AP Physics B
Section I: Multiple Choice
( ___________ ) – (1/4 x _________ ) x 1.2857 = __________= ___________
Number correct
Number
MultipleWeighted
(out of 70)
wrong
Choice
Section I
Score
Score
Section II: Free Response
Question 1
____________ x 1.0000 = ____________
(out of 15)
Question 2
____________ x 1.0000 = ____________
(out of 15)
Question 3
____________ x 1.0000 = ____________
(out of 15)
Question 4
____________ x 1.0000 = ____________
(out of 10)
Question 5
____________ x 1.0000 = ____________
(out of 10)
Question 6
____________ x 1.0000 = ____________
(out of 15)
Question 7
____________ x 1.0000 = ____________
(out of 10)
Sum = ____________
Weighted
Section II Score
Composite Score
__________ + ___________ = _______________
Weighted
Weighted
Composite Score
Section I
Section II
Score
Score
Possible scoring range:
106 – 180 = 5; 83 – 105 = 4; 54 – 82 = 3; 40 – 53 = 2; 0 – 39 = 1
390