Princeton WB phys

MCAT SciENCE WoRKBOOK
TABLE OF CONTENTS

PERIODIC TABLE OF THE ELEMENTS .......................................................

4

BIOLOGY
QuESTIONS AND PAssAGEs .................•....................•..•..••....•.•.•.....•
SOLUTIONS..............................................................................

5

139

PHYSICS
QuESTIONS AND pAS SAGES ......••....•...............•..•......•..•..•.......•....

223

SoLUTIONS ..............................................................................

353

GENERAL CHEMISTRY
QuESTIONS AND PASSAGES .........................................................

431

SoLUTIONS .....•...•..•.•.....•.......•..•........•......•........•...•....•.•..........

569

ORGANIC CHEMISTRY
QuESTIONS AND PASSAGES .........................................................

639

SoLUTIONS ..............................................................................

731

MCAT SciENCE

WoRKBOOK

2


PASSAGE GUIDE
BIOLOGY
Chapter
Number

1
2
3
4

5
6

7

8
9

10

MCAT Biological Sciences Review
MCAT Biology Chapter Title

Corresponding MCAT Science Workbook
Passage Numbers

Molecular Biology
Microbiology
Generalized Eukaryotic Cells
Genetics and Evolution
Nervous and Endocrine Systems
Circulatory, Lymphatic, and Immune Systems
Digestive and Excretory Systems
Muscle and Skeletal Systems
Respiratory and Skin Systems
Reproductive Systems and Development

5, 12, 16, 18, 23,25, 27-32,55
13, 17, 19, 20, 21, 26, 34,35
1,2, 4,6, 7,10,24
33,56,62, 63,64, 65,66
8,9, 15,22,38,39,58,59,67-74
40,42,43,44,45, 46,47,61, 75

14,57, 76, 77,78
41,48,49,50,51,60, 79
52,53,54, 80
3, 11, 36,37,81, 82,83

MCAT Physical Sciences Review
MCAT Physics Chapter Title

Correspond;ng MCAT Science Workbook
Passage Numbers

Kinematics
Mechanics I
Mechanics II
Mechanics Ill
Fluids and Elasticity of Solids
Electrostatics
Electricity and Magnetism
Oscillations and Waves
Sound
Light and Geometrical Optics

11 2

PHYSICS
Chapter
Number
1
2
3

4
5
6
7
8
9

10

4

3-9, 15-18
1Q-13, 19-24
31,32
25-30,33-39
14,40,45,46,48-55
42,43,56,57
41,44,47,58-60

GENERAL CHEMISTRY
Chapter
Number
1

2
3
4
5
6
7

8
9
10

MCAT Physical Sciences Review
MCAT General Chemistry Chapter Title

Corresponding MCAT Sqience Workbook
Passage Numbers

Atomic Structure
Periodic Trends and Bonding
Phases
Gases
Solutions
Kinetics
Equilibrium
Acids and Bases
Thermodynamics
Redox and Electrochemistry

1-4,6,9-18,70
5, 7,19-28,43,72
35,57,59, 60,62, 63,65,66
40,61,64, 67
31,41, 42, 45,68, 69
33,44, 71
29,37,39,46
30,32,34,36,38,47-55

58, 73-78
8,56, 79-91

ORGANIC CHEMISTRY
Chapter
Number

1
2
3

4
5
6

MCAT Biological Sciences Review
MCAT Organic Chemistry Chapter Title

Corresponding MCAT Science Workboo}f
Passage Numbers

Structure and Bonding
Substitution and Elimination Reactions
Electrophilic Addition Reactions
Nucleophilic Addition/Cycloaddition Reactions
Lab Techniques and Spectroscopy
Biologically-Important Organic Chemistry

1,2, 3
4,5, 6, 7,8,9, 10

11, 12, 13, 14, 15, 16, 17, 18
19,20,21,22,23,24,25,26,27-30
31,32,33,34,35
36,37,38, 39,40,41,42,43

3

INTRODUCTION


PERIODIC TABLE OF THE ELEMENTS

r--

r--

2
He
4.0

1

H
1.0
3

4

8

Be

B

c

7

Ll

N

0

6.9

9.0

10.8

16.0

12

13

12.0
14

14.0

11

16

Na

Mg

AI

Sl

23.0

24.3

27.0

28.1

15
p
31.0

.5

19

20

21

22

24

26

27

28

29

Ca

Sc:

Ti

v

2S

K

Cr

Mo

Fe

Co

Nl

Cu

39.1
37

40.1

4.5.0

47.9

.50.9

.55.8

40

41

43

44

58.9
4.5

58.7
46

Kb

Sr

Zr

Nb

Mo

Tc:

Ku

Rh

85 •.5

87.6

39
y
88.9

.52.0
42

54.9

38

91.2

92.9

95.9

(98)

101.1

5.5

.56

57

72

73

74

75

76

Cs
132.9

23

Ba

La*

ur

Ta

w

Ke

Os

137.3

138.9

178.5

180.9
10.5

Db
(2621

183.9

186.2
107
Bb
(262)

190.2

87

88

89

104

Fr

Ka

Act

Kf

(223)

226.0

227.0

(261)

•
t

SCIENCE WORKBOOK

s,

_(263)

108
Hs
(265)

Ar

32.1

3.5 . .5

39.9

32

33

34

3.5

36

As

Se

Br

Kr

63.5

69.7

72.6

74.9

79.0

79.9

83.8

47

48

49

50

51

Pd

Ag

52

Cd

lo

So

Sb

Te

102.9

106.4

107.9

112.4

114.8

118.7

121.8

127.6

53
I
126.9

54
Xe
131.3

77
lr
192.2

78

79

80

81

82

83
81
209.0

85

Po

At

(209)

(210)

86
Rn
(222)

175.0
103

Pt

Au

Hg

Tl

Pb

195.1

197.0

200.6

204.4

207.2

84

109

Mt
(267)

61

62

63

64

Sm

Eu

Gd

140.1

144.2

(145)

150.4

152.0

157.3

65
Tb
158.9

90

91·

92

93

94

95

96

97

Tb

Pa

Np

Pu

Am

Cm

Bk

(243)

(241}

(247)

(237)

Cl

Ge

Pm

238.0

s

31

60

(231)

17

10
Ne
20.2
18

Ga

Nd

u

9
F

19.0

30
Zn
65.4

59
Pr
140:9

58

Ce

232.0

MCAT

106

6

(244)

4

66

67

68

69

Dy
162.5
98

Ho

Er

Tm

164.9

167.3

168.9

70
Yb
173.0

cr

99

100

101

Es

102

Fm

Md

No

Lr

(251)

(252)

(257)

(258)

(259)

(260)

7l

Lu

MCAT PHYSICS
PRACTICE QUESTIONS AND pASS AGES

I
i
i

!'
I
I
!

I
223

~.


3. What is the magnitude ofthex-component of Vector P?

Passage 1 (Questions 1-7)

A.

A vector is a quantity that incorporates both magnitude
and direction. A vector can be pictured as an arrow whose
orientation indicates direction and whose length indicates
magnitude. A scalar quantity possesses magnitude only.

6m

B.

10m
C. 17m
D. 20m

Vectors can be added (or subtracted) using the "tip-totail" method and resolved into components using
trigonometry.

4. What is the magnitude of they-component of Vector P?
A.

Figure 1 shows three vectors plotted on a pair of x-y
coordinate axes. Vectors P and Reach have a magnitude of
20 m, and Q has a magnitude of 40 m.

6m

B. 10m
C. 17m
D. 20m

y

5. Which of the following vectors best illustrates the
direction of the vector -R?

A./

c.~

B.~

D./

R

6. Which of the following vectors best illustrates the
direction of the vector P + R?

A.

Figure 1

)

B. /

1. What are the horizontal and vertical components,
respectively, of Vector P?
A.
B.
C.
D.

20
20
20

20

MCAT

sin 30° and 20 cos 30°
sin 30° and 20 tan 30°
cos 30° and 20 tan 30°
cos 30° and 20 sin 30°

A.

B.

Velocity
Displacement
Speed
Acceleration

SciENCE WoRKBOOK

D.


7. Which of the following vectors best illustrates the
direction of the vector Q - P?

2. Which one of the following is NOT a vector quantity?
A.
B.

C.
D.

c.~

224

\
I

c.~

D.~


Passage 2 (Questions 1-7)

4. What is the car's average speed between times t = 10
sec and t = 15 sec?

A car travels in a straight line for 30 seconds. The graph
below represents the car's velocity as a function of time.

A. 5.0 m/sec
B. 7.5 m/sec
C. 10.0 m/sec
D. 12.5 m/sec

v (m/sec)

5. At time t = 25 sec, the car:
1

A. slowed down and changed direction.
B. slowed down but did not change direction.
C. sped up and changed direction.
D. sped up but did not change direction.

5,-t-----(
t

0

5

10

15

20

(sec)

25

6. Which of the graphs best represents the car's
acceleration, a, between times t = 0 and t = 30 sec?

Figure 1

A.
Since acceleration is defined as change in velocity per
interval of time, acceleration at any time equals the slope of
the velocity graph at that time. Similarly, since distance
traveled is directly proportional to time and speed, the distance
the car has traveled at any time equals the area under the
velocity graph up to that time. For the first 10 seconds the car
traveled at a fixed speed. The slope of the graph in that
section is, as expected, zero. Also, the area under the graph
between t = 0 and t = 10 sec is 50 m, the expected value.

c.

t

a

B.

t

a

D.

t

t

a

a

1. How far does the car travel between times t = 0 and
t

= 10 sec?

A.

B.
C.
D.

t

2m
5m
25m
50 m

---IIJoo-

7. Which one of the following graphs best represents the
distance traveled by the car as a function of time?

2. What is the car's acceleration between times t = l 0 sec
and t = 15 sec?
A.
B.

C.
D.

0.67 m/sec 2
1.0 m/sec 2
1.5 m/sec 2
25.0 m/sec 2
t

3. How far does the car travel between times
t = 15 sec?

t

=l 0 sec and

B.

A. 12.5 m
B. 25.0m
C. 37.5 m
D. 50.0m

J~
t

225

t

---IIJoo-

---IIJoo-

D.

---IIJoo-

!lL_
t

---IIJoo-

PHYSICS


6. A body is undergoing uniformly accelerated motion
over a period of time. Which of the following is true?

Questions 1 through 45 are NOT based on a
descriptive passage.

A. The final velocity of the object is greater than its
average velocity.
B. The final velocity of the object is equal to its
average velocity.
C. The final velocity of the object is less than its
average velocity.
D. The relationship between the final velocity of the

object and its average velocity cannot be
determined from the information given.

1. A racehorse makes one lap around a 500-meter track in
a time of25 seconds. What was the racehorse's average
speed?

A. 0 m/s
B. 5 m/s
C. 10 m/s
D. 20 m/s

7. A 2~kg rock is thrown vertically upward at a speed of
3.2 m/s from the surface of the moon. If it returns to its
starting point in 4 seconds, what is the acceleration due
to gravity on the moon?

2. A racehorse makes one lap around a 500-meter track in
a time of 25 seconds. What was the racehorse's average
velocity?

A.

A. 0 m/s
B. 5 m/s
C. 10 m/s
D. 20 m/s

B.

c.
D.

as velocity?

5m
5 m to the north
5 m/s
5 mls to the north

m/s 2
m/s 2
m/s 2
m/s 2

A. increases, while the horizontal component remains
constant.
B. decreases, while the horizontal component remains
constant.
c. increases, while the horizontal component
decreases.
D. decreases, while the horizontal component
increases.

4. An object which is accelerating must be:
A.
B.
C.
D.

0.8
1.6
3.2
6.4

8. In a series of experimental trials, a projectile is launched
with a fixed speed, but with various angles of elevation.
As the angle of elevation is increased from 0 to 90°, the
vertical component of the initial velocity:

3. Which of the following expressions could be interpreted

A.
B.
C.
D.

changing its direction.
traveling in a straight line.
increasing its speed.
changing its velocity.

9. The horizontal component of the initial velocity of a
projectile is directly proportional to the:
5. It is well known that the flash and the sound of thunder
produced by a lightning bolt are not observed
simultaneously. This is due to the fact that light waves
travel so much faster than sound waves. Light travels
so quickly that one can assume that lightning bolts
occur at the same time one sees them. Given that sound

propagates through air at a speed of 340 m/s, how far
away is a lightning bolt if the delay between hearing
and seeing it is 5 sec?

A.
B.
C.
D.

A.
68 m
B. 1700 m
C. 4250 m
D. 6120 m

MCAT

SciENCE WoRKBOOK

;
·<

226

angle of elevation.
sine of the angle of elevation.
cosine of the angle of elevation.
tangent of the angle of elevation.

10. A projectile is launched horizontally from a raised
platform. If air resistance is ignored, then as the
projectile falls to the earth, the magnitude ofthe vertical
component of the velocity of the projectile:

14. A garment hangs from a clothes line as shown below.
The tension in the clothes line is 10 N on the right side
of the garment and 10 N on the left side of the garment.
Find the mass of the garment.

A. increases, while the horizontal component remains
constant.

B. decreases, while the horizontal component remains
constant.
increases, while the horizontal component
decreases.
D. decreases, while the horizontal component
increases.

c.

11. Two projectiles are launched from the same point.
Projectile A has the greater horizontal velocity, while
Projectile B has the greater vertical velocity. Which
projectile will travel the greater horizontal distance?
A. Projectile A, because distance traveled is
determined by horizontal velocity.
B. Projectile B, because it will be in the air for more
time.

C. Both projectiles will travel the same distance.
D. Cannot be predicted from the information given

A.
B.

c.
D.

12. Where in its path does a projectile in free fall near the
surface of the earth experience the greatest acceleration?
A.
B.
C.
D.

0.5 kg
1 kg
2 kg
10 kg

15. A can of paint with a mass of 10 kg hangs from a rope.
If the can is to be pulled up to a rooftop with a constant
velocity of 0.5 m/s, what must the tension in the rope
be?

While it is ascending
While it is descending
At its greatest height
Acceleration is the same at all points in the path.

13. Two bodies of different masses are subjected to identical
forces. Compared to the body with sma'ller mass, the
body with greater mass will experience:

A.
B.

ON
SON

C.
D.

100 N
200 N

16. Which of the following best describes the direction in
which the force 9f kinetic friction acts relative to the
interface between the interacting bodies?

A. less acceleration, because the product of mass and
acceleration will be smaller.
B. greater acceleration, because the product of mass
and acceleration will be greater.
C. less acceleration, because the ratio of force to
mass will be smaller.
D. greater acceleration, because the ratio of force to
mass will be larger.

A. Perpendicular to the in-'&.rface and away from the
more massive body
B. Perpendicular to the interface and toward the more
massive body
C. Parallel to }he interface and opposite the direction
of the relative velocity
D. Parallel to the interface and in the same direction
as the relative velocity

227

PHYSICS


20. A box is resting on an inclined plane as shown below.
What is the magnitude of F?

17. Which of the following best describes the motion of a
body along a surface where friction must be taken into
account?
A. More force is required to start the object in motion
than to keep it in motion at constant velocity.
B. Once the object is set in motion. no force is required
to keep it in motion at constant velocity.
C. Less force is required to start the object in motion
than to keep it in motion at constant velocity.
D. The same force is required to start the object in
motion as to keep it in motion at constant velocity.

4.3

5.0
8.7
D. 11.5
A.
B.
C.

18. A 100-N trash can is pulled across the sidewalk at
constant speed by a force of 25 N as shown below. How
large is the force of friction impeding the motion of the
trash can?

21. A 50-kg crate slides down a ramp as shown below.
·Assuming that the ramp is frictionless, find the
acceleration of the crate.

25N

----)>

A.

N
N
N
N

0N

B. 25 N

C. 75 N
D. 125 N

A.

5.0 m/s 2
8.7 m/s 2
c. 10.0 m/s 2
D. 11.3 m/s 2

19. A 1-kg mass is hung at the end of a vertical spring with
a spring constant of 20 N/m. When the mass comes to

B.

rest, by how many meters will the spring have stretched?

A.
B.

c.

D.

0.05
0.5

2

22. The acceleration experienced by a block moving down

a frictionless plane inclined at a 30° angle:

20

A.
B.
C.
D.

MCAT SCIENCE

WORKBOOK

228

decreases as the block moves down the plane.
is constant.
increases as the block moves down the plane.
depends on the height of the plane.


23. A block is moving down the slope of a frictionless
inclined plane. The force parallel to the surface of the
plane experienced by the block is:
A.
B.
C.
D.

27. A block is being pulled by a rope up the surface of an

inclined plane at constant velocity. Which of the
following is true of the tension in the rope r, the force
due to friction f, and the component of the block's
weight parallel to the plane w P?

less than the weight of the block.
equal to the weight of the block.
greater than the weight of the block.
unrelated to the weight of the block.

A. w p = T+f
B. T= wP + f
C. f T + wP
D. T + f+ wP = 0

24. A block is moving down the slope of an inclined plane
at constant velocity. The normal force exerted by the
plane on the block:
A.
B.
C.
D.

28. An object is moving in a circle at constant speed. Its
acceleration vector must be directed:

increases with increasing velocity.
decreases with increasing velocity.
is independent of velocity.
depends on the coefficient of kinetic friction

between the plane and block.

A. tangent to the circle and opposite the direction of
motion.
B. tangent to the circle and in the direction of motion.
C. radially and toward the center of the circle.
D. radially and away from the center of the circle.

25. A block is sitting motionless on the surface of an
inclined plane as the angle of elevation is gradually
increased. The normal force exerted by the plane on the
block:
A.
B.
C.
D.

29. An object is traveling in a circular path. If the velocity
of the object is doubled without changing the path, the
force required to maintain the object's motion is:

A.

increases with increasing angle of elevation.
decreases with increasing angle of elevation.
is independent of angle of elevation.
depends on the coefficient of 1)tatic friction between
the plane and block.

B.

c.

D.

halved.
unchanged.
doubled.
quadrupled.

30. How far from the heavier end must the fulcrum of a
massless 5-m seesaw be if an 800-N man on one side is
to balance his 200-N daughter at the other end?

26. A block is sliding down the surface of an inclined plane
while the angle of elevation is gradually decreased.
Which of the following is true about the results of this
process?
A. The force due to friction decreases, and the weight
of the block remains constant.
B. The force due to friction decreases, and the weight
of the block decreases.
C. The force due to friction increases. and the weight
of the block decreases.
D •. The force due to friction increases, and the weight
of the block remains constant.

A.

0.5 m

B.
C.

1 m
2 m
4 m

D.

31. An object is traveling in a circular path. If the radius of
the circular path is doubled_,rithout changing the speed
of the object. the force required to maintain the object's
motion is:

A.
B.

c.

D.

229

halved.
unchanged.
doubled.
quadrupled.
(

PHYSICS


36. Assume that a massless bar 5 meters in length is
suspended from a rope and that the rope is attached to
the bar at a distance x from the bar's left end. If a 20-kg
mass hangs from the right side of a bar and a 5-kg mass
hangs from the left side of the bar, what value of x will
bring about equilibrium?

32. Water moves past a water wheel, causing it to turn. The
force of the water is 200 N, and the radius of the wheel
is 10 rn. Calculate the torque around the center of the
wheel.

A.
B.
C.
D.

20
200
2000
20,000

N-m
N-m
N-rn
N-rn

A. 3.0 m
B. 3.5 m

c.

4.0m

D. 4.5
33. A massless meter stick is fixed at Point C, which is 25
em from its left-hand end. The rod is free to rotate
about Point C. If a downward force of 60 N is applied
at Point A, what is the minimum force that must be
applied at Point B to keep the rod from rotating?

37. What horizontal force must be applied to an object with
a weight of 98 N in order to give it a horizontal
acceleration of 10 m/s 2 ? (Neglect the forces of friction.)
A.
9.8 N
B. 100.0 N
C. 490.0 N
D. 980.0 N

•
A
I
1

B

C

I 4

•

m

I
t

38. A man with a mass of 100 kg sits on a seesaw 5 m from
the center. l;'wo children, each with a mass of20 kg, are
seated on the other side of the seesaw. One child sits
10 m from the center. How far from the center should
the other child sit to balance the seesaw?

25cm '
lOOcm

A. 15 N, upward
B. 15 N, downward
C. 20 N, upward

A.
5m
B. 10m
C. 15m
D. 20m

D. 20 N, downward

34. A 50-g stone is tied to the end of a string and whirled in
a horizontal circle of radius 2m at 20 m/s. Ignoring the
force of gravity, determine the tension in the string.
A.
B.

5
10
C. 100
D. 500

39. A pulley is suspended from a cable that is attached to
the beam of a building 10 m above the ground. A rope
is slung over the pulley, and one end is attached to a
bucket of cement weighing 1000 N. The free end of the
rope is pulled, and the cement is raised above the
ground. The free end is then tied to a fixed point. What
is the approximate downward force exerted by the cable
attaching the pulley to the beam? (Assume that the
pulley and rope are massless.)

N
N
N
N

35. A 25-kg block is pushed in a straight line across a
horizontal surface. If a constant force of 49 N must be

A.
B.
C.
D.

applied to the block in order to maintain a constant
velocity of 2 m/s, what is the coefficient of kinetic
friction between the block and the surface?

500
667
1000
2000

N
N
N
N

A. 0.1
B. 0.2

c.

40. A block with a mass of 20 kg hangs from a spring with
a spring constant at 1000 N/m. How far will the spring
stretch from its equilibrium position?

0.4

D. 0.5

A.

2cm
20 em
50 em
D. 500 em

B.
C.

MCAT

SCIENCE WORKBOOK

230


41. A uniform meter stick weighing 20 N has a 50-N weight
on its left end and a 30-N weight on its right end. The
bar is hung from a rope. What is the tension in the rope
and how far from the left end of the bar should the rope
be attached so that the stick remains level?
A.
B.
C.
D.

80 N placed 37.5 em from the left end of the bar

80 N placed 40.0 em from the left end of the bar
100 N placed 37.5 em from the left end of the bar
100 N placed 40.0 em from the left end of the bar

42. An object with a mass of 50 kg moves across a level
surface with a constant speed of 15 m/s. If the coefficient
of kinetic friction is 0.7, which of the following must be
true about the forces acting on the object?
A. The force exerted on the object by kinetic friction
is negligible.
B. There must be some other horizontal force acting
on the object.
C. No forces are doing work on the object.
D. There are no vertical forces acting on the object.

43. A 2000-kg airplane flying at 50 m/s is slowed by
turbulence to 40 m/s over a distance of 150 m. How
much work was done on the plane by the turbulent air?

A.
B.

-10 kJ
-100 kJ
c. -900 kJ
D. -1800 kJ

44. A hockey puck is tied to a string· and whirled in a
circular path on a horizontal table, with the other end of
the string threaded through a hole in the center of the

table. If the puck has mass m and speed v, and the
tension in the string is T, which of the following
expressions gives the radius of the circular path?
A. mv/T
B. mv 2/T
c. (mv/D 112
D. (mv2fn112

45. Two springs are attached together so that they pull each
other in opposite directions. The first spring is pulled a
distance L from its rest position. Its spring constant is
known to be K. If the second spring is pulled a distance
L2 from its rest position by the first spring, what is the
spring constant of the second spring?

A. KL

B. KIL
C. KIL 2
D. J(2
231

PHYSICS


Passage 3 (Questions 1-6)

2. Which of the following statements applies to a system
in which two objects undergo an ideal elastic collision?

For an ideal elastic collision between two objects, the
sum of their linear momenta, p 1 + p 2, has the same value after
the collision as before. The total kinetic energy of the system
is also unchanged, that is, none of the system's kinetic
energy is converted into other energy forms.

I.
II.

III.

Kinetic energy is conserved.
Momentum is conserved.
The velocity of each object remains unchanged.

A. I only
B.

The principal condition necessary for a collision to be
perfectly elastic is the absence of friction. At atomic and
subatomic levels this condition usually exists, and atoms and
~uclear particles often undergo ideal elastic collisions. The
condition necessary for a perfectly elastic collision is not
achievable for macroscopic bodies situated on the earth. All
such bodies produce collisions that are, to some extent,
inelastic, in which the kinetic energy of each body is therefore
converted into other forms of energy.

II only

C. I and II only
D. I, II, and III

3. If the carriages were redesigned so that collisions
between them were perfectly inelastic, each collision
would cause energy dissipation of:
A.
B.

0 J.

4 J.
c. 8 J.
D. 12 J.

In order to simulate motion and contact that is free of
friction, researchers conduct experiments with miniature
carriages that slide along a track and which are supported by
air streams projecting from the track's surface. The air
streams allow the carriages to slide almost free of friction.

4. When the two carriages approach each other, collide,
and then separate, their movements are associated with
corresponding energy transfers of:

Researchers conduct an experiment involving the collision
of two miniature carriages situated on an air track. Attached
to each carriage at the front and back ends are light springs
that undergo compression and extension and obey Hooke's
law. One carriage has a mass of 1 kg and the other a mass of

2 kg. With the air streams turned off, the coefficient of
kinetic friction between each carriage and the surface of the
track is 0.4. When the air streams are activated, the coefficient
of kinetic friction drops to less than 0.01, so frictional effects
can be ignored. The carriages are made to slide toward each
other, and immediately prior to the collision, the lighter carriage
has a speed of 4 rnls, and the heavier carriage has a speed of
2 m/s.

A. kinetic to elastic potential to kinetic.
B. elastic potential to kinetic to elastic potential.
C. gravitational potential to heat to kinetic.
D. heat to kinetic to gravitational potential.

5. If the air streams are deactivated and the carriages are
in motion, what is the ratio of the frictional force acting
on the heavier carriage to the frictional force acting on
the lighter carriage?

A. 1 : 2
B. 2: 1
c. 1 : 4
D. 4: 1
1. Just before the collision, what is the total kinetic energy
of the system?

A.
B.

c.

6. If the plane on which the carriages are sliding is inclined
to an angle of 55° with the horizontal, what is the
magnitude of the component of a carriage's weight,
mg, normal to the plane?

0J
8J
12 J

D. 24J

MCAT

SCIENCE WORKBOOK

A. mg sin 35°
B. mg cos 35°
C. mg sin 55°
D. None of the above

232


passage 4 (Questions 1-5)

2. If the area of the dam exposed to water is quadrupled by
doubling the length of the dam and doubling the depth
of the water retained, then this will cause the torque due
to the water to increase by what factor?

Figure 1 depicts a dam preventing the flow of water.
Using the base of the dam as the pivot line (Line X in Figure
1), we can determine the torque exerted by the water on the
dam by using the equation
r = pgLd 3/6

1\_

A.

2

B.

4

c.

8

D. 16

Equation 1

3. If the dam is 5 m high, approximately how fast
where .P is the density of the water (1000 kg/m 3), g is the
acceleration due to gravity, L is the length of the dam, and
d is the total depth of the water behind the dam.

(neglecting friction) would water flowing over the top
be moving when it struck the river at the base of the
dam?

Knowing the shear strength of the dam's structure, it can
be determined whether the dam can withstand the fluid
pressure exerted by the water behind it. The pressure due to
the water at depth y below the surface is given by the
equation

A. 7 m/s
B. 10 m/s
C. 14 m/s
D. 20 m/s

p = pgy

4. Which one of the following graphs best depicts the
relationship between th'e magnitude of the torque, -r,
caused by the water and the depth, d, of the water
behind the dam?

Equation 2
The total pressure at depth y is equal to the pressure exerted
by the water plus the atmospheric pressure, which is
approximately 10 5 N!m 2•

c.

A.

t

'f

5. Assume that water has risen to a height d and exerts a
torque-r on the dam: Assume also that a single force F
is to be applied at a height d perpendicular to the
opposite face of the dam so that the its torque will
exactly cancel the torque due to the water. Which one
of the following expressions gives the magnitude of F?

1. What is the pressure exerted on the dam by the water at
a point 5 m below the surface?
A. 4.9 x 104
B. 9.8 x 10 4
C. 4.9 x 10!1
D. 9.8 x 10 5

N/m 2
N/m 2
N/m 2
N/m 2

A. pgLd 2/6
B. pgLd 3/6
C. pgLd 4 /6
D. pgLd 5/6

233

PHYSICS


6. A typical speck of dust has a mass of700 ng. How many
specks of dust would it take to make 1 kg?

Questions 1 through 98 are NOT based on a
descriptive passage.

A.
B.
C.
D.

1. Express a mass of 10 kg in grams.

A. 10-4 g
B. 10-2 g
c. 102 g
D. 104 g

A.
B.

microsecond.

c.
D.

A. 0.3 km/JJ.s
B. 300 krn/JJ.s
C. 3 X 103 km/JJ.S
D. 3 x 10 5 km/JJ.s

X
X
X

106
10 7
109
10 10

kg·m 2 /s 2
kg2·m2Js2
kg·m/s
kg 2·m/s 2

8. A particle's speed at timet is given by v = kt 2, where k
is some constant. What are the dimensions of k? .(L =
length, T = time)

3. The linear density of a certain homogeneous metal bar
is found to be 10 5 rng/cm. Express this density in kg/m.

A. LT

B. LT-1
C. LT-2

A. 10-3 kg/m
B. 10-2 kg/m
C. 10 1 kg/m
D. 10 3 kg/rn

D. LT-3

9. Which one of the following formulas could give the
speed v (in m/s) with which sound travels through a
medium whose bulk modulus is B (units: kg·m- 1·s-2)
and whose mass density is p (units: kg/m 3)?

4. The density of aluminum is approximately 2700 kg per
rn 3• What is this density in g/cm 3 ?
A. 0.27 g/cm 3
B. 2.7 g/cm 3
C. 27 g/cm 3
D. 2.7 x 104 g/cm 3

A.

v=.JBP

B.

v=~Bfp

c. v=~Bp2
D. v=~Bfp2

5. A speed of 1 mi/h is equivalent to x ft/min. What is x?
(Use 1 mi = 5280 ft.)
A. 0.011
B. 0.66
60
D. 88

10. Which one of the following formulas could give the
pressure P [in kg/(m·s 2)) at depth h (in m) below the
surface of the ocean, where p (the density of seawater)
has units of kg/m 3 , and g has units of rn/s 2?

c.

A.
B.
C.
D.

SCIENCE WORKBOOK

X

7. The work done in pushing an object of mass m (in kg)
from rest to speed v (in rn/s) is given by W = mv'-12.
Find the SI unit for work.

2. Through free space, light travels at a speed of
3 x 10 8 m/s. Express this speed in kilometers per

MCAT

1.4
7.0
1.4
7.0

234

P= pgfh
P=phfg
P= pgh
P= ghjp


15. Calculate your displacement after walking 3 mi north,
then 6 mi west, then 5 mi north.

Q

A.
B.

c.

D.

R

6 mi
8 mi
10 mi
14 mi

16. In the preceding question, if it took 1 h (= 1 hour) to
walk the 3-mi section and 1.5 h to walk each of the last
two sections, what was the magnitude of your average
velocity?

11. Which of the following best represents the direction of
the vector sumP+ Q + R?

A.,
B./

c."

A. 2 mi/h
B. 2tmi/h

D./

c.

3tmi/h

D. 3tmi/h

....T

17. A car accelerates uniformly from 0 to 60 mi/h in
6 seconds. What is the acceleration?

A. 10 mi/h
B. 10 mi/s 2

12. The vectors T and N above are perpendicular to each
other. T has magnitude .J7. and N has magnitude F2.
Which of the following best describes the sum of Nand

c.

D.

10 mi·h- 1·s- 1
10 mi/h 2

T?
18. What fraction of a mile does the car (described in the
preceding question) travel during those 6 seconds?

A. magnitude 3, direction /

B. magnitude 3, direction '
C. magnitude 3, direction '._
D. magnitude 9, direction /

A. 11720
B. 11200

c.

11120

D. 1120
13. A particle travels to the right along a horizontal axis
with constantly decreasing speed. Which one of the
following best describes the direction of the particle's
acceleration?

A.

-----?

B.

(-

19. An object travels along the x a:Ms at a constant speed of
3 m/s in the -x direction. If the object is at x =4 m at
t =0, where is it at time t =4 s?

A. x =-16m
B. x =-12m

C. i

D. -1.

c.

x= -8 m

D. x = -4 m
14. A particle travels to the left along a horizontal axis with
constantly increasing speed. Which one of the following
best describes the direction of the particle's
acceleration?
A. -----?
B. (-

C. i
D. -1.
235

PHYSICS


25. In the preceding question, what was the car's average
velocity during the acceleration period?

20. An object is presently travelin·g at a velocity of
6 m/s. Calculate its velocity 5 seconds later, if it
experienced a uniform acceleration of 2 m/s 2 during
this time interval.

A. 12
B. 14
C. 18

D. 28

A. 12 m/s
B. 16 m/s
C. 20 m/s
D. 24 m/s

26. Car #l starts to accelerate from rest just as Car #2
passes it. If Car #2 maintains a constant velocity of 20
m/s, and Car # l accelerates uniformly at 5/8 mls\
how long will it take for Car # 1 to overtake Car #2?

21. A particle with an initial velocity of 4 m/s moves along
the x axis under constant acceleration. Three seconds
later, its velocity is 14 m/s. How far did it travel during
those three seconds?
A.
B.
C.
D.

m/s
m/s
m/s
m/s

A.
B.
C.
D.

21m
24m
27m
30m

8 sec
16 sec
32 sec
64 sec

27. A particle moving along the x axis passes through the
point x = 0 (in the -x direction) at a particular instant.
If it experiences a constant acceleration of
-2 m/s 2, where could the object be three seconds later?

22. An object starting from rest is accelerated uniformly
(in a straight line) until its final velocity is v; it travels
a distances. If the object were accelerated at the same
rate from rest until its final velocity were 4v, then the
distance traveled would have been:

A. x =-3m
B. x -6 m
C. x -9 m
D. x=-12m

=
=

A. 2s.

B. 4s.

c.

8s.

D. 16s.

28. The position x (in meters) of an object traveling along
a straight axis is plotted as a function of time t (in
seconds) below. How far did the object travel from t
0 tot= 5?

23. An object decelerated uniformly from an initial velocity
of v0 m/s to a final velocity of (l/2)v0 m/s. If the
distance traveled was l/8 m, what was its acceleration
(in m/s 2)?

A.

-6v~

B.

-4v~

c.

-3vJ

D.

-2v~

t

8

3

MCAT

A.
B.
C.
D.

48 m
56m
72m
80 m

SCIENCE WORKBOOK

4

5

t (in s)--~~oo-

24. A car. originally traveling at 10 m/s, accelerates
uniformly for 4 seconds at a rate of 2 m/s 2• How far
does it travel during this period?

A.
B.
C.
D.

2

236

2m
7m
8m
9m


29. The velocity v (in m/s) of an object moving along the
x axis is plotted as a function of time t (in seconds)
below. Let the magnitude of the acceleration from 0
to P be denoted a 0 P, and let the magnitude of the
acceleration from P to Q be aPQ' What is the ratio of aPQ
to a 0 P?

I. At t = 5, the object had returned to its original
position.

11. The object's average speed between t = 0 and
t = 1 was greater than its average speed between
t = 1 and t = 5.
III. The object changed its direction of travel at t = 1.

,p

t

~

32. The velocity v (in m/s) of an object moving along the
x axis is plotted as a function of time t (in seconds)
below. Which of the following statements is (are) true?

2

51
:;:lo.

t

5
t (ins)_...

~

2

5

A. 1:4
B. 1:2
c. 2:1
D. 4:1

t

A.
B.
C.
D.

30. The velocity v (in m/s) of an object moving along the
x axis is plotted as a function of time t (in seconds)
below. How far does the object travel from t = 0 to
t = 5?

I and II only
I and III only
II and III only
None of the above-

33. A rock is dropped from a 128-ft cliff. How long does it
take to reach the ground? (Ignore air resistance and
take g = 32 ft/sec 2 .)

t

~

(ins)_.,..

2

A. 2.0 sec
B. 2.8 sec

c.

4.0 sec

D. 5.6 sec
A.
B.
C.
D.

34. A rock is dropped from a 128-ft cliff; find the speed of
the rock as it hits the ground. (Ignore air resistance and
take g = 32 ft/s 2 .)

4m
5m
6m
8m

A.
B.
C.

D.

31. The velocity v (in m/s) of ari object moving along the
x axis is plotted as a function of time t (in seconds)
below. What is the object's average speed between
t = 1 and t = 5?

0.50
0.75
1.00
1.25

'

35. An arrow is shot straight up, and it eventually falls
straight back down. Ignoring air resistance, which one
of the following statements concerning the acceleration
a of the arrow is correct?
A.
B.
C.
D.

t(ins)-

A.
B.
C.
D.

64 ft/s
80 ft/s
90 ft/s
128 ft/s

a
a
a
a

always
always
always
always

points down.
points up.
points in the direction of the velocity.
opposes the velocity.

m/s
m/s
m/s
m/s

237

PHYSICS

41. An object is dropped from a height of 980 m. Let T be

36. An arrow is projected straight up with an initial velocity
of v0 m/s. If g denotes the magnitude of the gravitational
acceleration (in m/s 2 ) and air resistance is ignored, how
high does the arrow go (in m)?

A.
B.

vof2g

c.

vJ/g

D.

2v~/g

the time required to fall the entire distance and let t be
the time required to fall the first half of the distance.
Calculate the ratio Tit. (Ignore air resistance.)
A. 1/2
B. F2

vJ/2g

c.

42. One second after being thrown straight down, an object
is traveling at a speed of 20 m/s. How fast will it be
traveling two seconds later? (Ignore air resistance.)

37. An object is dropped from the top of a meteor crater on
the surface of the Moon. How many times farther does
it fall during its second second of flight than during its
first? (Note: In the choices below, g stands for the
magnitude of the free-fall acceleration near the surface
of the Moon.)

A. 30 m/s
B. 40 m/s
C. 50 m/s
D. 60 m/s

A. 2
B. 3

43. An object is released from rest at height h above the
surface of the Earth, where h is much smaller than the
radius of the Earth. It takes t seconds to fall to the
ground. At what height should this object be released
from rest in order to take 2t seconds to fall to the
ground? (Ignore air resistance; g = magnitude of
gravitational acceleration.)

c.

2g

D. 3g

38. If an object (released from rest) takes 3 seconds to fall
to the Earth, from what height was it dropped? (Ignore
air resistance and take g = 10 m/s 2 .)
A.
B.
C.
D.

A. 2h

15m
45 m
90 m
180m

B. 2gh

c.
D.

39. If an object were thrown straight upward with an initial
speed of 8 mls, and it took 3 seconds to strike the
ground, from what height was it thrown? (Ignore air
resistance and take g 10 m/s 2 .)

A. 20m
B. 40m
C. 60 m

21m
24m
45 rn
69 m

D. 80 m

45. From a height of 100 m, a ball is thrown horizontally
with an initial speed of 15 m/s. How far does it travel
horizontally in the first 2 seconds? (Ignore air
resistance.)

40. If an object is dropped from rest off a cliff and strikes
the ground with an impact velocity of 14 m/s, from what
height was it dropped? (Ignore air resistance and take
g = 9.8 rn/s 2 .)

A.
B.
C.
D.

4h
4gh

44. An object is thrown horizontally with an initial speed of
10 m/s. How far will it drop in 4 seconds? (Ignore air
resistance and take g = 10 m/s 2.)

=

A.
B.
C.
D.

2

D. 4

A.
B.

20m
30m
c. 40m
D. 50 m

10m
20 rn
40 m
80 rn

~

MCAT

SciENCE WoRKBOOK

238


51. Under the action of a certain constant net force, an
object of mass 2 kg travels in a straight line with a

46. A ball is projected horizontally with initial speed
5 m/s from an initial height of 45 m. When the ball
lands, how far has it traveled horizontally from its
original position? (Ignore air resistance.}
A.
B.
C.
D.

constant acceleration of 4 m/s 2 • If this same net force
is applied to an object with four times the mass. the
acceleration will be:

15m
20m
25m
30m

A. 0.25 m/s 2•
B. 0.5 m/s 2 •

c.

D.

47. An object is projected upward at a 30° angle with the
horizontal with an initial speed of 20 m/s. How long
will it take to reach the top of its trajectory? (Ignore air
resistance.)

52. A force of 1 dyne will cause an object of mass 1 gram
to accelerate at 1 cm/s 2 ; therefore, 1 dyne is equal to x
newtons. What is x?

A. 10-s
B. 10-1
c. 10
D. 10 5

A. 0.5 sec
B. 1.0 sec

c.

1.5 sec

D. 2.0 sec

53. A hockey puck slides on a surface of frictionless ice.
If the mass of the puck is 250 grams, and it moves in a
straight line with a constant velocity of 4 m/s, find the
net force acting on the puck.

48. An object is projected upward at a 60° angle with the
horizontal with an initial speed of30 m/s. How far will

it travel horizontally in its first three seconds of flight?
(Ignore air resistance.)
A.
B.
C.
D.

45.0
63.0
77.9
90.0

1.0 mls 2 •
2.0 m/s 2 •

A.
B.
C.
D.

m
m
m
m

0 N
1N
62.5 N
1000 N

54. A 40-kg crate is being pulled along a frictionless surface
by a force of magnitude 140 N that makes an angle of
30° with the horizontal. What is the acceleration of the
crate?

49. Two bricks are released simultaneously from the same
height above the surface of the Earth. Brick #1 is
simply dropped, while Brick #2 1s given a purely
horizontal initial velocity of magnitude 10 m/s. If they
both strike the ground in 3 seconds, how far from Brick
#1 will Brick #2 land? (Ignore air resistance.)

A. 1.75 m/s 2
B. 2 m/s 2

c.

A. 15m
B. 30m
C. 45 m
D. 60m

D.

..

2.5 m/s 2
3 m/s 2

55. Two oppositely-directed horizontal forces, F 1 and F 2 ,

act on a block (of mass 3 kg) which can slide on a
frictionless table. F 1 has magnitude 8 N. and F 2 has
magnitude 20 N. If the block starts from rest, find its
speed after 4 se~onds.

50. An object is projected upward at a 30° angle with the
horizontal with an initial speed of 60 mls. How long
will it take to reach the top of its trajectory? (Ignore air
resistance.)

A. 1.5 sec
B. 3.0 sec

c.

A.

4 m/s

B.

8 m/s
12 m/s
16 m/s

C.
D.

4.5 sec

D. 6.0 sec

239

PHYSICS


61. Find the force that must be provided to lift a 49-N
object with an acceleration of 9.8 m/s 2• (g = 9.8 mJsl.)

56. An object is accelerated from rest to a final speed v in
t seconds by a constant net force F. If we wish to
accelerate this object to the same final speed in 2 t
seconds, then:

A.
B.
C.
D.

A. the acceleration will be halved, but the force should
stay the same.
B. the acceleration will be halved, and the magnitude
of the force should also be halved.
C. the acceleration will remain the same, but the
force should be halved.
D. the acceleration will double, but the force should
be halved.

9.8 N

49 N
98 N
147 N

62. How will the gravitational force between two objects
change if the distance between them is doubled?
A.
B.
C.
D.

57. An object is· being acted upon by two (and only two)
external forces, F 1 and F 2 • If the object has a nonzero
acceleration, which one of the following must be true?

It
It
It
It

will
will
will
will

decrease by a factor of 4.
decrease by a factor of 2
increase by a factor of 2.
increase by a factor of 4.

63. Let the mass of the Moon be M and let its radius be R.
If a small object of mass m is released a few meters
above the Moon's surface, with what acceleration will ,
it fall? (G = universal gravitational constant)

A. The object cannot move at constant speed.
B. The forces F 1 and F 2 have the same line of action.
C. The magnitude of F 1 can't equal the magnitude of
F2.
D. The sum F 1 + F 2 is not zero.

m

A. GR2
Mm

B. 0 R2

53. An object is moving on a flat surface and is being acted
upon by a net nonzero force F parallel to the surface.
The direction of the object's motion must be:

c.

A. the same as the direction of F.
B. at a 45° angle to the direction of F.
C. perpendicular to the direction of F.

OM
R'l

M2

D. GR2

D. None of the above is necessarily true.

64. Calcurate the tension in a cable used to pull a 1000-kg

59. A book whose mass is 2 kg rests on a table. Find the
magnitude of the force that the table exerts on the book.
(Use g =9.8 m/s 2.)
A.
B.
C.
D.

object straight upward at an acceleration of 0.7 m/s 2 •
(Use g 9.8 m/s 2.)

=

A.
700 N
B.
9100 N
C.
9800 N
D. 10,500 N

39.2 N

19.6 N
9.8 N
0N

65. An object has a mass of 36 kg and weighs 360 N at the
surface of the Earth. If this object is transported to an
altitude equal to twice the Earth's radius, then at this
new elevated position the object will have:

60. What force must be provided to accelerate a 64-lb
2

object upward at a rate of 2 ft/s ? (Use g

=32 ft/s

2

.)

A. 60 lb
B. 64lb

c.

A.
B.
C.
D.

68 lb
D. 72 lb

MCAT

SCIENCE WORKBOOK

240

mass
mass
mass
mass

4 kg and weigh 40 N.
36 kg and weigh 40 N.
9 kg and weigh 90 N.
36 kg and weigh 90 N.


66. An 0.2-kg apple rests on the surface of the Earth.
Approximate the gravitational force exerted by the
apple on the Earth. (Note: The universal gravitational
constant, G, is 6.7 x l0- 11 N-m 2/kg 2, the mass of the
Earth is 6.0 x 10 24 kg, and the radius of the Earth is
6.4 x 10 6 m.)
A.
B.
C.
D.

70. A crate of mass 100 kg rests on a horizontal floor. The
coefficient of static friction is 0.4. If a force of 250 N,
parallel to the floor, is applied to this mass, calculate
the magnitude of the force of static friction on the crate.
A.
0N
B. 150 N
C. 250 N
D. 400 N

10-23 N
N
7
4 x 10- N
2N

4
2

X

X lQ-IS

71. A 50 N horizontal force is applied to a 5 kg crate, and
it slides along a horizontal floor with an acceleration of
8 m/s 2 • What is the magnitude of the force of kinetic
friction acting on the crate?

67. During a rainstorm, you notice that the raindrops are

not always the same size: some are small, others are
larger. Raindrops fall with a constant velocity (called
their terminal velocity). Given that the upward force of
air resistance is proportional to the speed of the falling
drop, which raindrops-the smaller ones or the larger
ones-fall with the greater speed?

A. ON
B.
5N
C. 10 N
D. Cannot be determined since m is not given

A. The smaller drops, since the force of air resistance
on them is smaller.
B. The smaller drops, since their smaller mass gives
them greater acceleration.
C. The larger drops, since they acquire greater speed
before air resistance eventually balances out the
force of gravity.
D. Neither; even taking air resistance into account,
they fall at the same speed.

72. A person applies a horizontal force F on a block of mass
m resting against a vertical walL If the block slides
vertically down the wall at a constant speed, what must
be true about the coefficient of kinetic friction, J.l,
between the block and the wall? (g = magnitude of
gravitational acceleration)

A. J.l = mg!F
B. J.l = Fl(mg)

c.

68. A crate of mass 100 kg is being pushed in a straight line
across a horizontal floor at a constant speed of 4.0 m/s.
The coefficient of kinetic friction between the crate and
the floor is 0.3. Find the net force on the crate.

A.
B.
C.
D.

J.l = 1

D. J.l = g
73. A block of mass m begins to slide down a vertical wall.
If the wall is frictionless, what minimum horizontal
force F must be applied!"to the block to keep it from
sliding any further? (g magnitude of gravitational
acceleration)

ON
300 N
400 N
1200 N

=

A. F = mg
B. F = 2mg
C. F = 3mg
D. No horizontal force, however strong. can keep the
block from sliding down the wall.

69. A 2-kg block is sliding along a horizontal surface,
pulled by a rope that is parallel to the surface. If the
tension in the rope is 12 N. and the coefficient of kinetic
friction is 0.4, find the acceleration of the block.

74. A crate of rna~ 100 kg rests on a horizontal floor. The
coefficient of static friction between the floor and the
crate is 0.4. Let f denote the maximum static friction
force that the floor can exert on the crate. What happens
to f if a child of mass 20 kg sits on top of the crate?

A. 2 m/s 2
B. 4 m/s 2
C. 6 m/s 2
D. 8 m/s2

A. f increases by 8 N.
B. f increases by 20 N.
C. /increases by 80 N.
D. f will not change.

241

PHYS1CS


80. Which one of the following statements is true concerning
the magnitude of the normal force, N, acting on a block
sliding down a frictionless ramp whose incline angle
(with the horizontal) is e?

75. A biock weighing 40 N is held in contact with the
ceiling of a room by a upward force of 50 N. What is the
magnitude of the normal force exerted by the ceiling on
the block?

A.
B.
C.
D.

A.
0N
B. 10 N
C. 50 N
D. 90 N

81. Consider an inclined plane that makes an angle 8 with
the horizontal. What is the relationship between the
length of the ramp, L, and the vertical height of the
ramp, h?

76. A block slides down a frictionless inclined plane that

makes an angle e (where 0° < () < 90°) with the
horizontal. If g is the acceleration due to gravity, then
the acceleration of the block down the plane:
A.
B.
C.
D.

A. L = h sin ()
B. L = h tan ()

is always less than g.
is always equal to g.
is always greater than g.
can be less than g, equal to g, or greater than g
depending on the value of e.

c.

A.
B.
C.
D.

c.

8.5 m/s 2
D. 9.8 m/s 2

78. Which one of the following statements is true concerning

the magnitude of the acceleration, a, of a block sliding
down a frictionless ramp whose incline angle (with the
horizontal) is 8?

e.

A.
B.
C.
D.

79. A 5-kg block is released from rest at the top of a 10meter-long frictionless incline whose incline angle is
30°; it takes t 1 seconds for this block to reach the
bottom. The experiment is repeated with a 10-kg block,
and the time needed to reach the bottom is 12 seconds.
How do 11 and t 2 compare?

c.

11

< 12

= t2

m
m
m
m

to
to
to
to

the
the
the
the

left of the plank's center
left of the plank's center
right of the plank's center
right of the plank's center

6ft
9ft
c. 10 ft
D. 12ft
A.
B.

II

SCIENCE WORKBOOK

0.5
1.5
0.5
1.5

84. Three metal blocks are hanging from a 16-foot rod of
negligible mass. Blocks #1 and #2 each weigh 0.4 lb,
and the weight of Block #3 is 0.8 lb. Block #1 is at the
very left end of the rod, Block #2 is at the center of the
rod, and Block #3 is at the very right end of the rod.
How far from the left end is the center of gravity?

> 12
D. Cannot be determined from the information given

MCAT

p, =0
p, = sin ()I cos 8
p, =cos 8/ sin 8
p, = 1

83. Two masses are resting on an 8-meter-long, uniform
10-kg plank. Mass #1 is 15 kg and rests 2 meters to the
left of the plank's center, and Mass #2 is 5 kg and rests
3m to the right of the plank's center. How far from the
center of the plank is the center of mass?

a is constant, independent of
a is proportional to e.
a increases as ()increases, but not proportionally.
a is at its maximum value when () = 45°.

11

= L sin ()

82. An object slides down an inclined plane with constant
speed. If the ramp's incline angle is 8, what must be the
coefficient of kinetic friction, p,, between the object
and the ramp?

A. 2.5 m/s 2
B. 4.9 m/s 2

A.
B.

h

D. h = L tan ()

77. A block slides down a frictionless inclined plane that
makes an angle of 30° with the horizontal. Find its
acceleration.

A.
B.
C.
D.

e.

N is constant, independent of

N is proportional to e.
N is inversely proportional to 8.
N decreases as ()increases, but not proportionally.

242

1
t

l


88. The Earth is kept in orbit around the Sun by their
gravitational attraction. Assume that the orbit is circular
(of radius r) and the orbiting speed v of the Earth is
constant. If G is the universal gravitational constant,
what is the mass of the Sun?

85. The figure below shows a uniform bar supporting two
masses, with M 1 < M 2, one at each end of the bar. If the
mass of the bar is neglected, the position of the center
of mass, x, is calculated and marked as in the figure. If
X denotes the position of the center of mass with the
mass M of the bar included, then:

A.

M2

Ml

~,........._______.__._

G
v2 r

B. Gv1 r
X

c.
A. X=

X.

B. X is closer to M 1 than x is.
C. X is closer to M 2 than x is if M > M 1•
D. X is closer to M 2 than xis if M > Mr

D.

v2

Or
v 2r
G

89. Let F represent the net force on an object traveling in a
circular path (of radius r) at a constant speed v. If the
radius is reduced to ( 112)r, and the speed is increased to
2v, then the net force on this same object becomes:

86. For an object that travels in a circular path at constant
speed,
A. the velocity is constant since the speed is constant.
B. the acceleration is zero since the speed is constant.
C. the acceleration is not zero and is always directed
tangent to the path.
D. the acceleration is not zero and is always directed
toward the center of the path.

A.

F.

B. 2F.
C. 4F.
D. 8F.

.

90. A pendulum consi-sts of a 0.5 kg mass attached to the
end of 1-meter-long rod of negligible mass. When the
rod makes an angle of 60° with the vertical, find the
magnitude of the torque about the pivot.

87.

B

A.

B.

c.

D

D.

2.5 N·m
4.3 N·m
5.0N·m
10.0 N·m

...

91. A uniform bar is lying on a flat table. In addition to its
weight and the normal force exerted by the table (which
exactly balances the bar's weight), exactly two other
forces, F 1 and F 2 , act on the rod. If the net force acting
on the rod is zero, then:

A rock is tied to the end of a string and whirled
(counterclockwise as seen from above) around in a
circle at constant speed. If the string were to suddenly
break when the rock is at point P, which arrow would
best indicate the direction of the rock's subsequent·
motion?

A. the net torque on the rod must also be zero.
B. the rod cannot accelerate translationally or

rotationally.
C. the net torque will be zero if F 1 and F 2 are applied
at the same point on the rod.
D. the rod can accelerate translationally if F 1 and F 2
are not applied at the same point on the rod.

A. A
B. B

c. c

D. D

243

PHYSICS


92. A massless rod is attached to the ceiling by a string.
Two weights are hung from the rod: a 0.4-lb weight at
its left end and a 1.2-lb weight at its right end. If the
length of the rod is L, how far from its left end should
the string be attached so that the rod (with attached
weights) will be horizontal?

A.

U4

B.

2L/3

97. A bar extends perpendicularly from a vertical wall. The
length of the bar is 2 m, and its mass is 10 kg. The free
end of the rod is attached to a point on the wall by a light
cable, which makes an angle of 30° with the bar. Find
the tension in the cable.

A. 20N
B. 50 N
C. 100 N
D. 200 N

C. 3U4
D. 5U6

98. In the preceding question, what is the magnitude of the
vertical force exerted by the wall on the rod?

93. In the preceding question, what is the tension in the
string supporting the rod and the attached weights?

A. 30N
B. 50 N
C. 100 N
D. 150 N

A. 1.2 lb
B. 1.6 lb

c. 2.4 lb
D. 3.2lb

94. A uniform rod of mass M sticks out from a vertical wall
and points toward the floor. If the smaller angle it
makes with the wall is 8, and its far end is attached to
the ceiling by a string parallel to the wall, find the
tension in the supporting string.
A.
B.
C.
D.

Mg/2

(Mg sin 8)12
Mg
Mg sin 8

95. A uniform plank of mass 12 kg and length Lis positioned
horizontally, with its two ends supported by sensitive
scales. An object of mass 3 kg is placed a distance L/
3 from the left end of the plank. What weight does the
right-hand scale read?

A. 50N
B. 70N
C. SON
D. 90N

96. In the preceding question, what weight does the lefthand scale read?
A.
B.

60 N
70 N

C.
D.

80 N
150 N

;I

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MCAT

SCIENCE WORKBOOK

244

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