Tyler Casey
SP211 Practice Final Exam, Fall 2021
Below is the cover page as it will look on the final exam.
Getting set up:
• At your station should only be you, writing utensils, your TI36XPro (or a calculator
with a similar form factor, only one), a drink. Pack all else away in your bag. This
includes laptops, cellphones, smartwatches, and any network devices. Place your bag
where instructed.
• Provided: the exam, equation sheet, scratch paper, and (when done) a SCANTRON
form.
• After all is packed away, you may take care of the honor pledge below. Go no futher
though, we’ll begin the exam together.
Working the exam:
• This exam is a solo e↵ort, just you and what is allowed in the listing above. You
may not consult with anyone or employ outside resources nor may your instructor or
proctor aid you in the interpretation of any of the questions.
• 50 multiple choice questions, all weighted equally, no partial credit.
• Work directly on the exam and circle your answers. Use supplied scratch paper if
needed.
• Numerical answers are reported typically with 2 sig figs. Numbers in problem statements
are stated simply without conveying sig figs. This is to help make the exam more
readable.
• g = 9.8 m/s2 is used throughout the exam.
When done Working the exam:
• Obtain a SCANTRON form. Fill in everything with care and double check everything.
• Turn in your exam, equation sheet, used scratch paper, and SCANTRON form.
Write below this honor pledge:
The Naval Service I am a part of is bound by honor and integrity. I will not compromise
our values by giving or receiving unauthorized help on this exam.
Signature:____________________________________________ Date:___________________
Name (printed) and alpha:______________________________________________________
Instructor and section:________________________________________________________
1. You go for a 10 km “walk + run”. You walk the first 5 km at 6 km/hr and then you run
the next 5 km at 12 km/hr. Your average speed over the 10 km was
A. 9 km/hr
Say
=
&
de
5
Af
B. 11 km/hr
C. 10 km/hr
8
D.
8 km/hr
E
+F
=
2
8kmiler
so
E. 7 km/hr
2. A particle’s position as a function of time is described by x = 8.0 t + t3 where x is in
meters and t is in seconds. What is the particle’s instantaneous velocity at t = 1.0 s ?
A. vx = 12 m/s
+
u z + 3
2
=
B. vx = 9.0 m/s
8 +3 =11
C. vx = 10 m/s
=
MIS
D. vx = 11 m/s
8
E. vx = 8.0 m/s
3. A large transport aircraft (a Boeing C-17) must attain a speed of 82 m/s along an incredibly
short runway of length 930 m. What minimum constant acceleration is required?
->
J
A. 3.6 m/s2
B. 7.5 m/s2
C. 9.8 m/s2
v(x Vox=
+
not
cry
2a(X
-
X0)
D. 5.4 m/s2
E. 2.9 m/s2
0z0
+
2a(P30)
=
3.6m/s[
4. A super ball bounces up and down repeatedly impacting the ground. During the brief
intervals of contact with the ground, which choice below best describes the ball’s average
acceleration?
A. upward, large compared to g.
8
B. downward, large compared to g.
C. upward, NOT large compared to g.
D. downward, NOT large compared to g.
E. zero.
5. At t = 0, a particle’s velocity is vx = 30 m/s. Shown is the particle’s time-dependent
acceleration. At which of these times is the particle’s velocity closest to zero?
A. 5 s
y
B. 1 s
C. 2 s
If
ax (m/s2 )
Saxdt
8
t
D. 3 s
4
E. 4 s
0
I
24
8
1
2
3
4
322
5322
t (s)
5
6. The dashed line shows a car’s path. At time t1 , the car’s velocity is ~v1 . At a later time
t2 , its velocity is ~v2 . The direction of the car’s average acceleration from t1 ! t2 is
closest to
A. south
dag:
AUx
N
B. southeast
8
VI
p
C. west
D. southwest
E. northwest
~v2
~v1
-
W
E
S
38
7. A projectile is released from a diving airplane. At release, this projectile shares the
same velocity as the airplane itself. Neglecting air drag, where does the projectile land?
A. x = 1300 m
B. x = 190 m
Woy:
ax
-
P5sin27
0
=
-0.8
C. x = 400 m
ay
D. x = 940 m
Y: 480
E. x = 540 m
O
0: yo+Uog +
v0=05COS27
=
x
=
x0
0
=
+
Edyt
480-P5SinZ7FE(8.81CtY)
+VOx+
y
Eax +2
+
27
=
yf
Xi
v0 = 95 m/s
480 m
0
=
+= 6.43se
0
=
xf =?
x 0
=
x
+PSOS2)(6.43)
+
0
=
544
8. A projectile is launched towards a wall. Neglecting air drag, how high up the wall does
this projectile strike?
+
100 0 + YOLOS(65)
=
A. 43 m
8
B. 9.3 m
C. 16 m
+=
y
0
=
5.P15
+4OSin(05)(5.915)
-
E(p.8(<5.P15
--
-
.....
y 43m
=
D. 32 m
2
-
E. It strikes the ground, not the wall.
is
v0 = 40 m/s
65
100 m
9. Relative to the ground, ship A travels east at 24 knots and ship B travels northwest
at 13 knots. What is the speed of ship B relative to ship A?
A. 34 knots
y
B. 28 knots
C. 11 knots
D. 17 knots
E. 37 knots
&
M
1350
-in
v
=
REIABCOS4
-
2(24)(13(0)135)
A.
3x1ct)
10. A ball on the end of a cord is being whirled at constant speed in a horizontal circle.
Which choice describes the directions of the ball’s velocity ~v and acceleration ~a?
A. ~v and ~a are tangential to the ball’s circular arc.
B. ~v and ~a are radially outward.
C. ~v is tangential, ~a is radially outward.
ada
↑
D. ~v and ~a are radially inward.
E.
O
~v is tangential, ~a is radially inward.
f
11. A particle is traveling counterclockwise in a circle in the xy plane around the origin.
At some instant, its velocity is ~v = (1 m/s)î + (-3 m/s)ĵ. At this instant, the particle’s
o
position is in which quadrant?
x campanebt
velociy: posive
y
y: negren
A. quadrant 1
B. quadrant 2
C.
8
-
rU
d
x
quadrant 3
D. quadrant 4
2
1
x
~
-
(
3
vx > 0
4
av
vycy
;
2: Bradise
12. A centrifuge spinning at 16 rad/s is brought to rest at a constant angular acceleration
of magnitude 8.0 rad/s2 . Through how many radians does the centrifuge spin as it winds
down?
w=16 radise
A. 32 rad
B. 2.0 rad
8C.
16 rad
D. 4.0 rad
E. 8.0 rad
16?
0 +
=
2(8)(x)
x=
162crd
13. A 3.0 kg puck moves on a level frictionless table. Shown is the puck’s complete free-body
diagram for all forces in the horizontal xy plane. What is the magnitude of the puck’s
acceleration?
A. 4.8 m/s2
B. 2.8 m/s2
C. 3.5 m/s2
D. 6.7 m/s2
8
E. 6.0 m/s2
Fnet
=
md
y
F1 = 10 N
10Cos15=3C
25
FytF zy may
=
x
25
↓ Sin25-lOsin25
=
ma1
=
0
F2 = 10 N
14. This 3.0 kg block’s speed increases as it descends this frictionless incline.
Its acceleration is 1.6 m/s2 directed down the incline. This requires an
applied force directed up the incline of magnitude
A. 34 N
B. 29 N
C. 25 N
F:
mg
sin (10)
3 (0.8)
-
ma
(0.838)
F = 21.8 N
-
a = 1.6 m/s2
3(1.6)
↑
FGC:n8
FG
E. 32 N
70
15. A cement block is placed on a scale at rest. The scale reads 26 pounds.
You place this block and scale on the floor of an elevator and you ride the
elevator up to the 50th floor. As you are nearing the 50th floor and the
elevator is gradually slowing down, the scale might read
B.
8
v
22 pounds
C. 0 pounds
D. 26 pounds
E. The scale will read a negative number.
I
Fapplied = ?
D. 23 N
8
A. 30 pounds
ICOSE
scale
16. Suppose a planet has the same average volume mass density (kg/m3 ) as Earth, but
its radius is three times that of Earth’s. What would be the value of g near the surface of
this bigger planet compared to on Earth?
j
A.
F6=
gbigger planet = 3 ⇤ gEarth
B. gbigger planet = gEarth , same as on Earth.
DMM
G
C. gbigger planet = 9 ⇤ gEarth
D. gbigger planet = gEarth / 3
E. gbigger planet = gEarth / 9
17. A 15 kg block is pulled along the floor by a 40 N force directed 30 above the horizontal.
The coefficient of kinetic friction between the block and the floor is µk = 0.20. What is
magnitude of the block’s acceleration?
Fnetx
A. 0.35 m/s2
B. 0.71 m/s
C.
8
0.62 m/s
2
E. 0.54 m/s2
max
N=mg FSin38
-
= 127
2
D. 0.48 m/s2
=
FU
=
25.4N
M2O SL30)
-
Fix:
P
FE
&
Fo
FT = 40 N
30
0.10
8
tot
25.4= 15(a)
a 0.62
=
18. A block rests on a level track. The coefficient of static friction between the block and
the track is 0.62. Slowly raising one end of the track, at what angle (of the track above
horizontal) will the block slip?
A. 58
B. 38
C. 45
D. 32
E. 52
Freeres
19. A falling 100 kg object experiences a drag force of magnitude
Fdrag = cv 2
where c is a constant for this object in its orientation as it falls through the air. The object
eventually reaches a terminal speed of 67 m/s. What is the value of c?
A. 0.22 kg/m
B. 0.19 kg/m
C. 0.11 kg/m
D. 0.15 kg/m
E. 0.31 kg/m
20. A 120 kg linebacker tackles a 93 kg quarterback. How does the force the linebacker
exerts on the quarterback compare to the force the quarterback exerts on the linebacker?
A. The force the quarterback exerts on the linebacker is always less in magnitude than
the force the linebacker exerts on the quarterback.
B. When caught o↵ guard, the force the quarterback exerts is often less in magnitude
than the force the linebacker exerts.
C. With a proper stance, the force the quarterback exerts can match or even be greater
in magnitude than the force the linebacker exerts.
D. The force the quarterback exerts on the linebacker is equal in magnitude to the force
the linebacker exerts on the quarterback.
E. More than one of the above are possible.
21. After being released, the 2.0 kg block accelerates to the right along the frictionless
track as the 1.0 kg block accelerates downward. The pulley is massless and frictionless.
What is the tension in the string?
A. 9.8 N
B. 6.5 N
2.0 kg
C. 3.3 N
D. 4.9 N
E. 10 N
1.0 kg
22. A horizontal force is applied to the bottom block. The stacked blocks accelerate as
one due to static friction fs between the blocks. The floor is frictionless. Fnet x on the
TOP block is
y
A. 0
Fapp
B. +fs
C.
x
fs
D. Fapp + fs
E. Fapp
fs
23. A Ferris wheel is an amusement ride consisting of a very large upright wheel that
rotates in the vertical plane. Capsules with benches are attached to the wheel’s rim in
such a way as to keep passengers upright as the wheel rotates.
Suppose you are seated in one of the capsules as the wheel rotates at a constant rate.
How does the magnitude of the normal force n (the bench pushing on you) compare to
mg as you pass through the bottom of the wheel’s circle?
A. n > mg
B. n < mg, but n 6= 0.
C. n = mg
D. n = 0
E. More information is needed
to answer this question.
24. A 7.5 kg particle experiences a force that varies with position as shown. At x = 0, the
particle’s velocity is v0x = 4 m/s. The particle’s speed at x = 8 m is
A. 6.9 m/s
Fnet x (N)
B. 7.7 m/s
C. 5.7 m/s
30
D. 3.1 m/s
20
E. 4.0 m/s
10
2
4
6
8
x (m)
25. A 10 kg box moving at 8.0 m/s slides onto a stretch of floor where the coefficient of
kinetic friction between the box and floor is 0.24 . How far along this stretch does the
block slide as it comes to rest?
A. 18 m
v0 = 8.0 m/s
B. 14 m
C. 7.1 m
d =?
D. 11 m
E. 3.5 m
26. A 90 kg skydiver drops from rest from a high-altitude balloon. After falling 500 m, the
diver’s speed is 60 m/s. During this first 500 m of descent, by how much did the thermal
energy rise for this skydiver-Earth-air system?
A. 2.8 ⇥ 105 J
B. 4.4 ⇥ 105 J
C. 1.6 ⇥ 105 J
D. 6.0 ⇥ 105 J
E. More information is needed
to answer this question.
27. A 4600 kg elevator already in motion rises 30 m in 7.0 s at a constant speed by
means of a cable attached to a motor. What is the motor’s power while lifting the elevator
at this constant speed?
A. 1.9 ⇥ 105 W
B. 2.1 ⇥ 106 W
C. 9.5 ⇥ 106 W
D. 3.2 ⇥ 106 W
E. 9.7 ⇥ 105 W
28. Holding a 0.20 kg block in the palm of your hand, you attach the
block to an ideal spring being careful to keep the spring relaxed. You
then release the block and observe that the spring reaches a maximum
stretch of 0.70 m (at the turning point). The spring’s spring constant is
initially
relaxed
A. 2.8 N/m
B. 12 N/m
C. 1.6 N/m
0.70 m
D. 3.0 N/m
E. 5.6 N/m
lowest position
&
29. A particle’s motion is confined to the x axis. The particle’s potential energy is described
by the function
U (x) = x2 4x + 12
where x is in meters and U is in joules. For which position listed is the force associated
with this potential energy zero?
A. x = 2 m
B. x = 4 m
C. x = 6 m
D. x = 8 m
E. x = 12 m
30. This graph approximates a time-dependent net force experienced by a 2.2 kg object.
Just before the force begins, the object’s velocity is vix = 14 m/s. Just after the force
terminates, its velocity is
A. vfx = +14 m/s
Fnet x (N)
B. vfx = +50 m/s
800
C. vfx = +22 m/s
600
D. vfx = +28 m/s
400
E. vfx = +36 m/s
200
0.1
0.2
0.3
0.4
t (s)
31. The mass of cart A is 0.50 kg, the mass of cart B with its extra load is 1.5 kg. Initially
cart A is at rest. The speed of cart A after the inelastic* collision is
A. 2.3 m/s
B. 2.8 m/s
at rest
A
BEFORE:
C. 4.5 m/s
D. 3.9 m/s
AFTER: vA f = ?
E. 3.5 m/s
A
1.7 m/s
3.0 m/s
B
B
*While not perfectly inelastic,
thermal energy is generated.
32. These two incoming clay blobs have di↵erent masses, speeds, and directions. They
collide at the origin sticking together. What is the speed of the outgoing clay blob?
y
A. 17 m/s
B. 12 m/s
1.0 kg
C. 20 m/s
v1 = 30 m/s
x
D. 24 m/s
v2 = 10 m/s
E. 14 m/s
2.0 kg
33. The velocity of ship A relative to the ground is ~vAG = ( 5î + 3ĵ) m/s . The velocity
of ship B relative to the ground is ~vBG = (2î + 7ĵ) m/s . The velocity of ship B relative to
ship A is
A. ~vBA = ( 7î
B. ~vBA = (3î
4ĵ) m/s
10ĵ) m/s
C. ~vBA = (7î + 4ĵ) m/s
D. ~vBA = ( 3î + 10ĵ) m/s
E. ~vBA = (2î + 7ĵ) m/s
34. These three small spheres (they can be approximated as point particles) are fastened
to a massless rod that spins around the pivot. The speed of the sphere furthest out is
4.2 m/s. The kinetic energy of rotation of this system is
A. 24 J
B. 8.0 J
C. 4.0 J
D. 12 J
pivot
&
0.45 kg
0.30 m
E. 6.2 J
0.45 kg
0.45 kg
0.30 m
0.30 m
v = 4.2 m/s
35. The pulley has rotational inertia I = 0.0030 kg m2 and radius r = 0.050 m. The
0.60 kg block descends as the cord unwinds without slipping. The magnitude of the block’s
acceleration is
A. 8.9 m/s2
B. 3.3 m/s2
C. 4.5 m/s2
D. 9.8 m/s2
E. 6.5 m/s2
COM
.
50
60
D. 1.1 N·m clockwise
40
C. 2.2 N·m counterclockwise
30
30
B. 1.1 N·m counterclockwise
20
A. 2.2 N·m clockwise
x
10
36. A 0.45 kg meter stick is mounted to an axle at its end.
At the instant shown what is the torque exerted by gravity
on the meter stick about the axle?
y
axle
.
70
80
90
mg
37. A solid cylinder, a solid sphere, and a hoop, all have the same mass and same radius.
Each rolls without slipping along level ground with the same center of mass velocity
~vcom before rolling (still without slipping) up a hill. Which one goes farthest up the hill?
A. All go the same distance up the hill.
B. The hoop.
C. The solid sphere.
D. The solid cylinder.
vcom
38. A ball rolls without slipping down a ramp. What force delivers a torque about the
ball’s center of mass? Choose E if more than one in the list delivers a torque.
A. weight mg
↵
B. normal force n
C. kinetic friction fk
a com
D. static friction fs
E. More than one of the above.
39. A spinning ice skater is approximately a system on which no external torques act. A
skater initially spins crouched with arms and a leg extended. The skater then pulls in and
extends to become vertically needle like. Comparing these initial and final states, in the
final “needle like” state the skater’s
A. angular momentum is unchanged, kinetic energy is larger.
B. angular momentum is unchanged, kinetic energy is smaller.
C. angular momentum is larger, kinetic energy is larger.
D. angular momentum is larger, kinetic energy is smaller.
E. angular momentum and kinetic energy are both unchanged.
40. A satellite in a circular orbit is a distance r = 7.2 ⇥ 106 m from the center of the
Earth. The satellite’s speed is
A. 7400 m/s
B. 11000 m/s
C. 7900 m/s
D. 1900 m/s
E. 1200 m/s
41. A space capsule is at rest at a distance of 3.0 ⇥ 107 m from Earth’s center. If the
capsule drifts from this position only from Earth’s gravitational pull (no use of thrusters),
what will be its speed when it reaches a distance of 2.0 ⇥ 107 m from Earth’s center?
Assume no thermal energy is generated.
A. 4500 m/s
B. 6300 m/s
C. 8900 m/s
D. 3600 m/s
E. 5200 m/s
42. A common injury divers su↵er is trauma to the ear in the first meters of diving due
to an imbalance of pressure in the middle ear compared to the underwater environment.
How much will the pressure rise if you dive from the surface to a depth of 4.2 m?
A. 0.41 atm
B. 0.27 atm
C. 0.83 atm
D. 0.69 atm
E. 0.54 atm
43. A hollow sphere of outside radius 18 cm and inside radius 17 cm floats half submerged
in fresh water. What is the density of the material used to make this hollow sphere?
A. 2600 kg/m3
B. 3200 kg/m3
C. 5700 kg/m3
D. 4000 kg/m3
⇢material = ?
E. 4900 kg/m3
⇢water = 1000 kg/m3
Problems 46 and 47: A block slides back and forth by means of an ideal spring (one
end attached to the block, one end to a wall). The floor is frictionless.
Let’s now imagine changing the system somehow and restarting the motion in the way
described above. Let’s consider three scenarios:
• Scenario 1: Change the spring constant (swap out the spring).
• Scenario 2: Change the mass of the block (swap out the block).
• Scenario 3: Change the amplitude (choose a di↵erent starting position).
44. Which of these scenarios would change the block’s maximum speed after release?
A. Scenarios 1 and 2.
B. Scenarios 1 and 3.
C. Scenarios 2 and 3.
D. All three scenarios will work!
E. Only one of the three scenarios will work.
44. Which of these scenarios would change the period of motion?
A. Scenarios 1 and 2.
B. Scenarios 1 and 3.
C. Scenarios 2 and 3.
D. All three scenarios will work!
E. Only one of the three scenarios will work.
Problems 46 and 47: A block slides back and forth by means of an ideal spring (one
end attached to the block, one end to a wall). The floor is frictionless.
Let’s now imagine changing the system somehow and restarting the motion in the way
described above. Let’s consider three scenarios:
• Scenario 1: Change the spring constant (swap out the spring).
• Scenario 2: Change the mass of the block (swap out the block).
• Scenario 3: Change the amplitude (choose a di↵erent starting position).
45. Which of these scenarios would change the block’s maximum speed after release?
A. Scenarios 1 and 2.
B. Scenarios 1 and 3.
C. Scenarios 2 and 3.
D. All three scenarios will work!
E. Only one of the three scenarios will work.
45. Which of these scenarios would change the period of motion?
A. Scenarios 1 and 2.
B. Scenarios 1 and 3.
C. Scenarios 2 and 3.
D. All three scenarios will work!
E. Only one of the three scenarios will work.
17
46. A small mass swings from the end of a string. Shown is the string’s angle from vertical
as a function of time. What is the string’s length?
A. 1.6 m
B. 0.25 m
C. 2.2 m
D. 0.99 m
E. 0.35 m
✓ (rad)
0.10
0
1.0
2.0
3.0
4.0
t (s)
-0.10
47. One example of an equation that describes a wave on a string is
y = (6.0 cm) sin[(14 rad/m) x + (87 rad/s) t].
If the string’s tension is 22 N, what is the string’s linear mass density?
A. 0.81 kg/m
B. 0.57 kg/m
C. 0.25 kg/m
D. 0.64 kg/m
E. 0.45 kg/m
48. An attack sub moves at a speed of 12.0 m/s through still water. As it approaches
an underwater mountain it sends a 900 Hz sonar wave that travels through the water at
1482 m/s. The wave reflects o↵ the mountain and the sub detects this reflected wave.
The sub detects a reflected frequency of
A. 893 Hz
B. 907 Hz
C. 886 Hz
D. 915 Hz
E. 900 Hz
49. When this string under tension is driven at 240 Hz, you see the depicted standing
wave. If you continuously decrease the driving frequency, the next frequency for which
the string responds resonantly is
A. 192 Hz
B. 144 Hz
speaker
C. 171 Hz
D. 200 Hz
E. 160 Hz
50. Two speakers are driven in phase at 440 Hz. Both speakers emit sound waves that
travel in the +x direction. The first speaker is located at x = 0. The second speaker is
located at x = 0.78 m. For points along the +x-axis, the interference of the two sound
waves is
A. Maximum constructive.
B. Maximum destructive.
C. Constructive, but less than maximum.
D. Destructive, but less than maximum.
E. dependent on the particular location.