Physics 221 Spring 2006 Exam 1
PHYSICS 221
Spring 2006
EXAM 1: Feb 16 2006 8:00pm—10:00pm
Name (printed): ____________________________________________
ID Number: ______________________________________________
Section Number: __________________________________________
INSTRUCTIONS:
Each question is of equal weight, answer all questions. All questions are multiple choice.
Choose the best answer to each question.
Before turning over this page, put away all materials except for pens, pencils, erasers,
rulers, your calculator and “aid sheet”. An “aid sheet” is one two sided 8½×11 page of
notes prepared by the student. There is also a list of possibly useful equations at the end
of the exam.
"In general, any calculator, including calculators that perform graphing numerical
analysis functions, is permitted. Electronic devices that can store large amounts of text,
data or equations are NOT permitted." If you are unsure whether or not your calculator
is allowed for the exam ask your TA.
Examples of allowed calculators: Texas Instruments TI-30XII/83/83+/89, 92+
Casio FX115/250HCS/260/7400G/FX7400GPlus/FX9750 Sharp EL9900C.
Examples of electronic devices that are not permitted: Any laptop, palmtop, pocket
computer, PDA or e-book reader.
In marking the multiple choice bubble sheet use a number 2 pencil. Do NOT use ink. If
you did not bring a pencil, ask for one. Fill in your last name, middle initial, and first
name. Your ID is the middle 9 digits on your ISU card. Special codes K to L are your
recitation section, for the Honors section please encode your section number as follows:
H1⇒02; H2⇒13 and H3⇒25.
If you need to change any entry, you must completely erase your previous entry. Also,
circle your answers on this exam. Before handing in your exam, be sure that your
answers on your bubble sheet are what you intend them to be.
It is strongly suggested that you circle your choices on the question sheet. You
may also copy down your answers on a piece of paper to take with you and compare
with the posted answers. You may use the table at the end of the exam for this.
When you are finished with the exam, place all exam materials, including the bubble
sheet, and the exam itself, in your folder and return the folder to your recitation
instructor. No cell phone calls allowed. Either turn off your cell phone or leave it at home.
Anyone answering a cell phone must hand in their work; their exam is over.
Total number of questions is 30. Question 30 is “extra credit”
Best of luck, David Atwood and Paula Herrera-Siklody
Page 1 of 17
Physics 221 Spring 2006 Exam 1
Formula sheet for Exam 1 – Phys 221 – Spring 2006
z
Vectors and math
G
A = Ax2 + Ay2 + Az2
G G
A ⋅ B = AB cos θ = Ax Bx + Ay By + Az Bz
G G
A × B = AB sin θ
G G
A × B = ( Ay Bz − Az By ) iˆ + ( Az Bx − Ax Bz ) ˆj + ( Ax By − Ay Bx ) kˆ
k̂
iˆ
x
−b ± b 2 − 4ac
2a
d
d
sin x = cos x
cos x = − sin x
dx
dx
ax 2 + bx + c = 0
⇒
d n
x = nx n −1
dx
Geometry
x=
10−15
10−12
10−9
10−6
10−3
103
106
109
1012
perimeter circle: 2π R
area circle: π R 2
area sphere: 4π R 2
4
volume sphere: π R 3
3
1 revolution = 2π radians = 360D
Conversion factors (for barbaric units)
1 yard = 3 foot = 36 inches
1 inch = 2.54 cm
1 mile = 1.609 km
1 gallon = 3.788 liters
1 lb = 4.448 N
y
ĵ
Physical constants
g = 9.81 m/s 2
G = 6.67 ×10−11 Nm 2 /kg 2
General kinematics
G
G
∆r
G
G dr
vaverage =
v=
∆t
dt
Constant acceleration
1G
G G G
r = r0 + v0t + at 2
2
1
x = x0 + v0 x t + ax t 2
2
Circular motion
ω=
dθ
dt
α=
G
∆v
G
aaverage =
∆t
G G G
v = v0 + at
G G
v 2 − v02 = 2a ⋅ ∆r
vx = v0 x + axt
In 1D: vx 2 − v02x = 2ax ∆x
dω
dt
s = Rθ
1 2π 2π R
T= =
=
ω
f
v
Constant α:
G
G dv
a=
dt
arad
1
2
θ = θ 0 + ω 0t + α t 2
atan
v02
sin 2θ
g
atan = Rα
v = Rω
v2
= = Rω 2
R
R=
G
dv
=
dt
ω = ω0 + α t
Page 2 of 17
G G
G
a = arad + atan
ω 2 − ω 02 = 2α∆θ
femto- (f)
pico- (p)
nano- (n)
micro- (ì)
milli- (m)
kilo- (k)
mega- (M)
giga- (G)
tera- (T)
Physics 221 Spring 2006 Exam 1
Relative motion
G
G
G
G
G
G
rA relative to C = rA relative to B + rB relative to C
vA relative to C = vA relative to B + vB relative to C
G
G
G
aA relative to C = aA relative to B + aB relative to C
Forces
G
G
F
∑ = ma
FHooke = − k ∆x
G
G
G
Fg (≡ W ) = mg
fs ≤ µs N
G
Mm
FNewton = −G 2 rˆ
r
g =G
fk = µk N
ME
RE2
Work and energy
G G
1
p2
Wnet = ∆KE
W = ∫ F ⋅ dl
KE = mv 2 =
2
2m
G
G
r G
G
G
Wconservative = −∆U
U (r ) − U (r0 ) = − ∫G F ⋅ dl
r0
U=
1 2
kx + C
2
E = KE + U
U = mgy + C
∆E = Wnon-conservative
U = −G
W
∆t
G
G
F = −∇U
Pave =
Pinst =
dW G G
= F ⋅v
dt
( Fx = −
∂U
, etc)
∂x
Mm
+C
r
( When only conservative forces do work: ∆E = 0 )
Page 3 of 17
Physics 221 Spring 2006 Exam 1
[1] On the side of a pack of paper you can read: 500 sheets, 75 g/m2, 8 ½ inches × 11
inches. Estimate the weight of the pack (1 inch = 2.54 cm).
(A) 13 N
(B) 22 N
Block P
1kg
(C) 37 N
(D) 62 N
Block R
Block Q
T1
2kg
(E) 112 N
T2
F=6N
3kg
This Figure applies to questions 2 and 3
[2] Block P has mass 1kg, block Q has mass 2kg and block R has mass 3kg. The three
blocks are on a frictionless surface connected with massless strings as shown. A force of
6N is pulling on block R to the right. What is the magnitude of the acceleration of block
P?
(A) 6m/s²
(B) 4m/s²
(C) 3m/s²
(D) 2m/s²
(E) 1m/s²
[3] Continuing with the system in the last problem, if T1 is the tension of the string
connecting blocks P and Q and T2 is the tension of the string connecting blocks Q and R.
What is the ratio: T1:T2 ?
(A) 3:1
(B) 2:1
(C) 1:1
Page 4 of 17
(D) 1:2
(E) 1:3
Physics 221 Spring 2006 Exam 1
[4] A motor uses a massless string to pull a 5kg block at a constant speed of 2m/s across a
level table where the coefficient of kinetic friction between the block and the table is
µk=0.3. When the block has been pulled a distance of 1.5m, how much net work has been
done on it?
(A) 22. 1J
(B) 14.7
(C) 0.0J
(D) –14.7J
(E) –22.1J
[5] These are the snapshots of two objects that travel along parallel straight tracks. The
snapshots are taken at t = 1, 2, 3 and 4 seconds. Assume the motion is smooth (nothing
unexpected happens between the snapshots).
1
1
2
2
3
3
4
4
What is the direction of the velocity of the circle relative to the rectangle, at t = 2 s and at
t = 3 s?
(A)
(B)
(C)
(D)
(E)
t = 2 s:
t = 2 s:
t = 2 s:
t = 2 s:
t = 2 s:
→
→
→
←
←
t = 3 s:
t = 3 s:
t = 3 s:
t = 3 s:
t = 3 s:
→
←
0
←
0
Page 5 of 17
Physics 221 Spring 2006 Exam 1
G
[6] Consider the vectors A and
G
B shown in the diagram which
lie in the xy plane. If A=3 and
B=4, what is the scalar
G G
product A • B ?
G
B
B=4
y
15º
(A) +12
(B) +6
(C) 0
(D) −6
(E) −12
x
15º
G
A
A=3
G
[7] If the vector D = −15 iˆ + 16 ˆj − 12 kˆ , what is the unit vector D̂ ?
(A) Dˆ = +0.60 iˆ + 0.64 ˆj + 0.48 kˆ
(B) Dˆ = −0.60 iˆ + 0.64 ˆj − 0.48 kˆ
(C) Dˆ = +0.35 iˆ + 0.37 ˆj + 0.28 kˆ
(D) Dˆ = −0.35 iˆ + 0.37 ˆj − 0.28 kˆ
(E) Dˆ = −0.15 iˆ + 0.16 ˆj − 0.12 kˆ
[8] Sally weighs 1000N. She is standing in an elevator that is moving downwards at a
constant speed of 4.9m/s. What is the magnitude of the net force acting on Sally?
(A) 0N
(B) 500N
(C) 1000N
Page 6 of 17
(D) 1500N
(E) 2000N
Physics 221 Spring 2006 Exam 1
[9] A 100g block is propelled from rest along a frictionless track by a spring that is
compressed by 10cm from its relaxed length. Further along the track there is a frictionless
upwards incline sloped at 30º above the horizontal. The block slides up the ramp until it
is at a height of 1m above the ground level and then comes momentarily to a stop. What
is the force constant, k, of the spring?
Before
30º
10cm
1m
After
30º
(A) 49J
(B) 98N/m
(C) 196 N/m
(D) 392 N/m
(E) 588 N/m
[10] Consider the following acceleration versus time graph for an object constrained to
move along the x-axis. If at t=0s the object has a velocity of vx = 10 ms , what is the xcomponent of velocity at t=6s?
Acceleration
(m/s²)
6
4
2
1
(A) 15.5m/s
2
(B) 25.5m/s
3
(C) 17.5m/s
Page 7 of 17
4
5
Time (s)
(D) 27.5m/s
6
7
(E) 10.0m/s
Physics 221 Spring 2006 Exam 1
[11] If a particle travels at a constant speed along the track shown, what is the correct
ordering of the magnitudes
of the acceleration at the
G
labeled points? Let aP be
the acceleration at point P,
etc.
(A) a R < a S < a P < aQ
(B) aP < aQ < aR < aS
(C) aP = aQ = aR = aS
(D) a P < aQ < a S < a R
(E) aR < aS < aQ < aP
[12] A block slides up an incline where kinetic friction is present. Half way up the incline
a small rocket is fired that exerts a force on the block perpendicular and down into the
incline. Compare the system the instant before the rocket fires to the system the instant
after the rocket fires. Which of the
Velocity of
following statements is true?
Block
(A) After the rocket fires the weight of the
block increases.
(B) After the rocket fires, the normal force
of the ramp on the block increases
(C) After the rocket fires, the magnitude of
the friction force which the ramp exerts on
the block increases
(D) Both A and B are true
(E) Both B and C are true
Page 8 of 17
Rocket
Force of
rocket
Block
Physics 221 Spring 2006 Exam 1
[13] The figure below shows a position versus time graph for a particle that is constrained
to move along the x-axis. At which of the labeled point(s) is the acceleration positive?
(Note that the segments of the curve which cross the horizontal axis are linear)
Position
Time
(A) R only
(B) P, R and T
(C) S only
(D) Q and U
(E) P and T
[14] In case P a ball of mass m moves in a circle of radius R at a constant angular speed
of ω. In case Q a ball of mass 2m moves in a circle of radius 2R at a constant angular
speed of 2ω. What is the ratio:
(Net force on ball P):(Net force on ball Q)
angular
velocity=2ω
angular
velocity=ω
R
2R
Mass=m
Case P
(A) 1:2
(B) 1:4
(E) None of the above.
Case Q
(C) 1:8
(D) 1:16
Page 9 of 17
Mass=2m
Physics 221 Spring 2006 Exam 1
[15] A car of mass 1000kg traveling at a speed of 10m/s brakes to a stop over a distance
of 40m. What is the magnitude of the braking force acting on the car? Assume that the
braking force is constant.
(A) 1250N
(B) 2500N
(C) 125N
(D) 250N
(E) 625J
[16] A football is kicked from ground level at an angle of 60º with respect to the
horizontal. To make a field goal it must reach a height of at least 5m above the ground.
What is the minimum speed that the ball can be kicked at in order to achieve this height?
Neglect air resistance.
(A) 19.8m/s
(B) 14.0m/s
(C) 11.4m/s
(D) 10.0m/s
(E) 8.1m/s
[17] Robinhood shoots a 0.1kg arrow at the Sheriff of Nottingham from the top of a cliff
of height h=80m. The arrow is launched at a speed of 20m/s. The Sheriff is standing at a
distance d=70m
v0=20m/s
from the base of the
Robin
cliff when the arrow
Hood
strikes him. How
much work does
gravity do on the
arrow while it is in
h=80m
flight?
(A) 78.5J
d
(B) 19.6J
(C) 98.4J
(D) 9.8J
(E) The answer depends on the air resistance the arrow experiences in flight.
Page 10 of 17
Sheriff of
Nottingham
Physics 221 Spring 2006 Exam 1
[18] At t=0s a 5kg block is at point P on a ramp inclined at 10º with an initial velocity
sliding up the ramp of v0=10m/s. The coefficient of static friction between the block and
the ramp is µs=0.2 and the coefficient of kinetic friction between the block and the ramp
is µk=0.1. How long does it take the block to return to point P?
v0=10m/s
µk=0.1
µs=0.2
5kg
10º
P
(A) 2.0s
(B) 7.5s
(C) 10.9s
(E) The block never returns to point P.
(D) 27.2s
[19] A man exerts a 300-N force to pull an 80-kg crate up an incline with a rope that
makes an angle with the incline as shown below. What is the work done by the man when
he pulls the crate 2.0 m along the incline?
300N
30°
80kg
15°
(A) 400 J
(B) 420 J
(C) 520 J
Page 11 of 17
(D) 580 J
(E) 600 J
Physics 221 Spring 2006 Exam 1
[20] A block is placed near the edge of a horizontal turntable of radius 5m that is initially
at rest. It is attached to a motor that gives it an angular acceleration α. The coefficient of
static friction between the block and the turntable is µs=0.2. What is the maximum value
of the angular acceleration α that the motor can deliver so that the block will not slide the
instant after the turntable begins to move?
(A) 0.20 rad/s²
(B) 0.39 rad/s²
(C) 0.63 rad/s²
[21]
In the system depicted at right, a 1kg block
rests on a horizontal table. The coefficient of
static friction between the block and the table
is µs=0.6. The coefficient of kinetic friction
between the block and the table is µk=0.3.
The 1kg block is attached via an ideal
massless string over an ideal massless pulley
to a 3kg block which can move vertically
without resistance. Initially the 1kg block is
held fixed and is released at t=0. What is the
magnitude of the acceleration of the 1kg
block after it is released?
(A) 0.0 m/s²
(B) 5.9 m/s²
(C) 6.6 m/s²
(D) 23.5 m/s²
(E) 26.5 m/s²
Page 12 of 17
(D) 3.9 rad/s²
(E) 9.8 rad/s²
1kg
µs=0.6
µk=0.3
3kg
Physics 221 Spring 2006 Exam 1
[22] John travels 100km north at 50km/hr and then travels 100km south at 30km/hr.
What is the magnitude of his average velocity during the trip?
(A) 0.0 km/hr
(B) 40.0 km/hr
(C) 37.5 km/hr
(D) 35.3 km/hr
(E) 20.0 km/hr
[23] A particle of mass 0.5 kg moves on a circle of radius 2m. The angular position in
radians is given by θ = (4 s −4 )t 4 − (2s −2 )t 2 . What is the magnitude of the tangential
component of the acceleration of the particle at t=0.5s?
(A) 0m/s²
(B) 8m/s²
(C) 16 m/s²
(D) 64 m/s²
(E) 128 m/s²
[24] The graph below shows the position dependent net force acting on a 2kg particle
moving along the x-axis. The object is initially released from x=0m moving to the right.
When it gets to x=10m it has a velocity of 6m/s to the right. What was the object’s kinetic
energy when it was released?
(A) 12J
(B) 24J
(C) 30J
(D) 42J
(E) 48J
Force (N)
4
2
Position (m)
8
0
2
4
6
−2
Page 13 of 17
10
Physics 221 Spring 2006 Exam 1
[25] A cannon is fired at a medieval castle perched on a vertical cliff 124m high. The
cannon ball strikes the foot of the castle, just on the edge of the cliff. The cannon ball is
fired from a spot 300m from the base of the cliff and is aimed at an angle 45º above the
horizontal. How long after the cannon ball is fired does it strike the castle? Neglect air
resistance.
Impact
Castle
(A) 4s
Point
(B) 6s
(C) 8s
(D) 10s
t=?
124m
(E) Cannot be determined
without more information
45º
Cannon
300m
[26] Which of the arrows correctly indicates the direction of the acceleration of a particle
that moves clockwise at a constant speed around the path shown below?
(A) P, R and T
(B) P, R, T and U
(C) Q and S
(D) R and U
(E) None of the arrows correctly
indicates the direction of acceleration.
Q
P
R
U
T
S
Page 14 of 17
Physics 221 Spring 2006 Exam 1
[27] A 10-kg weight hangs from two ideal massless ropes as shown below. Find the
tension on the left rope.
(A) 33 N
(B) 49 N
(C) 85 N
(D) 98 N
(E) 113 N
60°
TL?
60°
10kg
[28] A 40N block is hung from a rope attached to a scale via a pulley as shown. The scale
is then attached to a wall and reads 40N. What will the scale read when it is instead
attached to another 40N block over another pulley, as shown in the second figure?
(A) 0N
(B) 20N
(C) 40N
(D) 60N
(E) 80N
???N
40N
40N
Page 15 of 17
40N
40N
Physics 221 Spring 2006 Exam 1
[29] A cannon that fires a shell at 300m/s is located on the slope of a hill. The slope is
inclined downwards at an angle 30°
E:120
below the horizontal as shown and
D:90°
extends very far in each direction.
C:60°
At which of the indicated angles
between the sloping ground and the
Horizontal
B:30°
initial velocity should the cannon be
Cannon
fired in order to maximize the time
A:15°
that the shell is in the air? Neglect air
resistance.
30°
(A) 15°
(B) 30°
(C) 60°
(D) 90°
(E) 120°
Ground
[30] (Note: Extra credit problem)
A cannon, located on planet X with acceleration of gravity gX , fires a cannon ball from
the top of a cliff of height h at an angle θ>0 above the horizontal. The projectile strikes
the ground with a speed of vf=49m/s at an angle of 60º below the horizontal as shown. If
the cannon ball was fired with a speed of v0=29.4m/s, what angle θ was the cannon ball
fired at? Neglect air resistance.
(A) 20º
(B) 34º
(C) 50º
(D) 56º
(E) The answer cannot be determined without more information.
v0=29.4m/s
Cannon
θ
h
60º
vf=49.0m/s
Page 16 of 17
Physics 221 Spring 2006 Exam 1
You may record your answers here and take this page with you to compare with the
posted answers.
1
11
21
2
12
22
3
13
23
4
14
24
5
15
25
6
16
26
7
17
27
8
18
28
9
19
29
10
20
30
Page 17 of 17