Mark answers in spaces 27-52 on the answer sheet
No class Friday March 12
No class Friday March 12
PHYSICS 221
Spring 2004
EXAM 2: March 11 2004 8:00pm—9:30pm
Name (printed): ____________________________________________
ID Number: ______________________________________________
Section Number: __________________________________________
INSTRUCTIONS:
Each question is of equal weight, answer all questions. All questions are multiple choice.
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. Note also formula sheets pages 11-13.
"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⇒31. 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 the record sheet (page 14) and take this page with
you for comparison with the answer key to be posted later.
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. There are 26
questions on this exam labeled 27-52.
Mark answers in spaces 27-52 on the answer sheet.
Best of luck, David Atwood and Anatoli Frishman
Physics 221 2004 S Exam 1
Page 1 of 16
Mark answers in spaces 27-52 on the answer sheet
[27] A particle of mass 1kg travels in uniform circular motion at the speed of 4m/s.
How much work is done in joules on the particle by centripetal force acting on it during
one quarter of one revolution
(A) 16π J
(B) 8π J
(C) 4π J
(D) 0 J
(E) None of the above
[28] A bullet with a mass of 3.00g and a speed of 400m/s penetrates a wooden block
horizontally to a depth of 2.00cm. Assume that a constant resistance force slows the
bullet. What is the magnitude of this resistance force?
(A) 6k N
(B) 12 kN
(C) 24 kN
(D) 48 kN
(E) 96 kN
[29] A 100g ball initially at rest is dropped from a height of h=50.0cm above a spring
of negligible mass. The ball compresses the spring to a maximum displacement of 5.0cm.
What is the spring force constant k?
(A) 19.6 N/m
(B) 196 N/m
(C) 294 N/m
(D) 392 N/m
(E) 490 N/m
[30] A 18g bullet is shot vertically upwards into a 10kg block. The block lifts upwards
9.0mm. If the bullet penetrates the block in a time interval of 1ms the initial kinetic
energy of the bullet is closest to:
(A) 0.0016 J
(B) 0.88 J
(C) 250 J
(D) 330 J
(E) 490 J
Physics 221 2004 S Exam 1
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[31] Particle #1 of mass 1kg is initially located on the –y axis and is moving with a
velocity of + 2 ˆj m / s while particle #2 of mass 2kg is initially located on the –x axis and
is moving with a velocity of + 1iˆ m / s . They meet near the origin and collide, after the
collision, the speed of the particle #1 is 1m/s in a direction 45º counterclockwise from the
x-axis. Which of the following statements is true concerning this collision. The system of
particle #1 and particle #2 is not subject to any external forces:
(A) The collision is elastic
(B) The collision is inelastic, but not totally inelastic
(C) The collision is totally inelastic
(D) The kinetic energy of the two objects increases after the collision
(E) This collision is not physically possible
[32] A cannon ball is fired at a speed of 80m/s from a cannon located 50m from the
base of a cliff which is 100m high. It follows a trajectory and strikes a spot on the level
ground above the cliff. What is the speed of the cannon ball on impact. Neglect air
resistance.
Impact
point
(A) 44.4 m/s
Cannon
(B) 50.0 m/s
(C) 66.6 m/s
(D) 73.6 m/s
(E) Cannot be determined with the given information.
100m
50m
[33] A force of 4.0N acts on a 12kg body initially at rest. Compute the instantaneous
power due to the force at t=3.0s
(A) 3W
(B) 4W
(C) 6W
(D) 8W
(E) 12W
Physics 221 2004 S Exam 1
Page 3 of 16
[34] Four blocks of mass m1=1kg, m2=2kg, m3=3kg, m4=4kg are on a frictionless
horizontal surface as shown on the figure below. The blocks are pressing against each
other. A force FL=30N is applied to the left block and is directed to the right. Another
force FR=50N is applied to the right block, and is directed to the left. Initially, the blocks
are moving left at a rate of 20m/s. When the 2kg block has slid 2m to the left, how much
work has the 3kg block done on it?
v0=20m/s
FL=30N
1kg
Displacement = 2m
Work done on 2kg block
by 3kg block =?
2kg
3kg
4kg
FR=50N
Frictionless surface
(A) –72J
(B) +72J
(C) –40J
(D) +40J
(E) –100J
[35] The figure below shows potential energy versus position for a particle that is
confined to move in 1 dimension. Which of the labeled points on the graph correspond to
points of unstable equilibrium?
(A) P and T
(B) R only
(C) R and P
(D) Q and S
(E) T only
Physics 221 2004 S Exam 1
Page 4 of 16
[36] The graph below shows the potential energy of a 1kg particle confined to move
along the x-axis as a function of position. The particle is released from point O with
initial kinetic energy K=20J and it is moving to the right. Which of the labeled points is a
turning point for the motion of the particle:
(A) Point A
(B) Point B
(C) Point C
(D) Point D
(E) Point E
[37] A 20g stone has kinetic energy of 100J and is not rotating in any way. What is the
magnitude of its momentum?
(A) 1.0 Ns
(B) 2.0 Ns
(C) 3.0 Ns
(D) 4.0 Ns
(E) 5.0 Ns
[38] If a collision is inelastic then which of the following must be true:
(A) The total kinetic energy is conserved
(B) The total linear momentum is not conserved
(C) The total kinetic energy is not conserved
(D) The velocity of the center of mass of the system changes.
(E) The two particles must stick together after the collision.
[39] On a 1 dimensional air track, a particle of mass 100g is moving with a velocity of
3m/s. The particle collides with another particle of mass 200g. After the collision, both
particles have the same velocity of 1m/s. What was the initial velocity of the 200g
particle?
(A) 0 m/s
(B) +1 m/s
(C) -1m/s
(D) +2m/s
(E) -2m/s
Physics 221 2004 S Exam 1
Page 5 of 16
[40] What is the y coordinate of the center of mass of the 3mX3m metal slab with a
1m × 1m square cut out of it depicted below. The slab is of uniform thickness and density.
(A) 1.375m
(B) 1.500m
(C) 1.625m
(D) 1.750m
(E) 2.000m
[41] The angular position of a turntable in radians is given as a function of time by
θ = Ae − Bt where A = 5 and B=2 s-1. What is the angular acceleration, α, of the turntable
at t=1s?
(A) +10.0 s−2
(B) +2.71 s−2
(C) –2.71 s−2
(D) +1.35 s−2
(E) –1.35 s−2
[42] Two blocks are free to slide along a frictionless track along the x-axis. At t=0s
block A is located at x=0m and block B is located at x=10m. Block A has a mass of 1kg
and an initial velocity of +5m/s. Block B has a mass of 4kg and an initial velocity of
+1m/s. The two blocks collide with a perfect elastic collision. What is the final velocity
of block A?
(A) +1.8 m/s
(B) +2.6 m/s
(C) +1.4 m/s
(D) –2.6 m/s
(E) –1.4 m/s
Physics 221 2004 S Exam 1
Page 6 of 16
[43] A wheel rotating with a constant angular acceleration turns through 12 revolutions
during a 3 second time interval. Its angular velocity at the end of the time interval is
13rad/s. What is the angular acceleration?
(A) -4.1 rad/s²
(B) -5.1 rad/s²
(C) -6.1 rad/s²
(D) -7.1 rad/s²
(E) -8.1 rad/s²
[44] A particle moves on a circle of radius 2m. The angular position of the particle is
given by θ = (3 s −4 )t 4 − (1 s −1 )t . What is the magnitude of the radial component of the
acceleration of the particle (towards the center of the circle) at t=1s?
(A) 3.0 m/s²
(B) 4.5 m/s²
(C) 22 m/s²
(D) 121 m/s²
(E) 242 m/s²
[45]
What is the cross product
(A) + 15iˆ − 10 ˆj − 12kˆ
(2iˆ + 3 ˆj ) × (4iˆ + 5kˆ) ?
(B) + 15iˆ + 10 ˆj − 12kˆ
(C) − 15iˆ + 10 ˆj + 12kˆ
(D) − 15iˆ − 10 ˆj + 12kˆ
(E) + 15iˆ − 10 ˆj + 12kˆ
[46] Consider the configuration below. The circles represent particles of mass 1kg.
The empty squares do not represent any mass but are proposed centers of mass of the
configuration. Which of the squares is the correct center of mass?
(A) Square A
(B) Square B
(C) Square C
(D) Square D
(E) Square E
Physics 221 2004 S Exam 1
Page 7 of 16
[47] A 2kg projectile is fired from a cannon resting on level ground as shown in the
diagram below. When the projectile reaches the highest point of its trajectory where the
vertical component of its velocity is 0, it
has move a distance of 100m
Impact of second piece
horizontally. At this point an explosive
charge breaks it into two 1kg pieces.
One of the pieces lands at the same
location as the cannon. At the same
moment the other piece of the projectile
hits the ground. How far from the
cannon does the other piece land?
Neglect air resistance.
Impact of
(A) 100m
(B) 200m
First piece
(C) 300m
(D) 400m
(E) Cannot be determined without
more information.
Both pieces strike the ground at the same time
[48] A uniform square slab is 4.00m on a side with negligible thickness. It has a mass
of 200kg. If it is originally lying on the flat ground, how much work is needed to stand it
on end?
(A) 7.84 kJ
(B) 5.88 kJ
(C) 3.92 kJ
4m
Slab
(D) 2.94 kJ
Mass=200kg
(E) 1.96 kJ
Work=?
Before
Physics 221 2004 S Exam 1
After
Page 8 of 16
4m
[49] Consider a hollow sphere where the mass M which is uniformly concentrated on
the surface. If the sphere is of radius R, what is the moment of inertia around an axis that
is tangent to the surface of the sphere.
(A) (2/3)MR²
(B) MR²
(C) (4/3)MR²
(D) (5/3)MR²
(E) 2MR²
[50] As shown in the picture below, four different 1kg objects with radius 5cm are
mounted on horizontal axels have identical cords of 2m attached to identical 1kg weights
wrapped around them. In all cases the cords unroll without slipping and the axels are
frictionless.
In case P, the object is a solid cylinder with uniform density. In case Q the object is a
hoop with the mass concentrated on the rim. In case R the object is a solid sphere of
uniform density. In case S the object is a hollow spherical shell with the mass
concentrated on the
surface. If the four
weights are released from
rest as shown from a
point 2m above the
ground, in which order do
they strike the ground?
(A) P, Q, R, S
(B) R, P, S, Q
(C) R, S, P, Q
(D) Q, S, P, R
(E) S, P, Q, R
Physics 221 2004 S Exam 1
Page 9 of 16
[51] Consider the arrangement depicted below. A block of mass 1kg is at rest at a point
4m above the ground on a frictionless ramp at angle 30° from the horizontal. The block is
released and slides down the ramp. It then slides along a rough surface where the
coefficient of kinetic friction µk=0.5. How far along the rough surface does the block
slide from the bottom of the ramp before coming to rest?
(A) 1.0 m
(B) 2.0 m
(C) 4.0 m
(D) 7.0 m
(E) 8.0 m
[52] The figure below shows three forces in the xy plane acting on a blob. Determine
the total torque on the blob due to these forces about the indicated center of torque. Take
the z-axis up, out of the page.
(A) +2.00 k̂
(B) –2.00 k̂
(C) +2.50 k̂
(D) –2.50 k̂
(E) +3.25 k̂
Physics 221 2004 S Exam 1
Nm
Nm
Nm
Nm
Nm
Page 10 of 16
Formula Sheet for Exam 1
1. Physical Constants
(numerical value used to derive answers in exam):
1.1) Acceleration of gravity on Earth’s Surface: g=9.8m/s²
1.2) Radius of Earth: Rearth=6.38×106m
1.3) Mass of Proton: mp=1.67×10-27kg
3. Vectors
G G
G G
3.1) Dot Product: A ⋅ B = Ax B x + Ay B y + Az B z =| A || B | cosθ
G
G
where θ is the angle between A and B .
G
3.2) Components: A = Ax iˆ + Ay ˆj + Az kˆ
G
G G
3.3) Magnitude: | V |= V = V x2 + V y2 + V z2 = V ⋅ V
5. One Dimensional Motion
5.1) Average Velocity: v = ∆x / ∆t
5.2) Instantaneous Velocity: v = dx / dt
2. Calculus
2.1)
n −1
d
dx
x = nx
d
dx
sin x = cos x
n
x n +1
∫ x dx = n + 1
d
dx cos x = − sin x
n
4. Algebra
4.1) The solutions to ax 2 + bx + c = 0
are x =
1
2a
(− b ±
b 2 − 4ac
)
6. Forces
G
G
6.1) Newton’s Second: F = ma
G
G
6.2) Newton’s Third: FAB = − FBA
6.2) Kinetic Friction: f k = µ k N
6.4) Static Friction: f s ≤ µ s N
6.5) Centripetal Force: F =
v x = v0 x + a x t
mv 2
R
x = x0 + v0 x t + 12 a x t 2
5.3) For Constant Acceleration only: v 2 − v 2 = 2a ( x − x )
0x
0
x
x
x − x0 1
= 2 (v x + v 0 x )
t
7. Three Dimensional Motion
G
7.1) Position Vector: r = xiˆ + yˆj + zkˆ
G
G
G
G
2 G
7.2) Velocity and Acceleration: v = dtd r
a = dtd v = dtd 2 r
G G G
v = v0 + at
G G G
G
r = r0 + v 0 t + 12 at 2
7.3) Constant Acceleration only: v 2 − v 2 = 2aG ⋅ (rG − rG )
0
G G0
r − r0 1 G G
= 2 (v + v 0 )
t
ω = 2πf
v = Rω
7.4) Circular Motion: f = 1 / T
7.4a) Angular Velocity: ω = dθ / dt
7.5) Centripetal Acceleration: a rad = Rω 2 = v 2 / R = ( 4π 2 R ) / T 2
G
G
G
7.6) Changing Reference Frames: v PA = v PB + v BA
Physics 221 2004 S Exam 1
Page 11 of 16
Formula Sheet for Exam 2
8. Kinetic Energy and Work
8.1) Linear Motion: K = 12 mv 2
8.2) Rotational Motion: K rot = 12 Iω 2
G G
8.3) Work by a constant force W = F ⋅ s = Fs cosθ
8.4) Work done by a variable force in 1 dim:
x2
9. Potential Energy
9.1) Gravitational: Ugrav=mgy
9.2) Spring: Uspring=kx²/2
dU
dx
9.4) Conservative force from potential in 3d: a
9.3) Force from potential in 1D: Fx ( x) = −
W = ∫ Fx dx
x1
G G P2
8.5) Work in 3D: W = ∫ F ⋅ dl = ∫ F cos φ dl
P2
P1
8.6) Power: P=dW/dt
P1
G G
P = F ⋅v
10. Momentum and Impulse
G
G
G G
10.1) Momentum: p = mv F = ddtp
G t2 G
G
G
10.2) Impulse: J = ∫ Fnet dt = p 2 − p1
t1
G
G
10.3) Center of mass position: M tot rcm = ∑ mi ri
G
G
10.4) Center of mass velocity: M tot vcm = ∑ pi
G
G
G
10.5) Center of mass acceleration: M tot a cm = ∑ Fi = Fexternal
11. Collisions
11.1) 1-dimensional totally inelastic collision: v1 f = v 2 f = v cm
11.2) 1-dimensional elastic collision:
v1 f = 2vcm − v1i
v 2 f = 2vcm − v 2i
G
G
G
11.3) 3-dimensional totally inelastic collision: v1 f = v 2 f = v cm
Physics 221 2004 S Exam 1
12. Rotation
12.1) Angular velocity ω = ddtθ
12.2) Angular Acceleration α =
dω
dt
2
12.3) Circular motion: a rad = Rω ; a tan = rα .
12.4) Moment of Inertia: I = ∑ mi Ri2
12.5) Parallel Axis Thm.: I P = I cm + Md 2
G G G
12.6) Torque: τ = r × F
Page 12 of 16
Physics 221 2004 S Exam 1
Page 13 of 16
Record Sheet
You may fill in this sheet with your choices, detach it and take it with you after the exam
for comparison with the posted answers
21
31
41
51
22
32
42
52
23
33
43
53
24
34
44
54
25
35
45
55
26
36
46
56
27
37
47
57
28
38
48
58
29
39
49
59
30
40
50
60
Physics 221 2004 S Exam 1
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Scratch Paper (intentionally left blank)
Physics 221 2004 S Exam 1
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Scratch Paper (intentionally left blank)
Physics 221 2004 S Exam 1
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