Physics 221.
Final Exam
Spring 2003
The situation below refers to the next two questions:
A block of mass m = 0.2 kg starts from rest at point A and slides down a frictionless
curved surface to point B, where its speed is v = 8 m/s. Then, it slides along a rough
horizontal surface for d =10 m and comes to rest at point C.
A
h
B
C
d
1. What is the initial height h of the block?
a.
b.
c.
d.
e.
h = 1.2 m
h = 2.5 m
h = 3.3 m
h = 4.6 m
h = 5.1 m
2. Find the coefficient of kinetic friction between the block and the horizontal surface
between B and C.
a.
b.
c.
d.
e.
µk = 0.1
µk = 0.2
µk = 0.3
µk = 0.4
µk = 0.5
Page 1 of 19
Physics 221.
Final Exam
Spring 2003
The situation below refers to the next two questions:
The graph below shows the potential energy U and the total mechanical energy E of a
particle as a function of position x. The only force acting on this particle is the force
associated to this potential energy.
U (J)
E = 5.0 J
x (m)
1
2
3
4
5
6
3. At which position does the particle have the greatest kinetic energy?
a.
b.
c.
d.
e.
At x = 1 m
At x = 2 m
At x = 4 m
At x = 5 m
At x = 6 m
4. Which of the following statements about the force on the particle at x = 3 m is true?
a. It is zero
b. It points in the −x direction
c. It points in the +x direction
d. The particle can never be at x = 3 m, so there is no force to be discussed.
e. The direction of the force depends on the direction of the velocity of the particle.
Page 2 of 19
Physics 221.
Final Exam
Spring 2003
The situation below refers to the next two questions:
A rope is attached to the handle of a bucket with a stone of mass m inside. A person
swirls the whole system in vertical circles as shown in the figure below. The distance
between the stone and the center of the circle is L = 1.5 m.
L
5. What is the minimum speed that the system must have at the highest point of the
trajectory if the stone is to stay in contact with the bottom of the bucket?
a.
b.
c.
d.
e.
vmin = 3.8 m/s
vmin = 4.2 m/s
vmin = 5.7 m/s
vmin = 6.1 m/s
vmin = 7.8 m/s
6. As the bucket moves from the highest to the lowest point in its trajectory, the work
done by the tension on the rope is ________ and the work done by gravity is ________.
a.
b.
c.
d.
e.
negative, negative
zero, negative
positive, negative
negative, positive
zero, positive
Page 3 of 19
Physics 221.
Final Exam
Spring 2003
The situation below refers to the next two questions:
A firecracker rocket is flying vertically up when it explodes in two fragments of masses
m and M (> m). The bigger mass is ejected to the left and the small mass to the right.:
7. During this process, it is reasonable to assume that:
a.
b.
c.
d.
e.
total kinetic energy is conserved, but total linear momentum is not conserved
total linear momentum is conserved, but total kinetic energy is not conserved
both total kinetic energy and total linear momentum are conserved
total linear momentum is conserved and the kinetic energy of each part is conserved.
both kinetic energy and linear momentum of each part is conserved
8. Immediately after the explosion, the center of mass of the system moves:
a. Up
b. Down
c. Up and to the left
d. To the left
e. It does not move.
9. A marble of mass m = 8.0 g is fired into a block of soft wood hung from two wires as
shown below.The block has a mass M = 2.0 kg and the marble imbeds itself in the
block causing it to rise to a maximum height h = 0.12 m. Find the speed v of the
marble just before impact. (Ignore the mass of the wires)
m
v
M
h
a. v = 290 m/s
b. v = 385 m/s
c. v = 400 m/s
d. v = 425 m/s
e. v = 440 m/s
Page 4 of 19
Physics 221.
Final Exam
Spring 2003
10. A car must achieve an average speed of 250 km/h on a track of total length of 1500
m. The car travels the first half of the track at an average speed of 200 km/h. Therefore,
the average speed needed in the second half of the track has to be:
a. 333 km/h
b. 300 km/h
c. 275 km/h
d. 265 km/h
e. 260 km/h.
11. Two balls are thrown from the roof of a building with an initial speed of 10 m/s. Ball
number 1 is thrown vertically downward and ball number 2 vertically upward. Ball 1 hits
the street below the building in 4 seconds. How much later does the second ball hit the
ground? (Take g=10 m/s2).
a. ∆t = 1s
b. ∆t = 2s
c. ∆t = 3s
d. ∆t = 4s
e. ∆t = 5s
12. An object is thrown at ground level with an initial speed of 20 m/s. It hits the ground
2 seconds later. At what angle above the horizontal was the object thrown?
a. 10o
b. 20o
c. 30o
d. 40o
e. 45o
Page 5 of 19
Physics 221.
Final Exam
Spring 2003
13. A point on the rim of a 25-cm-radius wheel has a constant centripetal acceleration of
4.0 m/s2. The tangential acceleration of that point is
a. 6.0 m/s2
b. 4.0 m/s2
c. 2.0 m/s2
d. 1.0 m/s2
e. None of the above.
14. When a man holding weights and spinning on a frictionless rotating stool extends his
arms horizontally and thereby doubles its moment of inertia, the rotational kinetic energy
is:
a. twice as much as before
b. half as much as before
c. the same as before
d. four times as much as before
e. one fourth as much as before.
Page 6 of 19
Physics 221.
Final Exam
Spring 2003
The situation below refers to the next two questions:
A uniform solid sphere rolls down an incline. The magnitude of the acceleration of the
g
center of mass is observed to be 10 .
15. What is the angle θ between the incline plane and the horizontal?
a.
b.
c.
d.
e.
θ = 4°
θ = 8°
θ = 15°
θ = 20°
θ = 33°
16. If a frictionless block were to slide down the same incline, its acceleration a would
be:
a.
b.
c.
d.
e.
g
10
g
a=
10
g
a<
10
The answer depends on the ratio of the block’s and sphere’s masses
The answer depends on the radius of the sphere and the height of the block
a>
Page 7 of 19
Physics 221.
Final Exam
Spring 2003
17. A uniform rod is free to rotate about its center of mass, that we shall take as the
origin, as shown in the figure. Its initial position is such that the end labeled P is at rP =
(2i − 3j) m. A force F = (2i + 5j) N is applied at that point.
y
●
x
P
What is the torque due to this force on the rod about the origin?
a.
b.
c.
d.
e.
τ=
τ=
τ=
τ=
τ=
(−27 k) Nm
(−11 k) Nm
(−3 k) Nm
(16 k) Nm
(21 k) Nm
18. The mobile shown below is made of four identical objects of mass m. The rods and
the strings are massless. The upper rod has length L and is supposed to be horizontal.
Find the distance d between the left end of the rod and the point from which the mobile
should be hung from the ceiling.
a.
b.
c.
d.
e.
L
4
L
d=
3
2L
d=
3
3L
d=
4
L
d=
2
d=
L
d
Page 8 of 19
Physics 221.
Final Exam
Spring 2003
19. A small dust particle with mass m = 10−9g and electrostatic charge q = 3×10–17 C has
been suspended between the plates of a horizontal parallel plate capacitor so that the
electrostatic force compensates the gravitational force. The magnitude of the electric
field inside the capacitor is:
a.
b.
c.
d.
e.
E = 105 V/m
E = 3×105 V/m
E = 3×10–5 V/m
E = 5×105 V/m
E = 5×10–3 V/m
20. Two point charges Q1 and Q2 are placed at (x = a, y = 0) and (x = 0, y = 2a),
respectively, as shown in the figure below. Find the work done by the electric field when
a third charge q is brought from infinity to the origin.
y
(x = 0, y = 2a)
Q2
Q1 = 3.0 µC
Q2 = 2 Q1 = 6 µC
q = –2.0 µC
a = 5.0 cm
Q1
q
a.
b.
c.
d.
e.
x
(x = a, y = 0)
W = 2.2 J
W = 1.1 J
W = 0.31 J
W = −1.3 J
W = −5.4 J
Page 9 of 19
Physics 221.
Final Exam
Spring 2003
21. A pear-shaped conductor (gray shape in the figures) has a certain net charge Q ≠ 0.
Which of the figures is a reasonable representation of the electric field lines in the region
around the conductor?
(b)
(a)
(c)
(d)
(e)
Page 10 of 19
Physics 221.
Final Exam
Spring 2003
22. Charge is distributed uniformly with the volume charge density ρ throughout the
volume of an infinitely long cylinder of radius R. Find the magnitude of the electric field
at a distance r>R from the cylinder axis.
E=
ρR
2ε 0 r
E=
ρR
2πε 0 r 2
E=
ρ
2ε 0 r 2
E=
ρ R2
2ε 0 r
E=
ρ
4πε 0 r 2
a.
b.
c.
d.
e.
23. Three capacitors with the same shape and dimensions are made of three different
conductors: gold, copper and aluminum. The conductivity of gold is greater than the
conductivity of copper, and the conductivity of copper is greater than the conductivity of
aluminum. Rank the capacitances of these capacitors.
a.
b.
c.
d.
e.
Cgold > Ccopper > Caluminum
Cgold < Ccopper < Caluminum
Cgold = Ccopper = Caluminum (if they are parallel plate capacitors only)
Cgold = Ccopper = Caluminum (always)
Not enough information to answer the question.
24. If you stretch a cylindrical wire and it remains cylindrical, how does this affect the
resistance of the wire (measured end to end along its length)?
Before
a.
b.
c.
d.
e.
After
It increases.
It decreases.
It remains the same.
The result could be different for different materials.
The result could be different for different cylinders and different stretchings.
Page 11 of 19
Physics 221.
Final Exam
Spring 2003
The situation below refers to the next two questions:
A copper wire has cross-sectional area 2.0×10–6 m2 and length 4.0 m. The resistivity of
copper is ρ = 1.7×10−8 Ωm. A current of 2.0 A is uniformly distributed across the crosssection.
25. What is the magnitude of the electric field along the wire?
a.
b.
c.
d.
e.
E = 1.7×10–2 V/m
E = 2.7×10–2 V/m
E = 3.7×10–2 V/m
E = 4.7×10–2 V/m
E = 5.7×10–2 V/m
26. How much electric energy is transferred to thermal energy in 30 min?
a.
b.
c.
d.
e.
185 J
245 J
375 J
435 J
525 J
27. The figure shows a circuit containing one ideal battery of emf ε =12 V, and four
resistances with the following values: R1= 20 Ω, R2 = 20 Ω, R3 = 30 Ω, R4 = 8.0 Ω. What
is the magnitude of the current through the battery?
ε
R3
R1
R2
R4
a.
b.
c.
d.
e.
I = 0.10 A
I = 0.20 A
I = 0.30 A
I = 0.40 A
I = 0.50 A
Page 12 of 19
Physics 221.
Final Exam
Spring 2003
28. In the circuit shown below, ε =12.0 V, R = 1.40 MΩ, and C = 2.00 µF. The capacitor
is initially uncharged and the switch is open. The switch is closed at t = 0. How long does
it take for the charge to build up to 16.0 µC?
a.
b.
c.
d.
e.
R
ε
t = 1.1 s
t = 1.4 s
t = 2.1 s
t = 2.8 s
t = 3.1 s
C
Page 13 of 19
Physics 221.
Final Exam
clamp
force
probe
spring
X
lab
table
135 cm
plate
motion
detector
mesh
Spring 2003
29. In lab, you studied the vertical oscillation of a
plate. Position data collected by the computer is
referenced to the X axis shown in the figure at the
right.
Assume that the plate hangs at its equilibrium
position of X = 50 cm. Consider two trials of its
motion which differ only in the way in which they are
begun, namely,
1. In trial #1, the plate is displaced
downward to X = 60 cm and released at
rest;
2. In trial #2, the plate is displaced
downward to X = 70 cm and released at
rest.
For these two trials, compare:
1. the time required for the plate to first return to its release point;
2. the maximum acceleration experienced by the plate.
For trial #2 (as compared to trial #1),
a.
b.
c.
d.
e.
the time to return is twice as long, while the maximum acceleration is the
same;
the time to return is twice as long, while the maximum acceleration is twice
as large;
the time to return is twice as long, while the maximum acceleration is four
times as large;
the time to return is the same, and the maximum acceleration is the same;
the time to return is the same, while the maximum acceleration is twice as
large.
Page 14 of 19
Physics 221.
Final Exam
X
0
Spring 2003
As you did in lab, consider the motion of a cart which
is given an initial velocity up an inclined track toward a
"motion detector". Assume the cart goes part of the
way up, and then returns back down the track. (As was
done in lab, assume the sensor gives positions relative
to the X axis illustrated above).
30. Which of the following best graphs illustrates the velocity, VX , of the cart (after
leaving your hand) versus time?
Vx
Vx
t
0
Vx
Vx
t
A
Vx
t
B
t
C
t
D
E
31. Which of the following best illustrates the acceleration, aX, of the cart versus time
(during the same period)?
ax
ax
ax
t
0
A
ax
t
B
ax
t
C
t
D
t
E
Page 15 of 19
Physics 221.
Final Exam
Spring 2003
32. Consider the collision of two identical hockey pucks on a smooth ice rink. Assume
that by analyzing the videotape of the collision, various but not all components of the
momenta of the two pucks before and after collision have been determined and are
recorded in the table below.
Assume that there is negligible friction with the ice, but that the pucks are soft and that
considerable kinetic energy is “lost” in the collision. Under these assumptions, what is
the value (if it can be determined) of the entry marked with the “X”?
Px
Py
a)
b)
c)
d)
e)
Before Collision
Puck #1 Puck #2
0.42
-0.92
0.70
0.30
After Collision
Puck #1 Puck #2
-0.26
X
0.60
-0.02
-0.24
+0.26
+0.76
Cannot be determined from the information given.
33. The trajectory of a puck sliding
freely on a level air table is recorded
(as done in 221 lab) on a piece of
(metric) graph paper, shown at the
right. Assume that the spark
generator was operating at a rate of
60 Hertz, and that the figure at the
right is approximately full scale.
Y
X
Estimate the magnitude of the
X component of the velocity
of the puck.
a) vx = 103 cm/s
b) vx =84 cm/s
c) vx =60 cm/s
d) vx = 0.02 cm/s
e) It is not possible to calculate an estimate without a protractor to measure
angles.
Page 16 of 19
Physics 221.
Final Exam
Spring 2003
34. In the rotational motion experiment, the following graph was obtained when the
wheel of the apparatus which you used was rotated by hand. Provide the t likely
explanation for this particular graph.
a.
b.
c.
d.
e.
#1
The wheel was rotated rapidly then stopped for a second or two, then rotated
rapidly, then stopped again, and so on.
The wheel was rotated at different velocities, increasing in steps as time went
on.
The wheel was rotated slowly, and the angular encoder on the wheel axis has
a resolution of 1/20 of a revolution.
The wheel was rotated slowly, and the angular encoder on the wheel axis has
a resolution of 1/200 of a revolution.
The apparatus likely was malfunctioning.
35. Consider two conducting spheres mounted on insulating
rods and located (with the relative positions shown) in a region
of large electric field, near a negatively charged rod as shown.
#2
Assume that both of the spheres are initially uncharged. Then
one of the two spheres is displaced slightly so that the two
spheres touch each other briefly. Assume that neither touches
the rod, and that their relative positions always are as shown.
Which of following are possible values for the resulting charge
on each sphere, #1 and #2, respectively, after the sequence of events described?
A
B
C
D
E
#1
+3.0 nC
−3.0 nC
−3.0 nC
+3.0 nC
0 nC
#2
−3.0 nC
+3.0 nC
−3.0 nC
+3.0 nC
0 nC
Page 17 of 19
Physics 221.
Final Exam
Spring 2003
36 As done in lab, a student, seat, chain, and two load cells are at rest and supported by
cables attached to the upper (sensitive) fittings of the two load cells. The cell readings
and those of the large protractors are
given in the table below.
protractors
load cells
0
0
chain
Y
seat
X
LEFT
RIGHT
Cell reading
531 N
600 N
Protractor
reading
60°
50°
Use this information to estimate the X component of the force exerted by the left cell
upon the end of the left chain.
a. +266 N
b. −266 N
c. −460 N
d. +460 N
e. 0 (The force must be zero, since nothing is accelerating.)
Page 18 of 19
Physics 221.
Final Exam
Spring 2003
Did you bubble in your exam version?
Page 19 of 19