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First Name: Last Name: Student #: Instructor: Dr. K. Foyle
Class: Physics 1BB3, Modern Physics for the Life Sciences
FIRST MIDTERM EXAMINATION DATE: Feb. 6th, 2014 TIME: 7pm PLACE:
T29 101 & 105 DURATION OF EXAMINATION: 2 hours This examination
paper includes 17 pages and 17 questions. You are responsible for
ensuring that your copy of the paper is complete. Bring any
discrepancy to the attention of your invigilator. Special
Instructions:
Answer multiple-choice questions (questions 1 to 16) on the
provided examination answer sheet. Answer the written answer
question (question 17) directly on this copy. Return both your
examination answer sheet and this copy at the end of the
examination, after verifying your name and student number are
written on both. A calculator can be used if necessary. A formula
sheet is provided on the back of this page.
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Mark: Multiple-choice questions (#1-16): /85 Written answer
questions (#17): /15 Total: /100 ---------DO NOT WRITE ABOVE THIS
LINE------------
FORMULA SHEET
Moment of inertia of a solid disk or solid cylinder about its
center: I=(1/2)MR2
Moment of inertia of a hollow cylinder about its center: I=MR2
Moment of inertia of a sphere about an axis through its center:
I=(2/5)MR2 Moment of inertia of a rod about one of its ends:
I=(1/3)ML2 g=9.81 m.s-2
a = v2
R(t) =0 +t
(t) = 0 +0t +12t
2
= F r sin
I = miri2i
Ekrotation =12 I
2
L = mv r sinL = I
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Part 1: Multiple-choice questions (questions 1 to 16) Answer
these questions on the provided examination answer sheet. (Make
sure you write your name and student number on the answer sheet!).
For questions with a numerical answer, if your answer does not
match any of the provided answers, pick the one with the closest
value. Questions 1 to 9 are completely independent questions.
Questions 10 to 16 are part of a problem, but still mostly
independent from one another.
Question 1. You are driving at a constant speed of 39.0 m/s
along a circular trajectory with radius 29.0 m. What is your
acceleration? A- 52.4 m/s2 B- 1.34 m/s2 C- 21.6 m/s2 D- 0.7444 m/s2
E- 8.45 m/s2
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Question 2. Which one of the following statements concerning the
moment of inertia I is false?
A- I may be expressed in units of kg.m2. B- I depends on the
angular acceleration of the object as it
rotates. C- I depends on the location of the rotation axis
relative to
the particles that make up the object. D- I depends on the
orientation of the rotation axis relative
to the particles that make up the object. E- Of the particles
that make up an object, the particle with
the smallest mass may contribute the greatest amount to I.
Question 3. A high diver in midair pulls her legs inward toward
her chest in order to rotate faster. Doing so changes which of
these quantities: her angular momentum L , her rotational inertia,
I , and her rotational kinetic energy torK ?
A- L only B- I only C- torK only D- L and I only E- I and torK
only
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Question 4. A 2kg disk having a radius of 20cm is pivoted at a
point on its circumference by a thin nail. The disk is pulled back
so that its center of mass is at the same level as the nail. With
what angular velocity must the disk be launched so that the center
of mass of the disk will just reach a point vertically above the
nail?
!!CM!
Nail!
ini)al!
nal!
A- 0 rad/s B- 20.3 rad/s C- 15.4 rad/s D- 12.8 rad/s E- 8.1
rad/s
Question 5. A 20 kg wooden beam 3.0 m long is tapered such that
the center of mass is located nearer one end. Two women are
carrying the beam horizontally, one woman at each end. If one is
supporting 50% more weight than the other, how far from the lighter
end of the beam is the center of mass located? A- 2.0 m B- 1.5 m C-
1.8 m D- 1.3 m E- None of the above
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Question 6: A boy is whirling a stone around his head by means
of a string. The string makes one complete revolution every second,
and the tension in the string is FT. The boy then speeds up the
stone, keeping the radius of the circle unchanged, so that the
string makes two complete revolutions every second. What happens to
the tension in the string? A- The tension is unchanged. B- The
tension reduces to half its original value. C- The tension
increases to twice its original value. D- The tension increases to
four times its original value. E- The tension reduces to one-fourth
of its original value. Question 7. If an object in circular motion
increases its angular velocity from 250 rpm to 500 rpm in 5
seconds, the tangential acceleration of a point of the object at 6
cm from its center of rotation is approximately
A- 0.3 m/s2 B- 0.8 m/s2 C- 1.5 m/s2 D- 3 m/s2 E- 6 m/s2
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Question 8. Consider two masses, each of 2 kg at the ends of a
light rod of length L with the axis of rotation through the center
of rod. The rod is doubled in length and the mass on the left side
is halved. Where can an additional mass of 2 kg be placed on the
rod in order to keep the rod balanced on its center?
A- At far left B- At the far right C- At L/4 from the left D- At
L/2 from the left E- At L/3 from the right
Question 9. A hockey stick, 2.00 m long and 1.2 kg, is rested up
against a wall. The torque about the pivot point caused by the
sticks weight is 5.0 Nm. What is the torque about the pivot point
caused by the force of the wall on the top of the stick? (Assume
that this stick is in static equilibrium)
A- 1.0 Nm B- 3.0 Nm C- 5.0 Nm D- 10. Nm E- Need to know the
angle between the hockey stick
and the vertical.
Pivot Point
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Read the following carefully before answering questions 10 to
16. Those questions are all independent, except for question 15
(you will need to answer several previous questions correctly to
answer question 15). A yoyo is a toy consisting of a flattened
spool around which a string can be wrapped. If a yoyo is released
without initial velocity, with the end of the string kept in a
fixed position, the downward speed of the yoyo starts by increasing
and but then it ends up decreasing. In the following series of
questions (10 to 16), we try to understand why. We will consider a
yoyo made of two identical solid disks (each with mass M1 = 0.050
kg and radius R1 = 0.075 m), joined by a concentric solid
cylindrical shaft (mass M2 = 0.0050 kg, radius R2 = 0.010 m), as
shown in Fig. 1. A string with negligible mass is wrapped around
the yoyo, a shown in Fig. 2 and 3. Initially, the length of string
wrapped around the yoyo is L = 0.85 m. The string is attached to
the yoyo at one end (so that the wrapped up part of the string
cannot slip around the shaft) and its other end is kept in a fixed
position as the yoyo falls (Fig. 3).
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Figure 1 Question 10: The moment of inertia of the yoyo with
respect to a horizontal axis passing through its center of mass
(this axis is indicated by a dashed line in Fig. 1 above) is: A- I
= 2.5 10-7 kg.m2 B- I = 1.4 10-4 kg.m2 C- I = 2.8 10-4 kg.m2 D- I =
5.3 10-4 kg.m2 E- I = 5.6 10-4 kg.m2
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Figure 2
Question 11: Which of the following statements correctly applies
to the yoyo during its fall (see Fig. 2 above for the orientation
of the wrapped up string with respect to the yoyo, and consider
that a counterclockwise rotation is positive, as indicated in the
figure): A- The net force exerted on the yoyo is zero. B- The net
torque exerted on the yoyo is zero. C- The net torque exerted on
the yoyo is negative. D- The net torque exerted on the yoyo is
positive. E- The angular momentum of the yoyo is conserved.
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Question 12: During its fall, the mechanical energy of the yoyo
is conserved. Why? A- Because the net torque exerted on the yoyo is
zero. B- Because the net force exerted on the yoyo is zero. C-
Because all the forces exerted on the yoyo are conservative. D-
Because, although at least one force applied to the yoyo is not
conservative, it does no work. E- Because none of the forces
exerted on the yoyo does any work.
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Figure 3 Question 13: If the zero for gravitational potential
energy is chosen at z=0 (that is when the yoyo is at its lowest
point, as indicated in Fig. 3 above), what is the value of the
mechanical energy of the yoyo during its fall? A- 0 J B- 0.46 J C-
0.88 J D- 1.8 J E- One would need more information to answer this
question.
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Question 14: If the thickness of the layer of wound-up string is
d (see Fig. 2 on page 6), what is the relationship between the
angular velocity of the yoyo () and its downward speed (v)? (If you
find it hard to answer this question, try considering how much
string is unwound during one rotation of the yoyo, and how that
length of string is related to the downward speed and angular
velocity of the yoyo). A- v=R1. B- v=(R1+d). C- v=R2. D- v=(R2+d).
E- v=(R1+R2).
Question 15: When the yoyo is halfway through its fall, at
z=L/2, the thickness of the layer of wound-up string is d = 0.030
m, but at z=0 it has decreased to d = 0.000 m. Making use of this
information, calculate the downward speed of the yoyo at z=L/2 and
z=0 (these speeds will be noted v1 and v2, according to the
notation in Fig. 3). A- v1 = 3.1 m/s and v2= 1.8 m/s B- v1= 2.5 m/s
and v2= 0.78 m/s C- v1= 2.5 m/s and v2= 0.62 m/s D- v1= 1.8 m/s and
v2=0.78 m/s E- v1= 1.8 m/s and v2=0.62 m/s
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Question 16: What happens to the linear and rotational
components of the kinetic energy of the yoyo as it falls from z=L/2
to z=0? A- Both the linear kinetic energy and rotational kinetic
energy of the yoyo decrease. B- Both the linear kinetic energy and
rotational kinetic energy of the yoyo increase, but the linear
kinetic energy increases more than the rotational kinetic energy.
C- Both the linear kinetic energy and rotational kinetic energy of
the yoyo increase, but the rotational kinetic energy increases more
than the linear kinetic energy. D- The linear kinetic energy of the
yoyo increases while its rotational kinetic energy decreases. E-
The linear kinetic energy of the yoyo decreases while its
rotational kinetic energy increases. --------------End of Part 1:
Multiple-Choice Questions----------
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Part 2: Written answer question (question 17) Answer this
question directly on your examination copy, explaining clearly and
concisely how you arrived to the answer. Question 17. A hollow,
vertical cylindrical drum of radius R = 2.45 m is rotated with
angular velocity about its central axis, as shown in the figure
below. A smaller cylinder (with mass M = 80.0 kg) rotates around on
its inner wall. The smaller cylinder is NOT in anyway attached to
the cylindrical drum.
a. Draw a free-body diagram of the mass, labeling all the forces
acting on it, and write a list of what the labels mean. b. What
angular velocity (in radians/second) would be required to make the
normal force pressing against the mass be twice the magnitude of
its own weight? c. At the value of obtained in (b), what is the
minimum coefficient of static friction, S, necessary to keep the
mass suspended on the inner wall of the cylinder as it rotates?
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----------End of Part 2: Written Answer Question----------
-------------------END OF EXAMINATION----------------