2010 midyear
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Queens University at Kingston
Faculty of Arts and Science
Department of Physics
PHYSICS 104 and PHYSICS 106
MidYear Examination
December 2010
Professor: A. B. McLean
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 1 / 18
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This examination is THREE HOURS in length.
The following aids are allowed:I The PHYS106 equation sheet that is provided.I The Arts and Science approved calculator (Casio fx-991).
When finished put your scantron sheet inside your answer booklet.
When finished please take the exam and the equation sheet with you.
The exam oce will not be administering this exam. So there will be noproctors. However, we are requested to include the following note that you
should disregard. Proctors are unable to respond to queries about theinterpretation of exam questions. Do your best to answer exam questionsas written.
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 2 / 18
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MULTIPLE CHOICE - Instructions
Put your student number on the scantron sheet in two places and(optionally) your name.
Attempt ALL TEN multiple choice questions.
Record your answers on the scantron sheet.
Each question is worth one mark.
Select test form A.
The boxes should be penciled so that the letter is not visible.
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 3 / 18
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Qu.1
x / m0
y / m
A
B
C
up
2
4
6
8
4 8 120
A projectile is launched into the air three times from point (x, y) = (0, 0)with the same launch angle. If tA, tB and tC are the flight times, the time
the projectile spends in the air, which of the following describes the ratioof the flight times (tA : tB : tC)?
A. 4 : 2 : 1 B. 16 : 4 : 1 C. 1 : 1 : 1 D. 0.25 : 0.5 : 1 E. 2 :p
2 : 1
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 4 / 18
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Qu.2
Using thruster rockets, the spaceship Discovery travels from position P1 to
positionP
2 along a anticlockwise circular path with an angular speed of0.01 rad/s. For this journey, what is the magnitude of the Discoverysaverage velocity? You may use the sin rule: a/ sin A = b/ sin B.
x/m
P
y/m
100 km
P
1
2
45o space shipmoon
A. 0.42 km/sB. 0.30 km/sC. 0.39 km/sD. 0.47 km/sE. 0.78 km/s
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 5 / 18
Find distance from P1
to P2 and calculate
average velocity.
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Qu.3
upx
v
The block slides up the frictionless incline, then back down. Which of thefollowing is the correct acceleration-time graph for the block?
ax
t
A B C D E
t t t t
ax ax ax ax
0 0 0 0 0
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 6 / 18
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Qu.4
up
m
0.1 mm
mspring0.2 m
A 0.1 kg pendulum bob, that is initially at rest, falls through a height of0.1 m and hits a block with an equal mass on a frictionless surface. The
block moves down the incline, falling through a height of 0.2 m beforehitting a block with an equal mass attached to a spring with a springconstant of 50 N/m. What is the maximum compression of the spring?A. 0.01m B. 0.08m C. 0.09m D. 0.10m E. 0.11m
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 7 / 18
Use conservation of
energy
x = [(2mg/k)*(h1+h2)]^0.5
Ei system = Ef system
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Qu.5
h
u
path of the ball
ground
tower
ball
G
F
F
m
forces onthe ball
x
y
0
ballwind
gravity
A girl threw a ball horizontally o a tower of height h = 40 m. She threwthe ball to the right and into the wind which is blowing to the left. Themagnitude of the force produced by the wind is equal in magnitude to theweight of the ball, |~F | = |~FG|. What is the initial speed of the ball (u) ifit is to land at the base of the tower, a distance h directly below therelease point.A 14 m/s B 18 m/s C 28 m/s D 34 m/s E 40 m/s
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 8 / 18
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Qu.6
A 0.01 kg rubber ball and a 0.01 kg clay ball are thrown at a wall withequal speeds. The rubber ball bounces, the clay ball sticks. Which ballexerts a larger impulse on the wall?
A They exert equal impulses because they have equal momentaB The clay ball exerts a larger impulse because it sticks.C Neither exerts an impulse on the wall because the wall doesnt move.D The rubber ball exerts a larger impulse because it bounces.E They exert equal impulses because they have equal kinetic energy and
equal momenta.
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 9 / 18
Impulse = change in momentum
Rubber ball completely changes direction,
change in momentum = 2mv
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Qu.7
V1 V2 Vf
Before After
1 221
In a green chemistry laboratory, two pieces of biological hazard areinadvertently thrown from a window. Piece 1 catches up with piece 2 and
they stick together, forming one piece of lethal biohazard. Then theycontinue on with velocity vf. Which of the following statements is true?
A vf is greater than v2 but less than v1.B vf is less than v2.
C vf = v2.D vf = v1.E vf is greater than v1.
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 10 / 18
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Qu.8
A wrench is used to turn a bolt. A scale
drawing is provided that can be used toextract magnitudes of forces anddistances. If (i) the torque associatedwith force ~Fi is ~i (ii) the magnitude of~F1 equals the magnitude ~F2 and (iii) themagnitude of~F3 equals the magnitude of~F4, which of the following is correct:
A. 1 > 2 > 3 > 4B
.
4 >
2C. 1 = 3 and 4 > 2 > 1D. 1 = 3 and 1 > 4 > 2E. 1 = 3 and 1 > 2 > 4
25
35o
o
F1
F2
F3
F4
10 N
2 cm
bolt
wrench
r
Force
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 11 / 18
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Qu.9
A wind turbine is slowing down. If positive angles (i.e. +) are measured
in an anti-clockwise sense, what are the signs of! and ?
A. ! is positive and is positiveB. ! is negative and is positiveC. ! is positive and is negative
D. ! is negative and is negativeE. None of the above
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 12 / 18
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Qu.10
Two boys, with masses of 40 kg and 60 kg, respectively, stand on ahorizontal frictionless surface holding the ends of a light 10 m long rod.The boys pull themselves together along the rod. What distance will the40 kg boy have moved when they meet?
A 4 mB 5 mC 6 mD 10 mE need to know the forces they exert
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 13 / 18
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LONG QUESTIONS - Instructions
Answer BOTH long questions.
Put your student number on the front of the answer booklet.
You may do rough working in the answer booklet.
Each question is worth five marks.
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 14 / 18
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LONG QUESTION A
x
2.0 m
up
y
hill
v20
o
ball
0
y = 0.1 x2
Baron von Benjamin Berg places his cannon at the foot of a hill at point0(x, y) = (0, 0). The hill is described by y = 0.1x2. The mouth of thecannon is located 2.00 m above the ground (i.e above 0). The Baron fires
the cannonball at a speed of 40.0 m/s with a launch angle of 20.0 abovethe horizontal plane. Calculate the x and y coordinates of the point wherethe cannonball and the hill collide.
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 15 / 18
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LONG QUESTION B
up
m
L
A pendulum swings back and forth between
= +45 (+/4 rad) and -45 (-/4 rad).Find two angles where the tension in thestring is half the maximum value?
CONTINUED OVER . . .
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 16 / 18
+/- 42.6 degrees
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LONG QUESTION B continued
Part marks will be awarded for:1 Drawing a free body diagram for the pendulum bob.
2 Correctly resolving the forces parallel to the string tension and therebyderiving an equation for the string tension.
3 Deriving an equation for the height of the bob as a function of theangle and the length of the string L.
4 Applying conservation of mechanical energy to derive an expressionfor the speed of the bob as a function of angle .
5
Calculating the maximum tension in the string.6 Calculating the angles at which the tension is half the maximum
value.
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 17 / 18
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THE END
Beware, beyond this point, there are dragons.
Alastair McLean () PHYS 106 FINAL 2009-10 December 16, 2010 18 / 18
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