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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.

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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.


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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


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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


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


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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


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

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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.


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.


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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


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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


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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


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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.


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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.


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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 . . .


+/- 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.


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THE END

Beware, beyond this point, there are dragons.


Documents

2010 Midyear