Cover Type B

University uf Technology, Sydney

TO BE RETURNED AT THE END OF THE EXAMINATION. THIS PAPER MUST NOT BE REMOVED FROM THE EXAM CENTRE.

SURNAME:

FIRST NAME:

STUDENTNUMBER: _________________

COURSE:

Spring SEMESTER 2010

SUBJECT NAME PHYSICAL MODELLING

SUBJECT NO. 68037

DAYIDATE TUESDAY, 16 November 2010

TIME ALLOWED 2 Hours plus 10 Min. reading time

STARTIEND TIME: 14:00 -16:10

NOTESIINSTRUCTIONS TO CANDIDATES:

THIS PAPER IS DESIGNED TO BE COMPLETED IN 2 HOURS. AN EXTRA 10

MINUTES HAS BEEN ADDED TO THE TIME ALLOWED AND IT IS RECOMMENDED

THAT YOU USE THIS 10 MINUTES TO READ THE PAPER BEFORE COMMENCING.

ALL QUESTIONS ARE TO BE ATTEMPTED

CALCULATORS MAY BE USED

MULTIPLE CHOICE ANSWERS ARE TO BE ENTERED

IN THE GENERAL PURPOSE ANSWER SHEET.

REQUEST A NEW ANSWER SHEET IF YOU MADE A MISTAKE ON YOUR

ANSWER SHEET.

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Data and Formulae Sheet

Mechanics ~ 1 2 x xo+vi+"2at

8 8 o+O)t+!2 al2

v=RO)

ma F=-kx

U=mgy

p=dW dt

1 N _

-~mr p=mvML.-i II

1

1:=Ia

Electricity

IEI=k;r

V iR iV

E=pJ

Thermal Q=mcAT

Q=nCvAT

P =A AT cond L(Llk) P"ad saAr

w= JpdV

K =IQLI cop IWI

Cv=f R 2

v2 =v~+2ax

0)2=0)2+2a8 o

P=Fv

dl 1:=­

dt

F=qE

. dq1

dt

Req = LR; j

pV=nRT

p=Q t

1 2 -3k T"2 mvrms-"2 B

1'T'vr-1-T VY­11 i - f f

r c v

s=R8 2 v

arad= R

v=.} 2gh

K mv2

u= k Q,q2 r

v =.J3RT rms M

AV=Vj3AT

...over

Waves and Optics

X(t)=Xm COS(cot +¢) v(t) coxmsin(cot+¢) aCt) a/Xm cos(OJt +¢)

T = 1 I k 2co 2rif E '2 Xmf ={fco

v ).1 v ~~ V~~ _IE _( r1l2 V-~B- &f.1

A v 2JT x =n X (n+!iA f =n- k =

2 2; 2 2L ).

y(x,t) =Yrn sin(kx- OJf +¢)

Vy(x,t) = -coYm cos(kx- cot +¢)

y'(x,t) 2Ym cos(11')sin(kx mt + 11') y'(x,t) =2Ym sin(kx)cos(cot)

P I J f3 (1 OdB) log-

A 10

1 1 1 1 1 1 1 - = + (n-rJ!-.!) -=-+ f P i f \'i r2 f fr J;

h' i c m =-­ n=Iml h p v

Fluids

m F p= p=­

V A

Rv = Q = A v =canst p+tpv2 +pgy = canst

Mathematical and Statistical Relations

-b±Jb2 -4ac sin A sinB sin C x=.----- --=--=-­

2a a b c

'A 'B 2·JA + BJ JA-BJsm + sm = S11\-2- CO\-2- a(m)

< 11m > <m> n n

Data

g= 9.81 mls2 c = 3.00 X 108 mls e 1.602 x 10,19 C

1 atm 1.013 x 105 Pa kB = 1.381 X 10'23 J/K a= 5.670 x l0-8W/(m2K4)

23R 8.314 J/(mol K) NA 6.022 X 10 mOrl k = 8.99 x 109 Nm2/C2

...over

Kinetics

Question 1 [1] Which one of the following five graphs showing position as a function of time represents

the motion of an object whose speed is increasing?

II III

IV V

A.I B. II C. III D. IV E.V

Question 2 [4] A baseball player hits a pitched ball when the center of the ball is 1.30 m above the

ground. The ball leaves the bat at an angle of 45° to the horizontal. With that launch, the ball should have a horizontal range (returning to the launch level) of 108 m. A 8.33m

high fence is 98.0m away (horizontally) from the launch point. At the fence, the distance between the fence top and the ball center is closest to:

A. 0.00 m B. 0.60 m C.1.30m 0.2.04 m E. 2.33 m

Page 1 of 10

Forces

Question 3 [1] The coefficient of kinetic friction:

A. is in the direction of the frictional force B. in the direction of the normal force C. is the ratio of force to area D. can have units of newtons E. is none of the above

Question 4 [4] A 19.0 kg monkey climbs up a massless rope that runs over a frictionless tree limb and back down to a 29.0 kg package on the ground. The magnitude of the least acceleration the monkey must have if it is to lift the package off the ground is

2 2 2 2 2A. 2.45 ms· B. 4.91 ms· C. 5.16 ms· D. 9.81 ms· E. 10.0 ms·

Page 2 of 10

Momentum &Energy

Question 5 [1] Find the center of mass of a uniform plate after a piece at the lower left comer is removed. The uniform square plate has edge lengths of 6.0 m; the plate is centered at Won the origin of an xy-coordinate system. The portion removed is a rectangle measuring 1.0 m by 3.0 m that has its center of mass D. What is the x component of the remaining plate's new center of mass?

.m_"_""'····~c.~.

-Ii U'

f)• i j

In.

A. 0.23 m B..0.25 m C. 0.28 m D.0.29m E. 0.30 m

Question 6 [4] A 12 g bullet moving directly upward at 1000 mls strikes and passes through the center of mass of a 9.0 kg block initially at rest. The bullet emerges from the block moving directly upward at 590 m/s. To what maximum height does the block then rise above its initial position?

A. 0.012 m B. 0.015 m C. 0.022 m D. 0.025m E. 0.32 m

Page 3 of 10

Equilibrium

Question 7 [4] A uniform sphere of mass m ::: 0.850 kg and radius r = 0.042 m is held in place by a massless rope attached to a frictionless wall a distance L = 0.080 m above the center of

the sphere as shown in the figure below. The normal force between wall and ball is closest to:

T L

_I

l--r~1

A. 2.20 N B. 4.40 N c. 6.60 N D. 8.80 N E. 8.13 N

Page 4 of 10

Rotation

Question 8 [1] The figure shows a cylinder of radius 0.7 m rotating about its axis at 10 rad/s. The speed of the point Pis:

OJ A. 7.0 mls B. 14rc rad/s C. 7.0rc rad/s D. 0.70 mls E. none of these

Question 9 [4] A constant horizontal force of magnitude 10 N is applied to a wheel of mass 10 kg and radius 0.30 m as shown in the figure below. The wheel rolls without slipping on the horizontal surface, and the acceleration of its center of mass has magnitude 0.60 m/s2

•

The rotational inertia of the wheel about the rotation axis through its center of mass is closest to:

A. 0.12 kg-m2 B. 0_50 kg·m2

C. 0.60 kg·m2 D. 2.00 kg-m2 E. 4.00 kg·m2

Page 5 of 10

Thermal

Question 10 [1] An annular ring of aluminum is cut from an sheet as shown. When this ring is heated:

o A the aluminum expands outward and the hole remains the same in size

B. the hole decreases in diameter

C. the area of the hole expands by the same percentage as any area of the aluminum D. the area of the hole expands by a greater percentage than any area of the aluminum

E. linear expansion forces the shape of the hole to become slightly elliptical

Question 11 [4] A circular hole in an aluminum plate is 2.800 cm in diameter at O.OOO°C. What is its

diameter when the temperature of the plate is raised to 75.00°C? The linear expansion coefficient of aluminum is 23.00 x 10-6rC.

A. 2.802 cm B. 2.803 cm C. 2.804 cm D. 2.805 cm E. 2.806 cm

Question 12 [1 ]

Pressure versus volume graphs for a certain gas undergoing five different cyclic

processes are shown below. During which cycle does the gas do the greatest positive work?

l~ Pb Pb Y v y

II III

IV V

AI B. II C. III D. IV E.V

Page 6 of 10

Question 13 [4] Materials M1 and Mz are brought together so that they come to thermal equilibrium while isolated from their environment. Neither material undergoes a change in phase (or

state); rather, only the temperature changes.

M1 M2 Mass (kg) 5 2 Specific heat (J/kg.K) 400 800 Initial temperature Tj ee) 50 -40

The final (equilibrium) temperature Tf of the materials is closest to:

A. -10°C B.O°C C. 10°C D. 20°C E. none of these

Oscillations. Waves

Question 14 [1] In simple harmonic motion:

A. the velocity is greatest at the maximum displacement B. the period depends on the amplitude C. the acceleration is constant D. the acceleration is greatest at zero displacement E. the acceleration is greatest at the maximum displacement

Question 15 [4] The left edge of a water bed mattress is briefly compressed (negative displacement) setting up a traveling wave. A time 0.62 s later, the wave forces the right edge (1.50 m away) to reach its maximum positive displacement for the first time. At that instant, the nearest point also at a maximum positive displacement is 12.0 cm from the right edge. The velocity of propagation of the wave is closest to

A. 1.07 mls B. 2.42 mls C. 2.52 mls D. 2.61 mls E. 2.70 mls

Page 7 of 10

Sound. EM. Propagation. Superposition

Question 16 [1 ] The speed of a sound wave is determined by:

A. its amplitude

B. its intensity C. its pitch D. the number of harmonics present E. the transmitting medium:

Question 17 [4] Of the five organ pipes described below, which one has the highest fundamental

frequency?

A. a 2.3-m pipe with one end open and the other closed B. a 3.3-m pipe with one end open and the other closed C. a 1.6-m pipe with both ends open D. a 3.0-m pipe with both ends open E. a pipe in which the displacement nodes are 5.0 m apart

Mirrors. Lenses

Question 18 [1]

A point source is to be used with a concave mirror to produce a beam of parallel light. The source should be placed:

A. as close to the mirror as possible B. at the center of curvature C. midway between the center of curvature and the focal point

D. midway between the center of curvature and the mirror E. midway between the focal point and the mirror

Question 19 [2] A certain lens produces a real inverted image 1/3 the size of the object. The object­image separation is 58.4 cm, measured along the central axis of the lens. How far from the object must the lens be placed?

A. 7.51 em B. 14.6 em C. 29.2 em D. 43.8 em E. 58.4 em

Question 20 [2] With reference to the previous question, what is the focal length of the lens?

A. 11.0 cm B. 7.5 cm C. 10 cm D. 12.5 cm E. 20 cm

Page aof 10

Electricity

Question 21 [1 ] A current of 0.3 A is passed through a lamp for 2 minutes using a 6 V power supply.

The energy dissipated by this lamp during the 2 minutes is:

A. 1.8 J B. 12 J C. 20 J D. 36 J E. 216 J

Question 22 [4] The circuit section AB shown below absorbs energy at a rate of 50 W when current i =1.00 A through it is in the indicated direction. Resistance R =2.0 O. The emf device X lacks internal resistance. From the potential difference (in V) between A and B calculate the emf (in V)?

A.O.OV B.22V C.48V D.50V E. 52 V

Page 9 of 10

Fluids

Question 23 [1] Select a statement that most accurately describes the displacement of water by two identical blocks of ice floating in water as shown.

A B

A. Block A displaces a greater volume of water since the pressure acts on a smaller bottom area.

B. Block B displaces a greater volume of water since the pressure is less on its bottom. C. The two blocks displace equal volumes of water since they have the same weight. D. Block A displaces a greater volume of water since its submerged end is lower in the

water. E. Block B displaces a greater volume of water since its submerged end has a greater

area.

Question 24 [4] A closed barrel of wine has a small opening 43.2 cm below the level of the liquid (of density 0.994 g/cm3

). What is the speed of the wine flowing through the opening if the pressure in the air space above the liquid in the barrel is 1.697 atm?

A. 2.57 mls B. 12.3 mls C. 20.9 mls D. 21.6 mls E. cannot be calculated unless the areas of the hole and the barrel are given

Page 10 of 10