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Unformatted text preview: Date: February 7, 2007 NAME (Print): UNIVERSITY OF \VATERLOO
DEPARTMENT OF PHYSICS
PHYSICS 125
WINTER 2007
MIDTERM EXAMINATION Time: 7:00 —~ 9:00 pm ID. #2 W5 PROFESSOR: . SECTION #: SIGNATURE: IMPORTANT INSTRUCTIONS  READ CAREFULLY TO AVOID PENALTY 1. Use PENCIL. Mark your ID# and three digit “Section number”. Check that you have not
missed, or put double marks in any row in the answer ﬁeld. (Keep sheet face down when not in
use.) 2. Fill in name, etc, at upper right on computer sheet and on this page. 3. HAND IN SHEET AND BOOKLET SEPARATELY. Booklets will be returned later. 4. Check that your exam has 12 questions. All questions are of equal value, so don’t get hung up
and miss the easy ones. Formula sheet should be attached 5. There is no penalty marking for incorrect answers. However, in the event that the computer
sheet cannot be completely read, credit will be given to correct answers only if work is shown in
the space below the questions in this booklet. 6. If you need more space for your calculations, use the back of the previous page and label it with
the question number. 7. Good luck! ! g : 9.8 m/s2, 10 = 10'”W/m2 1 7
=—mR‘
2 1 7
~mC'
12 Moment of Inertia for a circular disk through center of mass It”, Moment of Inertia for a circular rod through center of mass [m 2 Circle your Professor: Lecture Section 001 R. Jayasundera (Eleo) Winter 2007 Midterm Page 3 01‘8 l. The diagram shows the position ofa 20 g block oscillating in
SHM on the end ofa spring. What is the maximum kinetic
energy ofthe block? Answer in Joules. (a) 4.2 (b) 3.1 (c) 2.7 (e) 1.3 (£€)m% = ﬁMI/MZ; = é/m'” ,9... “10",” M you/4'
7 , 90 xiv—3 5“ Wle/c/I/ﬂ;
7 3 7.
‘K a771,» = 2/7 (20))”0 3 993’: '7’”
' ('r" 7‘ . .‘l (7x/o“)
.‘ ékﬂzr O. ,' /.’2.J v..
nan—ﬁt ll 2. An object in SHM has its initial position to be 1/3 ofthe amplitude (x = + 1/3 A) and its initial
velocity to be negative. Four seconds later it is at a position of 1/2 the amplitude (x = + 1/2 A) and its velocity is positive. From the information provided calculate the angular frequency of the object.
Answer in Rad/sec._ (a) 0.38 (b) 0.67 (a) 2.64 (e) 4.00 ea 7U“: Ate“ (we+59).
¢I9 (99(“‘14¢)= a” A (6): ’/’9 =7 3
M ( ’X— I .3 V..(wcw6;_f’ﬂ)://3 nae/+10: #13 0" 5'05.
Vgg)1—Aqu («Myra/l We» 40 ﬂaweﬁpl 70 W /*‘/ no”, “1 61 (q .ra an) 5, = yam—é
ce )  ﬁ/  Ac“ (49 6;”) = “’4 Q t" W
06 2. ' 9 " V052) >0 Mat 44,; (caéLf'll) <0 @ "Q (43 (5134”): 9
éa’e/ ’ 99C.
44) = ‘1‘
a) = / I" Winter 2007 Midterm Page 3 01‘7 Two students each of mass 75 kg are on a ﬂat circular
platform of mass 100 kg. The platform is attached to one end ofa giant slinky and the other end ofthe slinky to a tall crane. The systems oscillates in a vertical plane
beside a tall building with an amplitude of 20 m in SHM.
When the slinky is fully stretched and at a momentary stop
the platform just touches the ground. At this instant one
student steps off the platform. The second student continues
to oscillate for a while and then decides to step off the
platform when it reaches the highest point which also
happens to be the roof top of the building. If the slinky has
a force constant of 73.5 N/m. Find the height ofthe building. Answer in m. b) (a) 40 (b) 50 (c) (d) 70 (e) 80 0.5 a 0M J’W‘é'éﬁ‘“ ' A7 :2 7:17
ALE 9) Ne“) ﬂw‘ALM/W~ ‘1 c7 =(7r)(?.f)__ [OM . 734‘ .
1 = 10 frozzam. :9 d O
4. A horizontal lank of mass m and len th L is ivoted at one end. , a iv: 3 p g p i. 3255'", g} The plank other end is supported by a spring of force constant k ~"“~*$~—‘* and is in equilibrium when the plank is horizontal. When displaced a (3 M7 small angle as shown the plank produces SHM. Which expressions ‘7‘
gives its angular frequency. The moment ofinertia ofthe plank about the pivot is 1/3 mLZ. V “\ (a) 3km; (b) 5g— (c) \/k/m (d) X (e) Wg
\ __ "M/ 3m 2 g \ u 5"? a} zzm'd'gﬁzm We... Irz'njww WWW/y. M to» {Wakq’ .
mm) 52‘, = 0 (4/6 (W‘Z‘év'wj _ ,4 ,
Mae/2% “M” =7 “"4" V .
@9244 awA/ed and C24, W 9 —«6«. °\<<:¢o Q) 09w
9h.“ 2
zﬁﬁméﬁ‘ + ([k/Vo‘yjj) 1" 14' (:5? ... eﬁﬂ!‘ Winter 2007 Midterm 3, When the solid object is pivoted at P1 and at P3 it produces
SHM for small angles with same period of oscillation T sec.
P3 is directly below P1. lfll] + h: : 14 in ﬁnd the period ofoscillation. Answer in sec. r  """""" ﬂér'o/ M 1. Pa.
7/117; l. .124 .. :771'
Mjé’
' £2 5 1.2.? :27
h, h.
Tm. AL + Mhlté“ =
iemclyﬂ)‘ M‘ILLCVA’)
, 1cm .. M 4 AL : Page 4 of 8 6. A particle executes simple harmonic motion with an amplitude of3.0 cm. From energy
considerations, determine its displacement from equilibrium when its speed equals one halfofits maximum speed. Answer in cm.
\Q m
v» (a) 0.6 (b) 1.1 (c) 1.6 (d) 2.1 (e) 2.6 m m
'V
2. 1. mm: 1 A A
J/é(3x<o‘) 2* 32"”(‘Cm‘9 +41%“1 "‘5" 2 4“
02 2..
z 1.
:imrt/‘Zl “we
—: 1‘ .Lﬁmc“
:k(sxlp./: évh(33‘lo ) 4'"
1 ’L. 9L1.
(3xt0') “ 4/
2.
 3(3x’o‘l)
. 9L 4].
r Winter 2007 Midterm (a) (b) (C) y(x,f) : 0.55in(.57rx —4m + 7:) (e) Page 5 of8 A sinusoidal wave travels on a stretched string with am amplitude of cm. wavelength 4 m and
velocity 8 m/s. For the string element at x = 0 its diSplacement is zero at t = 0 and its transverse
speed is directed upward, also at t = 0. (up is considered positive). Which of the equations below
describes correctly, the travelling wave. I) ‘ z _. _ U: 9M/5‘
)(.\,I) 0.3s1n(.57rx 4m+7r/4) 7 : ’7 ‘ k: g = 0 Sn. . 7r ._
y(X,l)=0.5$1U(.57IX+47Tl+—£) U: Q/k =7( 8)(0.577) : w .. 9” y(x,l) = 0.5 sin(.57rx — 4m) gage): ﬁvdu'. Clex~ coé +911.)
um,“ =  x9e? Cw (ka—WGNP). None of the above QCCWAQJf 5Q“ fﬂ/wmalm 91m.
yam): o = Am(¢j=a
~“¢= 0W7?
— Oar J 70
ﬁ(o,o) 70 :3 6w ’9‘" r,”
Cwqﬂ4o
W s 77 444% A01‘ 0 arﬁx — 9/76 +77.) 7(306): j 8. y(x,l) = 20 sin(47rr + 7r/2) sin(67rx) (x in meters, t sec) describes a standing wave pattern on a string ofmass 1 kg ﬁxed at both ends. lfthis string is oscillating at its 4Ih harmonic calculate the
tension ofthe string. Answer in N. (a) 4/9 (b) 27/8 (c) 36/4 (d) 15/12 (@523 4—. ,Q ..__.__> 2?:6 4.41M éwcu'lm ,é: (77 :17? '3' Q=§M
€=%M' 6.2:?”
U“: 317:2
m 4 / 3 1673/ mw max. :23: "=/a. M‘
if; /A e 3/3 Winter 2007 Midterm Page 6 of7 9. An organ pipe A (one end closed) and organ pipe B (both ends open) have lengths in the ratio LA '
L3 = 0.5. The first harmonic is set up in pipe A and the fourth harmonic is set up in pipe B. What is the ratio of the frequencies fA / f8?
\ (a) 1/2 (b) 1/8 (c) 8 1—H La, , L P/ “(D 303 3,!1 P/ “C9
’ "(Lg f 3L“ 2.93 :6 1: 'L 9359:1‘ IlaLn Lo 2' LA
at»  3:. 2 a L
f ' l‘ LI.
in ,ﬂ, 10. Two strings of equal length but of unequal mass (the second string has four times the density ofthe
ﬁrst string) are joined and their ends tied to supports. With a tension of 1080 N, the first string is
Vibrating in the ﬁrst harmonic and the second string is Vibrating in the second harmonic. For what
tension will the ﬁrst string vibrate in the third harmonic and the second string Vibrate in the sixth harmonic, if the frequency of Vibration remains the same as before the tension was changed.
Answer in Newtons. (a) 30 (b) 60 (c) 90 123) (e) 240 \w‘M Winter 2007 Midterm Page 7 ot‘7 l 1. Two loud speakers emit sound in phase at a frequency of 220 Hz. A listener sits at a location which is 8 m from one speaker and l l m from the other. The sound level at the listener from
either loudspeaker acting alone is 35 dB. Calculate the sound level when both loudspeakers are
on. Assume speed of sound is 330 m/s. Answer in dB‘s. (b) 46 (c) 66 (d) 70 (e) none ofthcse a
.a A ,4
/o 71,, 35 3( 3M P
jmkﬂg4‘qa/é PALESJ‘Yzw/q“
$W’ 1,=I,.=z M.
1,454 7’5 ' Clio/1‘} 02430 "W " "
. ,. , 'm . 4m fig4’
' .90” [/K's 11/:3M =39 '0"; “c
A = '   2/)
M/ «1/
AK am 0‘27):— r_.___.73+ 3 if“: 7
. 'E z ’
we?  My + my?
D 2' Mo 4
35’ 94—1/6 1 VVU DIJMHAULD on» Ullvull U)“ llle baulv UDUllluLUJ U1 LlyLiLtVALVJ auu LLLA. J 11v utJvquvlu “1v Auvutvv on a vertical pole a distance 4.00 m from each other. A Biology student whose ears are in line
with the bottom speaker walks away from the pole in a direction perpendicular to the pole. How
far away from the pole will the student be when she hears a “minimum” sound for the second
time? Assume the speed of sound is 330 m/s. Answer in m. 2.43 (c) 8.41615 9.28) (6) 15.4 (a) 1.99 (b)
T 41w l __p ///////, ...
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