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Unformatted text preview: Physics 140 Winter 2004 Midterm 3 V 1. (P) The ﬁgure below shows an 18.0kg crate of salami sliding down a ramp on a
(massless) rope that is wrapped around a disk of radius 0.25m and mass 6.0kg. The coefﬁcient of kinetic friction between the crate and ramp is uk=0.24. What is the
magnitude of the disk’s angular acceleration? a) 3.1rad/sz‘ ‘
b) 6.7 rad/s2 @ 9.8 rad/s2 d) 11.4rad/s2
e) 13.7 rad/s2 2. g (P) A uniform solid sphere rests suspended from a cord anchored at point P along an
inclined plane. Which of the following statement(s) is(are) true? P C I
a) The torque about point P due to the Weight of the sphere is zero. )\(/ b) The torque about point P due to the tension in the cord is zero.
c) The torque about point C due to the normal force of the incline on the sphere is zero. V ((9 both b) and c) V
e) all of a), b) and c) X m
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ﬁcﬁ‘i‘éﬂz‘f (x #P "/“(5‘*')4'/%) Ks‘wﬂcgﬂﬁ D< :(S/Wﬁ—ﬂk (4&9) m‘xﬂ ~(o24>g.>( W m = wggz 39+ 3 0.2.5 Physics» 140 Winter 2004 Midterm 3 3. (P) A rigid assembly consists of a thin hoop of radius R and mass m attached to a thin
rod also of mass m and length 2R rests in the vertical position shown in the ﬁgure
below. Given a tiny'nudge (involving negligible energy) from behind, the assembly
rotates about the horizontal axis shown. What is its angular speed as it passes through
the inverted (upsidedown) orientation? 613(96g/65R)“2 ' b) (33g/15R)“2
c) (48g/17R)“2.
d) (17g/12R)“2
e) (8mg/15R)1/2 4. Kepler’s second law of planetary motion — the observation that the orbits of planets
sweep out equal areas around the Sun in equal times — mainly reﬂects the
conservation of which physical quantity? a) mechanical energy. @ angular momentum.
c) linear momentum. d) gravitational potential energy.
e) mass.  'Page, 226 473(me TM,” @ So/Vec/ z'xvx é€scussfon session. heal)
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L. A“ 2560. Physics 140 Winter 2004 Midterm 3 5. Three coplanar bodies A, B and C with masses m, 2m, and 8m, respectively, are
shown below. At what (x,y) location should a fourth body D of mass 8m be placed
such that the total gravitational force on body A is zero? a) (_21/4 d, 21/4 0:)
b) (21/4d, d/21/4)
@(21/4 ‘1, _21/4d)
d) ( d/21’4, —d/2“4)
e) ( (1721/4, _21/4d) 6. A 2kg box of pepperencrusted salamis sits 0.5m from the right edge of a uniform 4kg
beam of length 2m. The markings on the beam are at quarterlength intervals. Both
the beam and the salamis rest atop a pair of rollers A and B, located at the center and
right edge of the beam. What is the magnitude of the normal force acting on the
beam from roller A? Y
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& F7 ' Physics 140 Winter 2004 Midterm 3 7. A'puck tied to a string is revolving on horizontal, frictionless ice in a circle centered .
' on an anchor point 0. If the string breaks suddenly, then just after the break the
angular momentUm of the puck about the anchor point 0 Will
. * 7:667 2 7; I: 0
a) be smaller than before the break;
be the same as before the break.  , ='> .
c) be larger than before the break.
d) be zero. ' r.
e) be the same magnitude as before the break, but with opposite sign. 8. (P) The ﬁgure below is hinged about point P. The four forces applied at each Comer
have equal magnitude. Rank the forces according to the magnitude of the torque
they create about point P, greatest to least. '  géz‘ >45
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2: =§FSM ” a: v2 _ A F. Siaﬂ‘: o 211, :2— Physics 140 Winter 2004 Midterm 3 '9. (P) Starting from rest, a small hollow, uniform sphere of mass m=1.5kg and radius r=0.75cm rolls without slipping down a ramp and executes a looptheloop. The
initial height of the sphere’s center of mass above the bottom of the loop is H=25cm v and the loop radius is R=7.SCm. What is the center—ofmass velocity of the sphere at
the top of the loop? (Take into account the ﬁnite sizeof the ball when camputing the vertical displacement.) a) 0.75 m/s
b) 0.99 m/s
c) 1.08 111/5 10. (P) A uniform block of width W and height H rests on a rough inclined board with
coefﬁcients us and “4‘ 'of static and kinetic friction, respectively. As the angle 6 made a) always slide before tipping over. b) always tip over before sliding.
@ tip ﬁrst if [1.5 > W/H. (I) slide when tan 9 = pk. e) tip ﬁrst if us < W/H. [:3] MegﬂW/ZJ/ cfﬂ
,, $757 7"% %%= & ﬂ 6? /
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Zeal m Physics l40 Winter 2004 Midterm 3 11. (P) Consider the following thought experiment that could be performed in deep space.
A very small “test mass” m is released from rest a distance d from the edge of a thin shell of mass M and radius R. Gravity attracts the test mass toward the shell, and a
small hole drilled in the outer shell allows it to enter the interior. What is the velocity
of the test mass as it passes through the center of the shell? V  a) [GMR/ (R+d)]“2
b) [mm/(12+an
c) [2GM/ (R+ar)]“2
Q); [2GMd / R(R+d)] “2
e) [2GMR/d(R+d)]l/2 ‘ 12. (P) What is the total angular momentum about the origin '0 for the threeparticle
system shown below? ‘ ciﬁiiiiﬂi Z L =2 V“??? A; é A A
d; :V‘TXF7 +MziILXVLf—M3 r3 xvg .
e) 412kgm/S —'_—_ O +— Z. (7 XL? + 3 (_2 Q)x(_6</\) = 0 +24???) +36 2
= 12$ [E [xi/1% % ﬂ?ij /J‘ 'ﬂﬂ%% Jﬂ/g/j
% Wy/Ziz/I/e £54 ay/ﬁ/Q/Ww /‘f ZKZﬂ. 7/76 Wiﬂ’ /‘/ (25% mag/V W m i/é/Efwaw :
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R <3+R Page) ﬁr Wye/V wz/zww ﬂ? W020" ﬂg/ Physics 140 Winter 2004 Midterm 3 13. In the birdseye view below, the smileyface marks the location of’a child of mass
40kg standing at rest on the edge of a horizontal merrygoround that can be treated
as a disk of mass 60kg and radiusl.5m. 1A ball of mass 0.5kg is thrown with velocity
3m/s at the angle shown; After the child catches the ball, and assuming a frictionless
axle, how long will it take the child/ball/merry—goround system to rotate 1 radian? a) ZS
b) 133. .
c) 45s * mByB Sgﬂéso) = (1.8%. 1,: +1“) w
d) 88s ’ I 5
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' 1 ‘2' yWﬁ'e V3.SJ/)(§$x‘)i 14. (P) Imagine drilling a very thin hole straight down fr0m the surface to the center of a
spherical moon of mass M and radius R and uniform mass density. Further imagine
lowering a small mass m into the hole until it is a distance r from the center (r<R). If
you let the mass drop from rest, what will be its kinetic energy as it reaches the moon’scenter? W : AK = k; ~26 :: K1: " .— 3 .2 a) GMmr/R3 I r— _ r) __ i}; ' R3)
_ b) —GMmr2/R3 ‘ V . 
c) GMmr/R2 ' A ~> I \ [M l
_ QDGMmrz/‘m3 W :farF =/_<5r/~ L291” 2:
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2/33 1 Physics 140 Winter 2004 Midterm 3 15. In the static conﬁguration belOw, box A of mass mA=11kg lies on a frictionless ramp
inclined at an angle 6=30° while box B of mass mg=7kg and hangs from a vertical
cord. What is the magnitude of the tension in the upper cord C? a) 48N d) 235N
e) 471 N 16. Consider a can of tomato soup rolling up an inclined ramp Without slipping; Which]
one of the following statements about the motion is false? worn a) The magnitude of the can’s angular velocityvis decreasing.‘ b) The ratio Km/Kmms of kinetic energies in rotation and translation is constant. v
c) The torque about the contact point C due to the weight of the can is nonzero.
d) The torque about the can’s center of mass 0 due to thenormal fOrce of the ramp is zero.
® The force of static friction at the contact point acts in the direction opposite the center of
mass velocity vcom. [[53 77+ NA 7;} = M143 Xi‘ﬂé‘ TYT—M smﬁcaréL mAj Av ’93
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=>@/3‘7434€ Physics 140 Winter 2004 Midterm 3 l7. Comets A, B and C have equal mass and orbit a common Star as shown below.
Comets A and B have orbits with the same semimajor axis. Which of the following
statement(s) about their orbits is(are) true? a) C’s orbit has lower angular momentum than B’s. ,
b) A’s orbit has a more negative mechanical energy than B’s.
c) C’s orbit has a more negative mechanical energy than A’s.
d) A’s orbit has higher angular momentum than B’s. ® A’s orbit has the same period'as B’s. 18. (P) Two uniform rods, with centerof—mass locations CM shown below, are connected
to tables via frictionless pivots at their ends. Rod B is longer than rod A, but both '
' are made of the same material with ﬁxed mass per unit length. Both are initially
released from rest at the same angle 6. Which of the following statements about the motion is false? L. a) The initial linear accelerations of the CM locations of both rods are the same. CED The initial angular accelerations of both rods are the same.
c) The angular accelerations of the rods both increase in time. (1) At some time after release but before hitting the table, the kinetic energy of rod B is larger than that of rod A. I
e) The linear accelerations of the'CM location of the rods initially point in the same direction. 0< 2 m1} o< 2 _L,~ mjm/Qaiw)
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E) [(1. + UL‘ 1:? O +Mj(é__:)smc9 = K L3>LA =3> K8 >/</4 ==”> [CD "I 72416,. (e) 72% . 30% 07/3 /%/% Physics 140 Winter 2004 Midterm 3 ' 19. The gyroscope below — an aluminum wheel of mass m and radius r, spinning with
angular velocity (9 — is observed to revolve around the pivot with period T. If the
lever arm d from the pivot were doubled, what change could you make to the wheel
to keep the precession period T fixed? (Assume all other variables are held. ﬁxed ’ during the change.) a) halve its mass.
b) halve its radius. c) double its radius.
@double its angular velocity.
e) double its mass. V  20. A solid disk and a ring roll without slipping down an incline. When will the disk '
accelerate more quickly down the incline than the ring? a) Only if the disk is more massive than the ring.
b) Only if the disk has larger radius than the ring. ® In all cases. d) In no case. p
e) Only if the ramp is inclined at an angle greater than 30 degrees. 10 @mfw W %ﬂ/€5M/mq;,2
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Wow o/Ingy/ c —f2/ 2 (5/1? 2 2 q/f ~_QI
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M? Physics 140 Winter 2004 Midterm 3 Answer Key
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