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Unformatted text preview: 544mg Physics 140, Winter 2010 Second Midterm Exam: March 11,2010
Physics Department, University of Michigan FORM 1 Please print your name: Your DISCUSSION SECTION or INSTRUCTOR: INSTRUCTIONS AND INFORMATION 1. Fill in YOUR NAME, SECTION NUMBER and EXAM FORM NUMBER on the scantron.
2. RECORD YOUR ANSWERS ON THE SCANTRON USING A #2 PENCIL. Prof. Len Sander l2 14, 15
Mr Tim Cohen 3. Turn in this exam copy with your scantron answer sheet. 4. This is a 90minute, closed book exam. You may use two 3” x 5” cards on which you have
your favorite equations. You also may use a calculator but please do not share calculators. 5. All cell phones and other communication devices must be shut off and out of sight.
6 There are altogether 20 multiple choice questions. All questions are of equal value. 7. Equations that you may ﬁnd useful: Sf = s + vot + 1/2 a t2 0f = 9m + wt + 1/2 0c t2 Rod, axis through one end I =l/3ML2
Vf = v0 + at cof= (00 + 0L t Rod, axis through center: I = 1/ 12ML2
arad = vz/r = r0)2 vt = r 0), at = r on Solid sphere: I = 2/5 MR2
F= ma 1' = r x F = dL/dt=1a Hollow sphere: I = 2/3 MR2
p = mv L = r x p =10) Solid cylinder: I = 1/2 MR2
w = F.s w = 'c (92 — 91) K Hollow cylinder I = 1/2M(R.2+R22)
F = —VU Fk = MN Hoop: I = MR2
Frad = mVZ/r Uspring = 1/2 kx2 Impulse E J = lF.dt = Ap
w = AK 1 2,10,n + MR2 P = AW/At = F.v
AK + AU = Wm Krm = 1/. Icoz
v1,f = m1 —m2 vlin + 2m2 Vzm V2] 2 2m] V1 + m2 —M, V2.11: . .' , ,in
ml+m2 m1+m2 m,+m2 m1+m2 Problem 1:
The angular momentum of a system is constant when: A. the total kinetic energy is constant.
B. no net external force acts on the system. C. the linear momentum and the energy are constant. no external torque acts on the system. E. the moment of inertia is constant. Problem 2: An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev/min to 200 rev/min in 4.0 3. How many revolutions has the fan made
during those 4.0 s? A. 11.7 revs C. 43.6 revs D. 75.0 revs E. 116.5 revs (a. — $790M”— W
Q1/2260 ~011 270Z: ’24sz M :7005’04/3;
I1: 9 a n
g 543111;411 : 53253.9  {dig/é: /4é.éra/ fa 6 0 7' Problem 3: A graph in ﬁgure shows potential energy versus position for a particle moving in a straight line (along the Xaxis). From this curve and for the region displayed, we
deduce that: U(X) A. This could not represent an actual physical situation since the drawing shows the
potential energy going negative, which is not physically realizable. B. There are three positions of stable equilibrium. F:  ‘14} «VIZ/ﬂu" 0/X ,/ 194m 15 XL
@The force on the particle would be strongest when the particle is near the origin. 1&4» [ﬁzz
D. The force on the particle would be greatest when the particle is near point P. /‘. 7 N06: /jz‘
., ,1, .
E. For a given value of x, the particle can have a total energy that lies either above or
below the value given by the curve at that point. Problem 4:
A 7.0kg stone is subject to a variable force given by the equation F(x) = 6.0N—(2.ON/m)x+(6.ON/m2 )xz. If the stone is initially at rest at the origin,
ﬁnd its speed when it has moved 9.0 m. A. 11.6 m/s B. 20.2 m/s C. 36.7 m/s D. 42.3 m/s E. 51.5 m/s
Cl
' 2 .
W: AK => jaw. ._ gmpo
9 (7 ”z,
.  J .
f/é‘v—zx¢éf)dx : 51/ ~J/+/¢$”3’:/43/ ’5 z X; 2’”
0 7;: gut/37 = JO'QW/S €33 /’___——_J Problem 5:
A ball of mass m is suspended from a string of length R. The ball is set into freely swinging circular motion in a vertical plane. The centripetal acceleration of the ball at the top of the circle is 8g. What is the centripetal acceleration of the ball at the bottom
of the circle? A. 24g B. 16g C.14g E.10g R L ”
é/Mli/aaejmgg :Zl—mzép/A»
Z L :djp'l‘l/C’p g/Z R
WM“.— 62/ +177? J 1 d a"
a .2 ﬂ _ /2’
1,5414% 72 r ii Problem 6:
A long, thin bar of length L and crosssectional area A has its long axis parallel to the
xaxis as shown. If the density varies along the length of the rod as p(x) = orxn where 0L is a positive constant and n is an integer, where along the xaxis is the center of
mass of the rod? 4x Problem 7: A 58 kg runner is standing on the outer edge of a horizontal turntable mounted on
a frictionless axis through its center. The turntable has a radius of 2.9 m and
moment of inertia 500.0 kgm2 and is currently at rest. The runner starts his run
along the outer edge and is observed to run with a speed, relative to the earth, of
5.6 m/s. If he runs for 60 see, how many revolutions does the turntable make? A. 18.0 revs B. 15.4 revs C. 12.6 revs D. 9.2 revs E. 7.8 revs ,1} =7 O: meg+1; :7
CC) __, ,_ HRU' : .. b—d’x 2'915—é : __ /r37<lnfl’~(/5 I 500 he; 42/2” I744 mad; drﬂcjméﬁ oé’raC/{m / w/M/M 5): Cut = I.izf4x60=HI/3m/(
[/3 rap! 2 . —/apreu§ :77
// Problem 8: The force on a particle 13 given as F: 2 x j where j is a unit vector along the y
direction. The particle travels on a square“loop in a clockwise direction starting from the origin. How much work 1S done on the particle by the force Eduring one
complete trip around the square? (5,5) ‘ . g L A ‘ ‘ jﬂru IS Vawglé au/ pZN'éaZl/é/ a5?) / 7 4W5 I‘l/Qré I11 mi .102 ”111/ IX
5’ x= = 0
I w. = Imp? =0 +7 a)
0 Z s N /)
. Wm _. F (1 = 2 ’4 [[X L = O buéﬁ I :L
(0,0) (5,0) x .4 /~ / j "A N ,9 h, A. —250J B. l80J C. OJ D. 180.] E. 250.]
5’ f Physics 140, Winter 2010, Midterm 2 Problem 9:
A 12.0kg block is sliding on a rough, horizontal surface at 6 m/s and eventually
stops due to friction. The coefﬁcient of kinetic friction between the rock and the
surface is 0.3. What average power is produced by friction as the rock stops? A. 47W B. 62W C. 84W D.lO6W E.216W w 4A? => UALMJA:0Z*ML:7 d,;j:gL/7 WC "’P—Zﬁ pg.— wznn aJWM‘Z/ 5L0" rx’ X’ x 2: (44‘
ft: fa div:07  (73 /Z h? 3 Wm]; maﬂ/i‘ﬂg‘m/‘a <9 gawzﬁZaﬁuzmllw 6‘) 0 I] m v 6:
4:04. 1471—551” /:m1.a .=/2y2.(7)l/: 35“ ZfN :2) M]: :2fo 6‘IZSZ/é‘j ' I)
jt’
4 w: 24 _ MVr/OéJ
' z? ‘  m 6
Problem 10: (Zuﬁlzwjﬂ7/ﬁuw: 4 Block A with mass mA = 2.0 kg and block B with mass m; = 3.0 kg are forced
together, compressing a spring between them. The system is released from rest on a
level, frictionless surface. The spring, which has the spring constant k = 250 N/m
and negligible mass, is not fastened to either block and drops to the surface after it
has expanded. If block B acquires a speed of 2.0 m/s, by how much was the spring
compressed from its equilibrium position? )4.» mmﬁzm % 0,390" Physics 140, Winter 2010, Midterm 2 Problem 11:
Two identical masses are released from rest in a smooth hemispherical bowl of radius R = 1.2 m, from the positions shown in ﬁgure. You can ignore friction between
the masses and the surface of the bowl. If they stick together when they collide, how
high above the bottom of the bowl will the masses go after colliding? Problem 12: A ball with mass M moving horizontally at 5 m/s, collides elastically with a block
with mass 3M that is initially hanging at rest from the ceiling on the end of a 0.5 m
long thin wire of negligible mass. Find the maximum angle 0 through which the block
swings after it is hit. _ wan . 20.12/67
W “”7311 V... * yea 2'" / Problem 13: A box is sliding with a speed of 4.0 m/s on a horizontal surface when, at point P,
it encounters a rough section. On the rough section, the coefﬁcient of friction is not constant, but starts with uk = 0.0 at P and increases linearly with distance past P, reaching a value of uk = 0.30 at 6 meters past point P. How far past point P
does the box slide before stopping? A 2.8m B. 3.6m C48m
U’ r2”
im ﬂ>ﬂ _____ iﬁiﬁ U ng= Al<
“P at a
Z.
0 Wife???” 1 V a Z
a 1 ”/r
l MVZ :7 0495/33” ; X, o 0g ,9; =
._ «it—‘— = 5 7/07;
"‘ ' 7 a7
Problem 14: W i In ﬁgure, the pulley (a uniform solid disk) has radius R = 0.2 m and mass M = 0.8 kg.
The rope does not slip over the pulley and the pulley spins on a frictionless axle. Block
A has mass mA = 2 kg and block B has mass m; = 5 kg. The tabletop is frictionless.
With what acceleration is block B descending? Physics 140, Winter 2010, Midterm 2 Problem 15:
A hollow, thin walled sphere of mass 12 kg and radius 0.5 m is rotating about an axle
through its center. The angle (in radians) through which it turns as a function of time (in seconds) 1s given by 0(t) — 1 5t2 + 0. St“. At the time of 3.0 5, what IS its angular
momentum? A. 94.5kgm/s B. 126 kgm/s C. 148 kng/s D. 172 kng/s E. 189 kng/s 2 J1.
L:I,(,J ”90891.1 7L1”. "T“2 EHQifﬂZxQﬁ)
_ 02’3”“L ’
W” d5 MHZ +4105,§3_3£;‘2; 1
w/f35):3x3111w271: 7+.:§‘9 53 “(/5 L: ij; 92% 6,3; 416 ﬁm/S
:23 W Problem 16:
A mass m= 50 kg IS attached to a light string which Is wrapped around a cylindrical
spool of radius R — 0.1 m and moment of inertia I — 4 0 kg.2.m The spool is
suspended from the ceiling and the mass is released from rest a distance h— — 5 m
above the ﬂoor. How long does it take for the mass to hit the ﬂoor? h " Tin
mg—mq="2
mew”?
A 14s B175 C22s D26s @
W O .8 L
_. 3. 45110%
I)“ _P:L O+LOJVV
_L ‘1 7 If: 23‘ , “2"? = 303424,
Xi: Z—a‘é 2‘ a [:04 \ Problem 17: A 5 kg package slides down a long ramp that is inclined at 120 below the
horizontal. The coefﬁcient of kinetic friction between the package and the ramp is uk=0.31. If the package has a speed of 2.20 m/s at the top of the ramp, what is its
speed after sliding 1.50 m down the ramp? A. 4.46 m/s N B. 2.46 m/s C. 2.03 m/s D. 1.43 m/s E. Stops before
/ covering 1.5 m
. 7;. _ 3 on the incline
\AJWC‘ b 14* 43 L; L L Z
k — L/M mev«A:émlé"£/W‘/IL+O 07,
W’/ I J g ‘ é
L/f L 5”, — '5 “L szr mu+2jAme—kag/Mme Problem 18:
A block of mass m = 2 kg travels on a horizontal surface. There‘is a coefﬁcient of kinetic friction pk = 0.25 between the block and the surface. The block has a speed
v = 4 m/s when it reaches x = 0 where it encounters a horizontal spring. The block
compresses the spring, momentarily stops, and then recoils and travels in the opposite direction. When it reaches x = 0 on its return trip, it stops. What is the
spring constant k of the spring? ( A. 6.0 N/m ) B. 10.6 N/m C. 18.2 N/m D. 26.4 N/rn E. 34.5 N/m W ,:A14+AUS x) “/1ng (2x) = O~Zimvl+OO
414’ 92x {:5 M [4A1 0194/1”th M ééég ’7Lrtoi/cfg Zyéi
. f 0 ””1 {X m. [A h/ 5 ﬂing’W
ﬂ: 3 n? J C “70 ? {Abba/v
fam’m M X m /4« W; A“! 14/4?” ﬂu ,3 /4 WA‘W ' 9ng 9x 025‘x 79 ’ 497V/Jvf/V/ % 60”}?
7 = 5 . /l/91J et/céﬁxzf % 420/4? /A‘({‘m ZZQK AZOOZ ”hated/41L“ X 0 X 4“,.ij = 0— gay. #520 ® L m‘f— 21%; :2x42 _ 2wmwt 60%.
X Problem 19:
A meter stick with mass M = 0.2 kg is pivoted at its end. Neglect the friction at the
pivot. If the meter stick is released from rest in a horizontal position, what is its
angular velocity when it passes the vertical position? M,L m [Wryfjéu mecjéuic'z/ aha/ﬂ
H [i 01 71/ K ' Mam 4/ A
i: ,L. t 14 Ce «UV 2
:: z , 2
II N) A. : a l .TCJ (,H H 1’ j a + O L 7‘ 2. __~ 1 z
:i Ame/wk! fit/Otpz / [/1 611% [44 J: 3 ﬂL
'I
H /‘1 A =1 1 ”L260; :3
9 J 2 iii?) Co : t§€ ; V 317; ., 5;9rl{7;
A. 2.5 rad/s B. 5.4 rad/s C. 7.7 rad/s D. 8.9 rad/s E. 10.8 rad/s Problem 20: The object shown in ﬁgure is pivoted at 0 about an axis perpendicular to the
plane of the page. Five forces act on it in the directions shown: FA = 10N at point
A that is 8.0 m from 0; FB = 16N at point B that is 4.0 m from 0; PC = 19N at
point C that is 3.0 m from 0; Pp = 12 N at point D that is 5.0 rn from O; and FE =
15N at point 0. What is the net torque about 0. Take the direction of the torque as
positive if it is pointing out of the page towards you. a T ’ 3% 493+» 95’ = Jae/v». ”JV/730‘;
F. : ZI‘x/é 092. 700: 6400”,. mt /ﬂ/Dagg 7 .— 3.19..200:/a5?2€’1//>aﬁe C 0
(D: 5x /2 Who at 0
Z =0xKaO E A. —22.4 Nm B. 7.4 Nm C. 5.8 Nm E. 22.4 Nm 3.1: Z? r 5w +(—e9 H915: mm. 1.3/4, 3, C ' z.
a; W/ /9“ W‘zﬁd/ow e.
@ / 7“ ...
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