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Physics 140,
Winter 2013
March
SecondMidterm Exam
PhysicsDepartment, UniversityofMichigan
FORM 1
Please print your name:
OLUT1OJ
Your INSTRUCTOR:___________________
INSTRUCTIONS ANDINFORMATION
- Fillin YOURNAME, UM IDNUMBER, and the EXAM FORMNUMBER onthescantron.
2. RECORD
YOUR ANSWERSONTHE
SCANTRONUSINGA #2PENCIL.
- Turninthisexam copy withyour scantron answer sheet.
- Thisisa90-minute, closed bookexam. Youmayusetwo3” x5”cardonwhich youhave your favorite
equations.You also may use acalculatorbut pleasedonot share
calculators.
Allcellphones andothercommunication devicesmustbeshut off and out ofsight.
There arealtogether 20 multiple choice questions.Allquestionsareofequal value.
Equations/values that you
may find useful:
s(t) s 0
v 0 t
V 2 a
t 2
v(t)=v 0
at
7
arad v/r
F=ma=dp/dt
W
=f
F.ds
Fk=1kN
g=9.8m/s 2
F
=—dU(x)/dx
W=AK
e(t)
wot
‘ACLt 2
w(t) =(
CLt
vrw, atan=rct
rx F dL/dt=Ict
L rx
p
1w
Uspring= V
kx 2
P=AW/At =F.v
Impulse J =IF.dt
AK+AU
Rod, axisthrough one endI 1/3ML 2
Rod, axisthrough center:I 1/12ML 2
Solid sphere: I= 2/5MR 2
Hollow sphere: I
MR 2
Solid cylinder or disk:I =V 2 MR 2
Hollow cylinderI= V 2 M(R 12 +R 22 )
Hoop: 1MR
Ap IpIcm+Md 2
Krot
=V 2 1w 2
— m 1 —m 2m,
V 1. 1 = -
m,+m 7 m,+m 7
V 21
=
Vi,,,+
V2h 1
m 1 + in, m,+ m,
Table 92 Moments of Inertia of Various Bodies
(a) Slender rod,
axis through center
/
= ±M
(b) Slender rod.
axis through one end
1
=
(c) Rectangular plate.
axis through center
/
= ±
(d) Thin rectaitular plate,
axis along edge
—
/
(I
(e) Hollow cylinder
1=
MR
(g) Thin-walled hollow
cylinder
1 = MR 2
(h) Solid sphere
1= MR 2
(I) Thin-walled hollow
sphere
1=
—R-
Solid cylinder
1
= M(R ÷ R, 2 )
2012 Pearson Oducalnon. so
Problem 2:
Abodymoves underthe influence ofseveral forces alongaclosed-loop path shown in
thefigure. Itbegins in
the lowerleftcornerofthesquareand moves
counterclockwise
until itreaches the
same corner afteracompleteloop. Which statementaboutthework
donebythekinetic friction forceactingonthe body duringsuchmotionistrue?
Workisnegative. 1
B. Workiszero, because itisaconservativeforce.
C. Workiszero, because the overalldisplacementiszero.
D. Workiszero becauseofthe mutual orientationofthe force
and thedisplacement vectors
along each leg.
E. Work ispositive.
çf
< 0
ctose
rtk
Tk€
t
e;
ke
mc
k
d-t
j
fvL’c
er
CiLt
0 vj
rt4’L C
e..
(v)
t
krar
Lxtctkj
stJ
ke
v
srecQ6L-
(ga)
tc&
Wbfk.
Cia&,j)
e±ive i
Problem 3:
Two ladybugs are clinging to a rotating platter. Ladybug A is twice as
Far From the axis of
rotation as ladybug B. Which statements about ladybugs’ kinematic quantities below are
true?
- The angular acceleration of
ladybug A is twice the angular acceleration of ladybug B.
- The tangent component of linear acceleration of ladybug A is twice the tangent component
of linear acceleration of ladybug B.
- The radial component of linear acceleration of ladybug A is twice the radial component of
linear acceleration of ladybug B.
- The angular velocity of ladybug A is twice the angular velocity of ladybug B.
- The linear velocity of ladybug A is twice the linear velocity of ladybug B.
A. Statements 1, 2, 3, and 5 only.
B. Statements 2 and 5 only.
C.
Statements 2, 3,
4, and 5
only.
Statements 2, 3, and 5 only.
E. Statements 3
and 5
only.
AJI r&
aM
cL4tS
wu
-ke-
f
Lmj
&)
V
at
lL&(j
5o:
rA
V,
()v
Z;
t0A
0 A
A
B 3
2.1-
Okp
1
it..
rooJ
cifrip1ziI
(L4)A=
t&)
Problem 5:
In all three situations below, an object of mass rnl
originally moves with an initial velocity v,
and collides with another object of mass in 2 , which is initially at rest. As a result of this
collision, object mI
comes to a complete stop, and object m
moves with a final velocity v,rin
the same direction as the incoming object.
Which of the following three situations could
occur?
Before:
After:
I. in = 3m, 1112 = m, v 1 = v, v 1 3i’
mm2m,
v 1 =v 1 =3v
3v
3r
3v
C)
- in 1 = 111, 1112 = 3m,
v 1 = 3v,
Vf V
A. All three are possible.
B. Situation 2 only.
C.
Situations 1 and 3
only.
D. Situations I and 2 only.
Situations 2 and 3 only.
JPLO44C
AS(O1.
SO)
t 4 j rfri
__
()(o)
l_
wi)(v)+
i)(g 2 <
f(3)(o)÷
Cm)(3v) 2
3WLV
ç
()(3V)
.j)(oJ
= (i)Co)
t
Lw)(3V)
2.’ mvmV
L 4:
(h(w)+±(n1)(o5 2 =
()(
G
o
1 O1A
±k
(ved-)
&ttv’ ô
iS
ervet aAk.L
t(
fr.ivi€
eirctj
fk
cLLsfrvi
€fr
ss e-r
+t
t€
(-vi
eiieru
4 e
eo(Listc’.
Tk€
+it
k’L1C €r-S
,Le-tA
-&tzkte.:
-i-
KE
I(6 ± KEZf
c
3MV=3lV
x
I
C)C3v)
÷
C)(o)
C)(0)
t
(3)(V)
3mV3mV
)(3v)+(3)(o)>
L
J
Problem 6:
A sculptor welds three dense uniForm metal objects together. Their weights and dimensions
are shown in the figure. If the artist tosses this object in the air, how far from the left end is
the point that will follow a
lovely parabolic arc (in the absence of
air resistance)?
Tk€
+kd
kvJ’IJ
XCM
141
f). ‘ 24 z
‘f- $
)CCM
(n qe)
(i 1)(o.in) -i--
Ci
(bJ( 2 .)
= Iki
A. I in
B.
2 in
C. 3 in
in
E. 5 in
un 2 3
4 6in
L
I I I
1
1 lb
5l
C
4k€
cr
(c4)
•ft M Ce-Ld) /y44.
lii, -‘-
41 -i
Problem 8:
A body of mass m 1 = 2.0 kg makes a totally elastic collision with another body, m2,
at rest
and continues to move in the original direction but with one-fourth of its original speed.
What is the mass m2 if the
initial speed of mass mj was 4.0 m/s?
A. 0.4 kg B. 0.6 kg C. 0.9 kg D. 1 .0 kg 1.2 kg
4
C
vec) !ktAI a&d
*k€
ar. ciwz.
—
‘U,
L2)(4)÷-v =
‘I V 2 =
‘-V
vj
V
tk
/
:
V)1 2 = 4.2-
k.
Problem 9:
Consider a spring that does not obey the I-lookes law. Dependence of the force exerted by
the spring on the spring’s extension or compression x is given by the following relationship:
F-—Ic 2 (instead of F—kt). Which of the following expressions may represent the
elastic potential energy of such a spring?
A.
2/
B. /c 3 /
kx 3 /
D. 1c 3 /
E.
4/
=>
dx
x
Jdx(tt)
U
kJxx
I
Problem 10:
— awtr ?(‘C4.
A light rope is wrapped around a uniform solid cylinder of radius R = 0.3 m and mass M = 20
kg free to rotate without friction around an axle through its center of mass. The free end of
the rope supports a block of mass in = 50 kg. What is the tension in the rope as the mass m
descends?
Nere
1 o. r
p
roz w&j
err4lc’
A. 16.3 N
O-
B. 36.8 N
The
QeC A*rt
J2,
(V 0 zo”t/s) a*i
.
156.5 N
tr
QS I..AVj
&A1-4C
L*f•
ew
s - a
tk
p
uJ1ej’i
7ee at
&t-a±
tv.esit Is
9j* (o)f()
LM/V
I
4ni
=>
()v2=
fLm. ‘,
DZt
2(-M)h ‘e
WiNk
tke ki’nevvi-z’c
.eesj -÷2at’
(1ere
VozO)
F
r
L
Nw 1
h4j
u
Je
Sd L4b/
f
tt
7r
81.7 N
k
niv 2
Pevrt’fe
4-e 4cr
t’t
tiSkM
T- =
()
&C)A
aiV
c.
T,
d
2n-itM
=
?nq i — —
2m+M
1
Zni-i-M
Problem 11:
A large frog of mass 0.2 kg sits at one end of a uniform wooden bar and another frog of mass
0.3 kg sits at its other end. The bar has mass 0.5 kg and length 0.
rn. The bar floats on the
surface of a calm lake and has negligible friction with the water.
The two frogs manage to
trade ends without falling in the water. How far does the bar move on the surface of the
water?
A. 0.01 rn B. 0.02 m C. 0.04 m D. 0.06 m
iii
t
at
e
4± le
)2Lt
i-ad.
MSO, -&± a
-j
crid &,1f
cfr -&t e& £d
M
t’
o.5kj
L
o.
vi
o+os)o.)+(o. 3 )oL
o.LfLJM
0-f-
(o5J(o.L)÷
(o.2)Co.8)
-... ... .-——
XCMç
—
XCM
cMf—xa.4:
-°.3°.t4.°S.
CM
Q.O
Pe4ive
tk 4AW€V,
ttte c2M
d(-
eca*Ae
n.
IODZtI
•éL
/e tvi,nwf
+ke
fr-
th
rP
(cxct
-rtc).
So,
&)
bb
tt’&
rt td
j
I
M(CM
I
I &rdir
fr,.-
i+ 1 i C-M
Re
I4’L,e
4
Problem 12:
— csô-tker
pr
A bowling ball travelling
to
the right with speed 2 rn/s and a ping-pong ball travelling to the
left with speed 3 m/s undergo a head-on totally elastic collision. After the collision, what is
the speed of the ping-pong ball? The bowling ball is much, much heavier than the ping-pong
ball.
A. 2 rn/s
1-le
i
4
QizoL &ot o
fr
-f.
/4 ‘
rô c 1e- tft
ti’e
cthi 4 o- 3 - t
9M 47 tW1 2 ..
2n
—
7)1,
-i- 12
Yi4, *Wl
—I-
j
rili 4 #yl 1
C.
‘
-i-fl 2.
-1- —
yy1,+Mi
4
—
f’ /i_
Lfl1 1
)±Ly
B. 3m/s
C. 5rn/s
7 rn/s
E. 8m/s
O
M 11
—in 1
=_—
7’1l
*f1 2
dVLCA1j
ct1k’
(Vf
044 &d
d4’v
.J
yyi
(ti)
cUkd
tt
4
tke
£w 2
_c
Y>lj
/L
_I’-i
_(.T1iJ
÷
(.,,
(3i
yn 1 >)12,
14—c’
I
a
4-i-oj
—
i’’1i ‘
LWli.
JtL
Problem 13:
A 0.25 kg rubber ball
is
dropped from
the windov that is 50 rn above the sidewalk.
After
striking the sidewalk, the ball rebounds 25 m up. What is the magnitude of the impulse
imparted to the ball due to the collision with the sidewalk’? Neglect air resistance.
C. 23.2 N s D. 48.8 N s E. 61.3 N s
4
t
tLt
,a-tLL
frJ
Ip
d#
-e
Lz.
j(o)+mU
-y.(o)
J
m
(b ÷JhJ
I3.3(
1s
A. 6.8Ns
®13.4N
5
C*)
kç
Problem 15:
A hoop has a mass of 0.2 kg and a radius of 0.25 rn. It rolls without slipping along a level
ground at 5 rn/s. What is its total kinetic energy?
A. 2.5J C. IOJ
D.25J E.45J
E t
k
E
——---P1V
1CM = CY
Problem 16:
A
1-meter long 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 vertical position and given a very tiny
nudge, what is its angular velocity when it passes the horizontal position?
A. 2.5 rad/s
5.4 rad/s
C.
rad/s
D. 8.9 rad/s
E. 10.8 rad/s
ep5O - -
(t’s
‘I
1/)
I
=
I
z)
£::t)
if
5.’i
M, L
pivot
L
