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Exam2_2013_Winter_Solutions, Exams of Mathematics

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Physics
140,
Winter
2013
March
14,
2013
Second
Midterm
Exam
Physics
Department,
University
of
Michigan
FORM
1
Please print your
name:
OLUT1OJ5
Your
INSTRUCTOR:___________________
INSTRUCTIONS
AND
INFORMATION
1.
Fill
in
YOUR
NAME,
UM
ID
NUMBER,
and
the EXAM FORM
NUMBER
on
the
scantron.
2.
RECORD
YOUR
ANSWERS
ON
THE
SCANTRON
USING
A
#2
PENCIL.
3.
Turn
in
this
exam copy
with
your scantron
answer
sheet.
4.
This
is
a
90-minute, closed
book
exam.
You
may
use
two
3”
x
5”
card
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.
Equations/values
that
you
may
find
useful:
s(t)
s
0
+
v0
t
+
V
2
a
t
2
v(t)
=
v0
+
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
+
‘A
CL
t
2
w(t)
=
(0
+
CL
t
vrw,
atan=rct
r
x
F
dL/dt=Ict
L
r
xp
1w
Uspring
=
V2
kx
2
P
=
AW/At
=
F.v
Impulse
J
=
IF.dt
AK
+
AU
Rod,
axis
through
one end
I
1/3ML
2
Rod,
axis
through
center:
I
1/12ML
2
Solid
sphere:
I
=
2/5
MR
2
Hollow
sphere:
I
=
2/3
MR
2
Solid
cylinder or
disk:
I
=
V
2
MR
2
Hollow
cylinder
I
=
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
=
-
+
-
V
2
m,+m
7
m,+m
7
-
2m
1
m
7
—m,_
V
21
=
Vi,,,
+
V2h
1
m
1
+
in,
m,
+
m,
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13
pf14
pf15
pf16
pf17
pf18

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Download Exam2_2013_Winter_Solutions and more Exams Mathematics in PDF only on Docsity!

Physics 140,

Winter 2013

March

SecondMidterm Exam

PhysicsDepartment, UniversityofMichigan

FORM 1

Please print your name:

OLUT1OJ

Your INSTRUCTOR:___________________

INSTRUCTIONS ANDINFORMATION

  1. Fillin YOURNAME, UM IDNUMBER, and the EXAM FORMNUMBER onthescantron.

2. RECORD

YOUR ANSWERSONTHE

SCANTRONUSINGA #2PENCIL.

  1. Turninthisexam copy withyour scantron answer sheet.
  2. 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 = -

    • V 2

m,+m 7 m,+m 7

  • 2m 1 m 7 —m,_

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

/

= ±

  • h-)

(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

  • r’ve

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?

  1. The angular acceleration of

ladybug A is twice the angular acceleration of ladybug B.

  1. The tangent component of linear acceleration of ladybug A is twice the tangent component

of linear acceleration of ladybug B.

  1. The radial component of linear acceleration of ladybug A is twice the radial component of

linear acceleration of ladybug B.

  1. The angular velocity of ladybug A is twice the angular velocity of ladybug B.
    1. 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)

  1. 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 .)

  • (5Ib)(i 1 ,)

= 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

  • “‘)c:—1v 4 /

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 ‘

  • f’°’°

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*)

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

  • 3:

L