Exam 2: Tomorrow 8:20-10:10pm

R. Field 11/5/2013 University of Florida

PHY 2053 Page 1

Exam 2: Tomorrow 8:20-10:10pm

Last Name RoomA-E NPB 1001F-L NRN 137M-R WEIM 1064S-Z MCCC 100

You may bring a single hand written formula sheet on 8½ x 11 inch paper (both sides).

• Room Assignments:

• Crib Sheet:

• Breakdown of the 20 Problems

• Calculator:

Material # of ProblemsChapter 6 2Chapter 7 5Chapter 8 6Chapter 9 6

Chapter 10 1

You should bring a calculator (any type).

• Scratch Paper: We will provide scratch paper.


PHY 2053 Page 2

Exam 2 Fall 2010: Problem 9• A projectile is fired straight upward from Earth's surface

with a speed that is half the escape speed. If R is the radius of Earth, the highest altitude reached, measured from the surface of the Earth, is:

Answer: R/3% Right: 9%

E

Eesc

f

E

Eesci

RGMv

ER

mGMmvE

20

221

Escape Speed

EE RRrh 31

E

E

E

E

Eesc

E

if

Ef

E

Eesci

RrR

mGMR

mGMvmrmGM

EErmGME

RmGMvmE

34

412

21

221

)1()2/(

)2/(


PHY 2053 Page 3

Exam 2 Fall 2012: Problem 7

• Two point particles with equal mass M are released from rest a distance d apart and are attracted toward each other due to the gravitational force. They move toward each other at equal speeds v as shown in the figure. What is the speed v of the two particles when they are a distance d/5 apart?Answer: % Right: 29%

dGM

ddGM

ddGMv

dGMMvMv

dGM

EEd

GMMvMvE

dGME

if

fi

if

ff

ii

415/

1112

22

212

21

2

22

212

21

2

v v

dGM /2

dGMv 2


PHY 2053 Page 4

Final Exam Spring 2011: Problem 12• A uniform disk with mass M, radius R = 0.50 m, and moment of

inertia I = MR2/2 rolls without slipping along the floor at 2 revolutions per second when it encounters a long ramp angled upwards at 45o with respect to the horizontal. How high above its original level will the center of the disk get (in meters)?

Answer: 3.0% Right: 39%

x-axis

v v

H

R

)(2212

21 RHMgEMgRIMvE fi

mssmmf

MRI

gR

MRI

gR

MIR

gMIv

gH

0.3)/2(23

/8.9)5.0(2121

2

21

21

22

222

2

222

2

2

22222

f

Rv

2


PHY 2053 Page 5

Exam 2 Spring 2012: Problem 39• A modern sculpture has a large horizontal spring, that is

attached to a 60-kg piece of uniform metal at its end and holds the metal at rest at an angle of θ = 60° above the horizontal direction as shown in the figure. The other end of the metal is wedged into a corner and is free to rotate. If the spring is stretched 0.2 m what is the spring constant k (in N/m)? Answer: 849 % Right: 31%

0cos2

sin MgLxLk

BABABA sincoscossin)sin(

Mg

kx

mNm

smkgx

Mgk /849)60cot()2.0(2

)/8.9)(60(cot2

2


PHY 2053 Page 6


R FT

Mg

y-axis

• A cloth tape is wound around the outside of a non-uniform solid cylinder (mass M, radius R) and fastened to the ceiling as shown in the figure. The cylinder is held with the tape vertical and then release from rest. If the acceleration of the center-of-mass of the cylinder is 3g/5, what is its moment of inertia about its symmetry axis?

Answer: % Right: 48%

2

32 MR

R

yT MaFMg

RIa

IRF yT

)( yT agMF

2322

53

53

22

MRMRggg

MRaag

aFRI

y

y

y

T


PHY 2053 Page 7

Exam 2 Fall 2010: Problem 13• A uniform plank is 6 m long and weighs 80 N. It is

balanced on a sawhorse at its center. An additional 160 N weight is now placed on the left end of the plank. To keep the plank balanced, the sawhorse must be moved what distance to the left?

Answer: 2 m % Right: 48%

Mg

d L/2

mg

mLLNN

NLMgmg

mgd 231

216080160

2

mLNmgNMg

616080

02

MgddLmg


PHY 2053 Page 8

Exam 2 Fall 2011: Problem 10• Two pendulum bobs have masses MA = 3 kg and MB

= 2 kg and equal lengths L as shown in the figure. Bob A is initially held horizontally while bob B hangs vertically at rest. Bob A is released and collides with bob B. The two masses then stick together and swing upward to the right to a maximum angle . What is the maximum swing angle ?

Answer: 50.2o % Right: 31%

222

121 vMEgLME AA

90o

L A

L

B

Before

L A+B

After

L A+B

After

Lcos

h

gLv 22

90o

L A

L

A

1

2

A+B

V ghMMEVMME BAfBAi )()( 2

21

VMMpgLMvMp BAfAAi )(22

)cos1( Lh

LMM

Mg

VhBA

A

22

2

2516

259111cos

2

BA

A

MMM

Lh

2.50


PHY 2053 Page 9

Final Exam Fall 2010: Problem 12

m

• A block of mass m is attached to a cord that is wrapped around the rim of a flywheel of radius R and hangs vertically, as shown. The rotational inertia of the flywheel is I = MR2/2. If when the block is released and the cord unwinds the acceleration of the block is equal to g/2, what is the mass m of the block?Answer: M/2 % Right: 51%

m

R

M FT

mg y-axis

TRFI

RaRvRs

yT maFmg

yT aRI

RIF 2

yy maaRImg 2

Mgg

gRMR

aga

RIm

y

y21

21

21

2

221

2


PHY 2053 Page 10


• A uniform solid disk with mass M and radius R is mounted on a vertical shaft with negligible rotational inertia and is initially rotating with angular speed . A non-rotating uniform solid disk with mass M and radius R/2 is suddenly dropped onto the same shaft as shown in the figure. The two disks stick together and rotate at the same angluar speed. What is the new angular speed of the two disk system? Answer: 4/5% Right: 47%

R M

M

ffffiii MRMRILMRIL )( 222

1212

1212

1

54

22

2

22

21

21

)2/(

RRR

RRR

f


PHY 2053 Page 11


Initial

P

R

M

m

• A mouse of mass M/6 lies on the rim of a solid uniform disk of mass M that can rotate freely about its center like a merry-go-round. Initially the mouse and disk rotate together with an angular velocity of . If the mouse walks to a new position that is at the center of the disk what is the new angular velocity of the mouse-disk system?Answer: 4/3 % Right: 58%

Final

P

R

M

m )( 2mRIIL diskiii

fdiskfff IIL

)( 2mRII disknewdisk fi LL

34

221

22 2111

Mm

MRmR

ImR

disknew

2291

22

22MR

IL

IL

EEE

i

i

f

f

if

Note that energy is not conserved in

this problem!


PHY 2053 Page 12

Exam 2 Fall 2010: Problem 20• Suppose that you release a small ball from rest at a depth

of 39.2 m below the surface in a pool of water (with density water) near the surface of the Earth. If the density of the ball is 1/3 the density of water, how long does it take the ball to reach the surface?Answer: 2 s % Right: 53%

Mg

d

water

Fbuoyancy

y-axis

yballballwater aMgMgM

221 tad y yballballballballballwater aVgVgV

yadt 2

gga

ball

water

ball

ballwatery

1

sssm

m

g

dt

ball

water

24)/8.9(13

)2.39(2

1

2 22


PHY 2053 Page 13

Final Exam Fall 2010: Problem 13• A block of wood has a mass of 4 kg and density of 600

kg/m3. It is loaded on top with lead (density = 11,400 kg/m3) so that the block of wood will float in water with 90% of its volume submerged. What is the mass of the lead if the water density is 1,000 kg/m3?

Answer: 2 kg % Right: 46%

water

Fbuoyancy

y-axis

(Mwood+Mlead)g

Mwood

Mlead

0)()( yleadwoodleadwoodwater aMMgMMgM

kgMMmkgmkg

MVVM

VMV

MVMMM

woodwood

woodwoodwood

watersubwood

woodwood

woodwatersub

woodwatersubwoodwaterlead

21/600

)/000,1(9.0

1

21

3

3


PHY 2053 Page 14


Air

Fspring = W0

Mg

• An object hangs from a spring balance. When submerged in water the object weighs one-half what it weighs in air. If when submerged in an unknown liquid with density X the object weighs three-fourths what it weighs in air, what is the density of the unknown liquid?Answer:% Right: 41%

water21

Liquid

Fspring = Wliquid

Mg

Fbuoyancy MgW 0

0 gMMgW liquidliquid

VggMWW liquidliquidliquid 0

VgWW waterwater 0

21

021

0

043

0

0

0

WWWW

WWWW

water

X

water

X

VgWW XX 0

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Exam 2: Tomorrow 8:20-10:10pm