R. Field 4/21/2013 University of Florida PHY 2053Page 1 Final Exam: 4/27/13 12:30pm-2:30pm Last NameRoom A-GTUR L007 H-KTUR L005 L-MTUR L011 N-RWEIL 270

R. Field 4/21/2013 University of Florida

PHY 2053 Page 1

Final Exam: 4/27/13 12:30pm-2:30pm

Last Name Room

A-G TUR L007

H-K TUR L005

L-M TUR L011

N-R WEIL 270

S-Z WM 100

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

• Room Assignments:

• Crib Sheet:

• Breakdown of the 20 Problems

• Calculator:

Material # of Problems

Your Exam 1 4

Your Exam 2 4

Chapter 11.1-12.8 4

Chapter 1.1-10.8 8

You should bring a calculator (any type).

• Scratch Paper: We will provide scratch paper.


PHY 2053 Page 2

Make-Up Exam: 4/24/13 5:10-7:00pm

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

• Room:

• Crib Sheet:

• Breakdown of the 20 Problems:

• Calculator: You should bring a calculator (any type).

• Scratch Paper: We will provide scratch paper.

Similar to the Final Exam.

For anyone who had to miss an exam during the semester.

1220 NPB.


PHY 2053 Page 3

Final Exam Fall 2010: Problem 9

• Near the surface of the Earth a startled armadillo leaps vertically upward at time t = 0, at time t = 0.5 s it is a height of 0.98 m above the ground. At what time does it land back on the ground?

Answer: 0.9 s% Right: 47%

v0

y-axis )()( 2

1221 gtvtgttvty oo

)(0)( 21

foff gtvtty

g

vt of

2

221)( hhoh gttvhty

h

ho t

gthv

221

ssssssm

mt

gt

h

gt

gth

g

vt h

hh

hof 9.0)5.0()4.0()5.0(

)5.0)(/8.9(

)98.0(22)(222

221


PHY 2053 Page 4

Final Exam Fall 2011: Problem 7

• Near the surface of the Earth a suspension bridge is a height H above the level base of a gorge. Two identical stones are simultaneously thrown from the bridge. One stone is thrown straight down with speed v0 and the other is thrown straight up a the same speed v0. Ignore air resistance. If one of the stones lands at the bottom of the gorge 2 seconds before the other, what is the speed v0 (in m/s)?

Answer: 9.8% Right: 36%

)()( 2221

0 downupdownup ttgttv

221

221

0)(

)(

upupoupup

oup

gttvHty

gttvHty

Hgttv

Hgttv

downdowno

upupo

221

221

y-axis

x-axis

H

221

221

0)(

)(

downdownodowndown

odown

gttvHty

gttvHty

smssmttgtt

ttgv downup

downup

downup /8.9)2)(/8.9()()(

)( 221

21

22

21

0


PHY 2053 Page 5

Exam 1 Fall 2010: Problem 12

Mg x-axis

y-axis

fs FN

• Near the surface of the Earth, a block of mass M is at rest on a plane inclined at angle to the horizontal. If the coefficient of static friction between the block and the surface of the plane is 0.7, what is the largest angle without the block sliding?

Answer: 35o

% Right: 83%

M

0sin xs MafMg

0cos yN MaMgF

35

cossin MgFfMg sNss

7.0tan s


PHY 2053 Page 6

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)?


x-axis

v v

H

R

)(2212

21 RHMgEMgRIMvE fi

mssm

mf

MR

I

g

R

MR

I

g

R

M

IR

gM

Iv

gH

0.3)/2(2

3

/8.9

)5.0(21

21

2

2

1

2

1

22

222

2

222

2

2

22222

f

Rv

2


PHY 2053 Page 7


• A thin hoop (I = MR2) and a solid spherical ball (I = 2MR2/5) start from rest and roll without slipping a distance d down an incline ramp as shown in the figure. If it takes 2 s for the ball to roll down the incline, how long does it take for the hoop (in s)?

xMafMg sin

xRa

Rv

Hoop or Ball

d


x-axis

f R Mgsin

RfaR

II x

xx MaaR

IMg

2sin

221 tad x

21

sin

MRI

gax

ssballthoopt 39.2)2(1952.1)(1952.1)(

7.0

11

1

1

1

)(

)(1075

2

2

2

MR

IMRI

balla

hoopa

hoop

ball

x

x

xa

dt

2

1952.17.0

1

)(

)(

)(

)(

hoopa

balla

ballt

hoopt

x

x


PHY 2053 Page 8


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

R

IaIRF y

T )( yT agMF

2322

53

53

22

MRMRg

ggMR

a

ag

a

FRI

y

y

y

T


PHY 2053 Page 9

Exam 2 Spring 2012: Problem 10

• A cannon on a railroad car is facing in a direction parallel to the tracks as shown in the figure. The cannon can fires a 100-kg cannon ball at a muzzle speed of 150 m/s at an angle of above the horizontal as shown in the figure. The cannon plus railway car have a mass of 5,000 kg. If the cannon and one cannon ball are travelling to the right on the railway car a speed of v = 2 m/s, at what angle must the cannon be fired in order to bring the railway car to rest? Assume that the track is horizontal and there is no friction.

Answer: 48.2o % Right: 57%

iBallcarix VMMp )()(

v

x-axis

)cos()( muzzleiBallballBallfx VVMVMp

2.48

fxix pp )()( )cos()( muzzleiBalliBallcar VVMVMM

6667.0)/150)(100(

)/2)(5000(cos

smkg

smkg

VM

VM

muzzleBall

icar


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/(

RR

R

RR

Rf


PHY 2053 Page 11


• A toy merry-go-round consists of a uniform disk of mass M and radius R that rotates freely in a horizontal plane about its center. A mouse of the same mass, M, as the disk starts at the rim of the disk. Initially the mouse and disk rotate together with an angular velocity of . If the mouse walks to a new position a distance r from the center of the disk the new angular velocity of the mouse-disk system is 2. What is the new distance r?

Answer: R/2% Right: 65%

ffiiii MRMrLMRMRIL )()( 212

212

22

1

4

3

2

1

2

3 RRRr

f

i


PHY 2053 Page 12


d water y-axis

Mg

Fbuoyancy

• Two small balls are simultaneously released from rest in a deep pool of water (with density water). The first ball is reseased from rest at the surface of the pool and has a density three times the density of water (i.e. 1 = 3water). A second ball of unknown density is released from rest at the bottom of the pool. If it takes the second ball the same amount of time to reach the surface of the pool as it takes for the first ball to reach the bottom of the pool, what is the density of the second ball? Neglect hydrodynamic drag forces. Answer: 3water/5% Right: 22%

2

21 tad y

upballupballupballwater aVgVgV

ya

dt

2

ggaup

water

up

upwaterup

1

Mg

d

water

Fbuoyancy

y-axis

downballdownballwaterballdown aVgVgV

ggadown

water

down

waterdowndown

1

gagadown

waterdown

up

waterup

11

waterwater

downwater

waterup

5

3

312/2


PHY 2053 Page 13

Exam 2 Spring 12: Problem 46• What is the minimum radius (in m) that a

spherical helium balloon must have in order to lift a total mass of m = 10-kg (including the mass of the empty balloon) off the ground? The density of helium and the air are, HE = 0.18 kg/m3 and air = 1.2 kg/m3, respectively. Answer: 1.33% Right: 37%

0)( gmVgV ballonHEballonair

0)( gmMF HEbuoyancy

(MHE+m)g

Fbuoyancy

y-axis r

m

HEairballon

mrV

3

34

mmmkg

kgmr

HEair

33.134.2)/02.1(4

)10(3

)(4

3 31

31

31

33


PHY 2053 Page 14


• An ideal spring-and-mass system is undergoing simple harmonic motion (SHM) with period T = 3.14 s. If the mass m = 0.5 kg and the total energy of the spring-and-mass system is 5 J, what is the speed (in m/s) of the mass when the displacement is 1.0 m?


2212

212

21 kxmvkAE x

22

22222 4222

xTm

Ex

m

Ex

m

k

m

Evx

T

m

k

2

smsmsm

skg

Jx

Tm

Evx /4)/()/20()1(

14.3

4

5.0

)5(242 222222

22

2

2


PHY 2053 Page 15


• In the figure, two blocks (m = 5 kg and M = 15 kg) and a spring (k = 196 N/m) are arranged on a horizontal frictionless surface. If the smaller block begins to slip when the amplitude of the simple harmonic motion is greater than 0.5 m, what is the coefficient of static friction between the two blocks? (Assume that the system is near the surface of the Earth.)


mgF

Fmaf

N

Nsxs

ga smax

AmM

kAa spring )(

2max

5.0)5.0()/8.9)(20(

/196

)(

m

smkg

mNA

gmM

ks

)( mM

kspring


PHY 2053 Page 16


Ambuance Car VA Vcar

vsound

Ambuance Car Vcar VA

• An ambulance moving at a constant speed of 20 m/s with its siren on overtakes a car moving at a constant speed of 10 m/s in the same direction as the ambulance. As the ambulance approaches the car the driver of the car perceives the siren to have a frequency of 1200 Hz. What frequency does the driver of the car perceive after the ambulance has passed? This takes place on a cold night in Alaska where the speed of sound is 320 m/s.

Answer: 1127 Hz% Right: 53%

vsound

0

0

fvv

vvf

fvv

vvf

Asound

carsoundaway

Asound

carsoundtoward

))((

))((

carsoundAsound

Asoundcarsound

toward

away

vvvv

vvvv

f

f

HzHzfvvvv

vvvvf toward

carsoundAsound

Asoundcarsoundaway 1127)1200(

)10320)(20320(

)20320)(10320(

))((

))((

Documents

R. Field 4/21/2013 University of Florida PHY 2053Page 1 Final Exam: 4/27/13 12:30pm-2:30pm Last NameRoom A-GTUR L007 H-KTUR L005 L-MTUR L011 N-RWEIL 270