Physics 1101

Final Exam 2003

1.A copper utility wire 80.0 m long and 1.90 m in diameter is stretched by a force of 600 N.

A.Determine the longitudinal Stress.

2

4dA

23 )10*90.1(4

A

2610*8.2 mA

A

Fstress

2610*8.2

600

m

Nstress

2810*14.2

mNstress

B. Find Young’s modulus for copper if the length after stretching is 80.145m.

strain

stressE

oLLA

F

)145.0

145.80)(10*14.2( 2

8

m

mm

N

21110*18.1

mN

2. A wheel having a radius of 30cm is initially rotating at 5.0 rev/s. It then undergoes a constant acceleration of 6.0 rad/s.

A.What is the angular speed of the wheel after completing 50 revolutions?

22

0

2

)314)(0.6(2)80.0( 222 rads

srad

srad

37692

3769

srad4.61

B. Find the linear speed of a point on the edge of the wheel at that instant.

rV )30.0)(61( ms

radV

smV 3.18

3. A 70.0g aluminum calorimeter cup is partially filled with 200.0g of water, and the system is at an initial temperature of 20.0 C. How many grams of steel shot at 98.0 C must be added to the system if the equilibrium temperature of the mixture is to be 31.0 C? The specific heat capacity of steel is 448 J/kg C.

HeatGainedHeatLost

TcmTcmTcm OHalusteel 2

)11)(4186)(200.0()11)(900)(070.0()67)(448( CkgC

JkgCkgC

JkgCkgC

Jm

kgm 330.0

1.A cylindrical rod having a diameter of 2.0125 cm is to be fitted into a 1.9975 cm hole in a brass block. These dimensions were taken at 20.0 C. To what temperature must the block be heated for it to just fit into the hole? The coefficient of linear expansion for brass is 19E/C.

TLL o )20)(9975.1)(10*19(9975.10125.2 6 T

45 10*80.7)10*80.3(015.0 T

)10*80.3()10*80.7(015.0 54 T

T )10*80.3(

01578.05

CT 26.415

Water is flowing through a closed pipe system. At one point the speed of the water is 2.8m/s where the diameter is 3.0 cm.

A. Find the speed of the water at a point 4.0 m higher where the pipe diameter reduces to 1.5 cm?

2211 VAVA 2

1 4dA

2

112 A

VAV

24

24

2 10*77.1(

)/8.2)(10*07.7(

m

smmV

smV /2.112

22

1 )10*0.3(4

A

4

1 10*07.7 A

2

2 4dA

22

2 )10*5.1(4

A

4

2 10*77.1 A

B. If the pressure at the lower point is 84 kPa, what is the pressure at the upper point?

2

2

221

2

11 2

1

2

1ghVPghVP

)0.4)(80.9)(1000()11)(1000(2

1)0)(80.9)(1000()8.2)(1000(

2

1)10*84( 2

2

23 P

)0.4)(80.9)(1000()11)(500()8.2*500()10*84( 223

2 P

2

2 /11780 mNP

6. A metal specimen having a specific gravity of 2.7(i.e. a density of 2.7 times that of water) and mass of 54 kg is attached to a spring and immersed in a tank of pure water.

A. Sketch a free body diagram for the mass and determine the volume of water displaced.

3/2400 mkg

kgm 54

v

m

m

v

3/2700

54

mkg

kgv

210*0.2 v

T

m

WFB

B. Find the tension in the string

0 WFT B

BFWT

vgmgT )81.9)(10*0.2(1000)81.9(54 2T

196529 T

NT 340

7. An object is placed 39.9 cm in front of a concave spherical mirror of radius 24.0 cm.

A. Locate the image using a ray diagram. Calculate the position of the image.

fdd io

111

12

11

0.39

1

id

39

1

12

11

id

cmd i .17

B. A submerged diver shines a light toward the surface of the water at angles of incidence of 40 degrees and 50 degrees. Will either beam of light emerge from the waters surface? Justify you answer mathematically.

2211 sinsin nn

2

112

sinsin

n

n

00.1

)40(sin33.1sin 2

0.59sin 2

Yes! The 40 degree angle will emerge!

8. An object is placed 30 cm in front of a thin convex lens of focal length 20 cm. A. Locate the image using a ray diagram. Calculate the position of the image.

fdd io

111

20.0

11

30.0

1

di

md i 60.0

cmd i 60

B. To a submerged diver from under water, the altitude of the sun (the angle between the sun and the horizon) appears to be 45 degrees. What is the sun’s actual altitude? The index of refraction for water is 1.33.

2211 sinsin nn

2

112

sinsin

n

n

00.1

45sin33.1sin 2

)94045.0(sin 1

13.70

Therefore the sun is 18o above the horizon.

A 1.5 kg mass attached to a spring vibrates in SHM with an amplitude of 20 cm and a frequency of 5.0 Hz.A. Find the spring constant k and the maximum velocity.

kxF

m

Nk

20.0

7.14

mNk /5.73

22

2

1

2

1kamv

m

kav

2

5.1

)20.0)(5.73( 2

v

smv /4.1

maF )/81.9(5.1 2smkgF

NF 7.14

B. What is the acceleration 0.20 s after the mass is released from maximum (positive) displacement.

)sin(2 tAa

)2sin(2 ftAa

))20.0)(11.1(2sin())11.1(2(20.0 2 a

)0243.0)(74.7(20.0a2/038.0 sma

m

kf

2

1

5.1

5.73

2

1

f

Hzf 11.1

1. A piano string is 73 cm long and has a mass of 4.1g. The string is under a tension of 510N.A. Determine the speed of the string and the frequency of the fundamental.

TFv

mkg

Nv

/00561.0

510

smV /302

L

m

73.0

0041.0

00561.0

fv

v

f

56.1

302f

Hzf 194

2

L

)73.0(2

m56.1

B. What is the wavelength of the second overtone of the resulting sound wave in the air? Sound waves in air travel at a speed of 343 m/s.

fv

Hz

sm

582

/343

m59.0

Hz582194*3

The second overtone is the 3rd harmonic

10. Find the power output for a sound generator that produces 65 db of sound at a distance of 100 m.

oI

Ilog10

212 /10log1065

mw

I

1210loglog5.6 I

125.6log I26 /10*16.3 mwI

A

PI

IAP

24 rA

)4( 2rIP 26 )100)(4)(10*16.3( P

wP 40.0

Notice I used the inverse log function, which is 10x button. Therefore you would Press the 10x button and enter in the difference of 6.5-12 to get I.

B. Find the intensity of this sound at a distance of 500m from the source.

oI

Ilog10

)/10

/10*26.1log(10

212

26

mw

mw

db61

2

1

2

2

2

1

r

r

I

I

2

2

2

112

r

rII

2

26

2 500

)100)(10*16.3(

I

26

2 /10*26.1 mwI

Part C1.Water flows in the horizontal pipe shown in the figure. At point a the cross-sectional area is 25.0 cm2 and the speed of the water is 2.40

m/s. At point B the cross-sectional area is 16.0 cm2. the fluid in the manometer is mercury, which has a density of 13600 kg/m3. What is the manometer reading h?

ghP

2211 VAVA

2

112 A

VAV

16

)4.2(252 V

smV /75.32

2

2

221

2

11 2

1

2

1ghVPghVP

)()(2

1)( 21

2

2

2

111 hhgVVPP

)(2

1 2

2

2

1 VVgh

)75.340.2)(1000(2

1)81.9)(13600( 22 h

mh 031.0

We need Δ P

2. An 800g piece of iron at 100 Co is dropped into a calorimeter of negligible heat capacity containing 50.0g of ice at 0 Co and 92.0g of water, also at 0 Co. What is the final temperature of the system? The specific heat of iron is 448J/kg Co and the latent heat of fusion of water is 33.5E4 J/kg. The specific heat capacity for water is 4186 J/kg Co.

HeatgainedHeatlost TmcTmcmcTmc firon

)0)(4186(092.0)0)(4186(050.0)10*5.33)(050.0()100)(448(800.0 4 TTT

TTT 3852091675035835840

1675035840)385209385( T

952

19090T

20T

3. A hot air balloon plus cargo has a mass of 327 kg and a volume of 687 m3. The balloon is floating at a constant height of 6.25 m above the ground. What is the density of the hot air in the balloon? Unheated air has a density of 1.29 kg/m 3.

Wair

FBWB

0 BAB FWW

gVWA )81.9)(327(

3208 gVWA 3208)687)(81.9)(29.1( AW

32088694 AW

NWA 5486kgmA 559

V

m

3687

559

m

kg

3/814.0 mkg

Note: change WA to ma by dividing by g.

4. You are driving along the highway at 35 m/s when you hear the siren of a police car approaching you from behind and you perceive the frequency as 1390 Hz. You are relieved that she is in pursuit of a different speeder as she passes you, but once she’s ahead of you the siren frequency seems to be 1320 Hz. What is the frequency of the siren in the police car? The speed of sound I air is 343 m/s.

)(1

s

o

o vv

vvff

)343

35343(1390

s

o vf

)343

308(1390

s

o vf

)308()343(1390 os fv

os fv 3081390476770

308

1390476770 so

vf

)(1

s

o

o vv

vvff

)343

35343(1320 0

svf

)343

378(1320

s

o vf

os fv 378)343(1320

os fv 3781320452760

378

1320452760 so

vf

308

1390476770

378

1320452760 ss vv

)1390476770(378)1320452760(308 ss vv

ss vv 525420180219060406560139450080

139450080180219060525420406560 ss vv

40768980931980 sv

smv s 7.43

)(1

s

o

o vv

vvff

)7.43343

35343(1390

of

)029.1(1390 of

ofHz 7.1350

Note that you will need two equations to solve this problem. One for when the sound is behind the drive and one for when the sound is ahead of the driver.

Equation 1Equation 2

2 unknowns, solve for fo

Substitute equation 2 into equation 1

Now that we have the speed of the Police, we now can substitute this answer back into the original equation