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XF.14a

H

PHYS-205(H14) (Kaldon-15032)

Name

________S

O L U T I O

N_______

Final Exam - 200,000 points + 40,000 WMU-Spring 2004

points

Check-Out:

Q

X

T

HNRS-290___

04/18/2004•Rev.8a

State Any Assumptions You Need To Make – Show All Work – Circle Any Final Answers

Use Your Time Wisely – Work on What You Can – Be Sure to Write Down Equations

Feel Free to Ask Any Questions

2a

2b

2c

2e

FINAL EXAM [FORM - A]

PHYS-205H (KALDON-14)

SPRING 2004

WMU

CSI

:

Miami

in

Helsinki,

Finland

(!)

Physics 205H/ Final Exam [Form-A]

Spring 2004

1.) (a) The Earth has a mass of 5.98 × 10 As The World Turns (50,000 points)

24

kg and an average radius of 6,370,000 meters. Find the

average mass-to-volume ratio of the Earth.

V

r

m

m

m

V

kg m

kg

m







34

3

34

3

21

3

24 21

3

3



,

,

.

.

.

/

b

g

(b) Find the moment of inertia, I, of the Earth.

Assume it is a uniform solid

.

I

MR

kg

m

kg m

solid sphere







52

2

52

24

2

37

2

(5.

)( ,

,

)

.

(c) Find the period (T), frequency (f) and the angular velocity (

) in SI units of the Earth as it spins on its

axis.

T

hours

hour

f

T

Hz

f

Hz

rad

.

(

sec/

)

,

sec

,

sec

.

.

.

/ sec





b

g

(d) Find the angular momentum (L) and kinetic energy (K

rot

) of the Earth as it spins on its axis.

L

I

kg m

rad

kg m

K

I

kg m

rad

J

rot















37

2

37

2

21

2

21

37

2

2

29

.

.

/ sec

.

/ sec

.

.

/ sec

.

c

hb

g

c

hb

g

Physics 205H/ Final Exam [Form-A]

Spring 2004

Page 3

(e) The Earth is located an average distance of 1.496 × 10

11

meters from the Sun, which has a mass of

1.991 × 10

30

kg. Starting from Newton’s Law of Universal Gravity, find the tangential speed,

v

, of the

Earth as it goes in Uniform Circular Motion in orbit around the Sun.

G = 6.67×

-

N·m²/kg²

F

GmM

r

ma

mv

r

GM

r

v

r

v

GMr

r

v

GM

r

N m

kg

kg

m

m

s

G

c









2

2

2

2

2

2

11

2

2

30

11

;

.

/

.

.

,

/

c

hc

h

c

h

Physics 205H/ Final Exam [Form-A]

Spring 2004

Page 4

Survivor: All-Star Points

(50,000 points)

2.)

(a) For the following

x(t)

find the acceleration as a function of time.

All other constants of

integration are zero.

x t

m

m

s t

m

s

t

( )

.

(.

/

)

.

/





100

2 00

4 00

21

2

2

c

h

x t

m

m

s t

m

s

t

v

d tdx

d

d t

m

m

s t

m

s

t

m s m s t m s t

a

d td x

dv

d t

d

d t

m

s

t

m

s

( )

.

(.

/

)

.

/

.

(.

/

)

.

/

(.

/

)

( )

.

/

.

/

.

/

.

/













0

21

2

2

21

2

2

21

2

2

2

2

2

2

c

h

c

h

e

j

c

h

c

h

c

h

e

j

(b) For

( )

.

/

t

rad

s

4 00

2

,

find the angle as a function of time.

All other constants of integration are

zero.









z

z

z

z

d t

rad

s

d t

rad

s

t

C

rad

s

t

d t

rad

s

t d t

rad

s

t

C

rad

s

t

2

2

2

2

21

2

2

2

2

.

/

.

/

. /. /. /

. / c h c h

c

h

c

h

c

h

c

h

(c) A plate of mass m = 5.00 kg has dimensions a = 1.00 m and b = 0.480 m.

Find the center of mass coordinates

x

cm

by integrating

x

M

x dm

cm

z

1

. The

origin is located at the lower left corner.

H GF

K JI



H G F

K JI

z

z

z

M

L

kg m

m a

dm

dx

x

M

x dm

M

x

dx

M

x dx

M

x

m

a

m

a

a

m

m

cm

a

a

a

0

0

0

2

0

2

.

.

;

.

.

Physics 205H/ Final Exam [Form-A]

Spring 2004

Page 5

pivot is located a distance(d) A 3.00 meter long teeter-totter has a 25.0 kg kid on the left end and a 40.0 kg kid on the right end. The

d

from the left end. Find

d

.

Ignore the weight of the teeter-totter itself.

















m gd

m g L

d

m gd

m g L

d

m d

m L

m d

m d

m d

m L

m

m

d

m L

d

m L

m

m

kg

m

kg

kg

m

1

2

1

2

1

2

2

1

2

2

1

2

2

2

1

2

0

(

)

(

)

(

)

(

)

.

.

.

.

.

b

gb

g

b

g

(e) A mass on a spring has its position as a function of time given as

x t

A

t

B

t

( )

cos(

)

sin(

)



.

Find the speed

v

and acceleration

a

at time

t = 0

.

x t

A

t

B

t

v

dx

d t

d

d t

A t B t A t B t

v

A

B

B

B

a

d tdv

d

d t

A t B t A t B t

a

A

B

A

A

( )

cos(

)

sin(

)

cos(

)

sin(

)

sin(

)

cos(

)

( )

sin( )

cos( )

sin(

)

cos(

)

cos(

)

sin(

)

( )

cos( )

sin( )

































b

g

b

g

0

0

0

0

2

2

2

2

Physics 205H/ Final Exam [Form-A]

Spring 2004

CSI: Crime Scene Investigators

(50,000 points)

3.)

On April 8

th

, 2004, CBS had a rerun of a

CSI

episode. The “B-story” was about an idiot target shooting a 9mm

full-load shot at 1100 ft/sec (336 m/s) will penetrate 12".analysis leads them to determine that a 9mm bullet penetrating 4" is traveling at only 550 ft/sec (168 m/s), while ashot went high. A woman several blocks away was killed when the wayward bullet penetrated 4". Forensicautomatic pistol in his backyard. He was “distracted” when the neighbor next door yelled at him to stop – and one

“How far does a 9mm bullet have to travel to slow

down from 1100 ft/sec to 550 ft/sec?” “1800 feet.”

(a) Find the constant acceleration

a

that will slow a

bullet from 336 m/s to 168 m/s in 1800 feet (549 meters).

†

v

v

a x

x

x

v

v

ax

ax

v

v

a

v

v

ax

m

s

m

s

m

m

s

2

02

0

0

2

02

2

0 2

2

0 2

2

2

2

0















(

) ;

/

/

. / b g b g

b

g

“Can a 9mm bullet even travel 1800 feet? That’s three football fields.” “600 feet to drop to ground if

fired horizontally. But it could have been fired at an angle.”

(b) Find the time

t

it takes for a bullet

traveling at an average speed of 252 m/s to fall from a horizontal gun held 1.50 meters above the ground.

y

y

v

t

gt

y

v

y

gt

y

gt

t

y

g

m

m

s

y

y







0

0

21

2

0

0

21

2

0

21

2

0

2

0

0

0

;

,

(.

)

.

/

.

sec

(c) Find the horizontal distance

d

traveled for a bullet traveling at an average horizontal speed of 252 m/s

for the time

t

from part (b).

d If you didn’t get a time in (b), use t = 1.50 seconds.

v t

m

s

m

/

.

sec

.

b

gb

g

† In the “old days”, however, one used a ballistic pendulum – basically a block of wood hanging by a cable. (d) Modern electronics allow one to measure the muzzle speed of a bullet as it leaves the barrel of a gun.

Actually, the bullet would be slowed by the high-speed drag force, F = -cv², but you do not want to work this problem with a

variable, velocity dependent force. (grin)

Physics 205H/ Final Exam [Form-A]

Spring 2004

Page 7

Suppose a 100. kg cube-shaped block of wood (

= 650. kg/m³) is suspended from the ceiling by a cable

so a better answer is: But wait – the length of the cable is to the center-of-mass of the bob…firearms involved).1.75 meters long. Find the period T of this simple pendulum if it is displaced slightly from rest (no

















m

V

V

m

kg

kg

m

m

V d d V m m L L d m m m

L g

f

L g

T

f

g L

m

m

s

;

.

.

/

.

;

.

.

.

.

.

;

.

.

/

.

sec

3

3

3

3

3

3

0

21

21

2

b

g

concepts. 5000 points for the Law and 5000 points for the Conservation principle. (e) The recoil of the pistol when it is fired can be described by two different, but important Physics

Short answers

.

Newton’s Third Law & Conservation of Linear Momentum

(recoil is a totally inelastic collision run backwards in time)









L g

f

L g

T

f

g L

m

m

s

;

.

.

/

.

sec

2

Physics 205H/ Final Exam [Form-A]

Spring 2004

4.00 seconds?550. hp at full power. How much work does the engine do in 4.) (a) A 2000 Lamborghini Diablo (mass = 1625 kg) generates The Dr. Phil Show (50,000 points)

1 hp = 746 W.

550

746

410300

410300

400

1641000

.

/

,

,

.

sec

,

,

hp

W hp

W

P

W

t

W

Pt

W

J

b

gb

g

b

gb

g

done in (a), how much energy is wasted? (b) The actual efficiency of the hot engine at full power is 54.0% (0.540). For the work

If you didn’t get an answer to (a), use W =

162,000 J.

actual

H

H

actual

H

C

C

H

W

Q

Q

W

J

J

Q

W

Q

Q Q W J J J







;

,

,

.

,

,

, , , , , ,

Find the 2(c) The operating temperatures of the V-12 engine of the Diablo are 105°C (221°F) and 866 K (1100°F).

nd

Law Efficiency of this engine.

T

C

K

T T

K K

CarnotC

H C

nd Law

actual

Carnot







9583%

2

.

.

.

.

.

slipping, no non-conservative forces.(d) Starting from rest, how fast will the Diablo be going after 4.00 seconds of full power? Assume no

W K K K K W

mv

v

W

m

J

kg

m

s

mph

f

i

f





;

,

,

.

/

(

!)

21

2

b

g

Physics 205H/ Final Exam [Form-A]

Spring 2004

(e) For a constant speed, power can be written as

P = F·v

.

of the formis limited by the maximum power and high speed air dragIf the top speed of the Diablo is 225 m.p.h. (101 m/s), and

F

drag

= - C v²

, find

C

.

P

Fv

F

Cv

P

Cv

v

Cv

C

P

v

W

m

s

W s

m

kg

m

W s

m

s mJ s

N m s

s m

kg m m s

s

s m

kg m











H G F

K JI







H G F

K JI











H G F

K JI

HGF

KJI

; , /. /. /

/

2

2

3

3

3

3

3

3

3

3 3

3

3

3

2

3

c

h

b

g

c

h