Fall 2008 Page 1 of 5

General Physics I Final Exam Tuesday, December 16, 2008

1. Albert pushes a 10 kg crate up the entire length of a 3.0 m-high 300 frictionless slope by pushing it with a constant horizontal force of 60 N. What is the speed of the crate as it reaches the top of the slope? (a) 0.6 m/s (b) 1.3 m/s (c) 1.6 m/s (d) 1.9 m/s 2. A 2.0 m-long 1.0 kg rod is hinged at one end and connected to a wall. It is held out horizontally and then released. What is the speed of the tip of the rod when it hits the wall?

(a) 7.7 m/s (b) 4.8 m/s (c) 6.6 m/s (d) 5.8 m/s

3. A 3.0-m-long rigid beam with a mass of 80 kg is supported at each end. A 60 kg student stands 2.0 m from support 1. How much upward force does support 2 exert on the beam?

(a) 590 N (b) 1,370 N (c) 780 N (d) 1,180 N

Fall 2008 Page 2 of 5

4. A 20-cm-diameter, 2.0 kg solid disk is rotating at 100 rpm. A 20-cm-diameter, 1.0 kg circular loop is dropped straight down onto the rotating disk. Friction causes the loop to accelerate until it is riding on the disk. What is the final angular velocity of the combined system?

(a) 100 rpm (b) 50 rpm (c) 25 rpm (d) 200 rpm

5. A 200 g, 20 cm-diameter plastic disk is spun on an axle through its center by an electric motor. What torque must the motor supply to take the disk from 0 to 1200 rpm in 3.0 s? (a) 1.9 x 102 N m (b) 4.2 x 102 N m (c) 6.2 x 102 N m (d) 2 x 103 N m 6. Three identical train cars, coupled together, are rolling east at 3 m/s. A fourth car traveling at 6 m/s catches up with the three and couples to make a four car train. A moment later , the train cars hit a fifth car that was at rest on the tracks, and it couples to make a five-car train. What is the speed of the 5-car train? (a) 15 m/s (b) 4.5 m/s (c) 3.75 m/s (d) 3 m/s 7. A 50-g bullet is fired up into a block of wood of mass 1.00 kg. The bullet lodges in the block, which rises to a height of 7 m. The speed with which the bullet struck the block is: (a) 246 m/s (b) 379 m/s (c) 410 m/s (d) 444 m/s 8. A pendulum bob of mass 500 g is suspended from a string of length 1 m and released from rest when the string is hori- zontal. It collides elastically with a block of mass 2.5 kg on a frictionless horizontal surface. To what height does the bob rebound? (a) .44 m (b) .55 m (c) .33 m (d) .65 m

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9. Let the earth have a mass ME and a radius RE. The mass of the moon is ME/81 and the distance from the center of the earth to the center of the moon is 60 RE. An object placed between the earth and the moon will feel no force if it is located a distance d from the center of the earth. The value of d is (a) 41 RE (b) 50 RE (c) 75 RE (d) 54 RE 10. A mass at the end of a spring oscillates in simple harmonic motion with amplitude A. At what displacement, as a fraction of A, is the energy 3/4 kinetic and 1/4 potential? (a) A/3 (b) A/2 (c) A/4 (d) A/6 11. A block attached to a spring is pulled to the right and released at a time t=0 s. It passes the point x=4.00 cm at t= 0.56 s, and the point x= -4.00 cm at t=0.85 s. What is the angular frequency? (a) 1.1 rad/s (b) 1.6 rad/s (c) 2.2 rad/s (d) 3.3 rad/s 12. A spring is hung from the ceiling. When a block is attached to its end, it stretches 3.0 cm before reaching its new equilibrium length. The block is then pulled down slightly and released. Its frequency of oscillation is: (a) 1.6 Hz (b) 2.9 Hz (c) 4.2 Hz (d) 5.8 Hz 13. A block is executing simple harmonic motion on a frictionless horizontal surface with an amplitude of 0.10 m. At a point 0.06 m away from the equilibrium position the velocity is +0.36 m/s. The period for this motion is: (a) 8.1 s (b) 5.6 s (c) 1.4 s (d) 3.6 s 14. Four objects with different masses, m1 < m2 < m3 < m4 are made of the same material (so they have the same density). The masses are m1 = 0.5 kg, m2 = 2 m1, m3 = 2 m2 and m4 = 2 m3. The four objects float in water. Let V1 = volume of object 1, V2 = volume of object 2, V3 = volume of object 3, and V4 = volume of object 4. Rank the objects from largest to smallest by the fraction of the objects volume that is submerged when the object floats in water. (a) object 1 > object 3 > object 2 > object 4 (b) object 4 > object 3 > object 2 > object 1 (c) object 1 > object 2 > object 3 > object 4 (d) object 1 = object 2 = object 3 = object 4

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15. If you are exposed to 120 dB of sound and seek to reduce it to 80 dB, then by what factor does the intensity of the sound, in W/m2, have to be reduced? (a) 40 (b) 10,000 (c) 1.5 (d) 1,000 16. The picture shows a man with mass M = 75 kg and an elephant supported on a hydraulic lift. The diameter of the piston where the man is standing is 0.5 m and the density of oil is 900 kg/m3. If the elephant is to be raised 2.0 meters how much additional force has to be applied on the piston where the man is standing?

(a) 8.5 x 105 N (b) 6.9 x 102 N (c) 1.1 x 103 N (d) 5.9 x 104 N 17. The diagram shows a fluid in a pipe with varying widths and heights. We want to compare the pressures at points 1, 2, 3 and 4. Point 1 is at the highest elevation, points 2 and 3 are at the same elevation and point 4 is at the lowest elevation. The widths of the pipe at points 1 and 2 are the same, the width at 3 is greater than at points 1 and 2 and the width at point 4 is greater than the width at point 3.

How do the pressures at points 2 and 3 compare when the fluid is not flowing, to the situation when the fluid has a constant, non-zero, flow rate? (a) The pressures at 2 and 3 are equal when the fluid is not flowing and the pressure is higher at 2 when it is flowing. (b) The pressure at 2 is larger when the fluid is not flowing, but is equal to the pressure at 3 when the fluid is flowing. (c) The pressures at 2 and 3 are equal when the fluid is not flowing and the pressure is higher at 3 when it is flowing. (d) The pressure at 3 is larger when the fluid is not flowing, but is equal to the pressure at 2 when the fluid is flowing.

Fall 2008 Page 5 of 5

18. The displacement of a traveling wave is

1 cm if 3 3 1( , )

0 cm if 3 3 1

x tD x t

x t

=

>

where x is in meters (m) and t in seconds (s). Determine the wave speed. (a) 3 m/s (b) 1 m/s (c) 2 m/s (d) 1/3 m/s 19. A galaxy moves away from Earth at 0.1c. Light emitted by the galaxy with a wavelength of 540 nm is detected on Earth having a wavelength of (a) 570 nm (b) 547 nm (c) 515 nm (d) 597 nm 20. A traveling wave on a string is described by y(x,t) = 0.2 sin [2(x/0.80 - t/0.4) + /3] where x and y are in meters, and t is in seconds. The maximum vertical speed of any point on the string is: (a) 3.1 m/s (b) 2.0 m/s (c) 4.5 m/s (d) 1.0 m/s

Fall 2008

FOLLOW THESE INSTRUCTIONS CAREFULLY 1. For questions requiring a numerical answer, choose the one you believe to be the closest to the correct

answer. 2. Carefully detach the answer sheet; only this sheet will be graded. Do not return the question sheets or

scrap paper. 3. Be sure the circles are filled in darkly so they can be read by the scanner. 4. Only one circle should be filled in for each questionno credit will be given otherwise. __________________________________________________________________________________________ Constants: G = 6.67 x 10-11 N m2/kg2 g = 9.8 m/s2 = 3.14 Rearth = 6,370 km Formulas: (letters in boldface are vectors)

2 2 2C A B= + sin /AC = cos /B C = tan /A B =

ssvt

= s

svat

= sdsvdt

= ss dva dt= 2

0 0 /2s ss s v t a t= + + 0s s sv v a t= + 2 20 02 ( )s s sv v a s s= + Fnet = F1 + F2 + F3 + Fnet = m a

( )2 1 2If 0 then (2 ) 4ax bx c x a b b ac+ + = = ;s s k kf n f n = If , , and ,

then ( ) ( )x y x y

x x y y

A A i A j B B i B j C A B

C A B i A B j

= + = + = += + + +

r r rr rr

20 2

02gy y xv

= ( )20 sin 2vRg

=

2 20 0 = + 2(- )

0= + t

22

rv ra = r =

dtd

rv ==

rat=

= 2/T w mg=

1 yag

w mg + =

2

0 0 /2t t = + +

Fall 2008 Page 2 of 5

Exam 2 Formulas:

x

y

dxvdtdyvdt

=

=

( )( )

22

net

net

r rr

t tt

mvF F ma m rr

F F ma

= = = == =aa

v

orbitv rg=

grT 2=

earthearthearthG R

RGMRg

mF

g 222 ===

p mv=r r

x x xp J F t= = D

tFJp yyy == ext on netk

k

dP F Fdt

= =r r r

f iP P=r r

1 1 2 2 3 3P v v vm m m= + + +r r r r L s = r F FAB BA= r r

1 1 2 2v v v vB BA A B A A Bm m m m+ = +r r r r ( )sp sF k s=2 D

( )2s 12U k s= D

f iU U U =

Fall 2008 Page 3 of 5

if KKK =

0UK =+

( ) ( )( ) ( )

1 2f i1 1

1 2

1f i2 1

1 2

2

x x

x x

m mv vm m

mv vm m

= += +

212

K mv=

gU mgy= Exam 3 Formulas:

f

i

s

ssW F ds=

cosW F r F r = = r rD

( )i c i ffU U U W = =2 S

sdUFds

=

th dissE W=D 2

th mech th sys extK U E E E E W+ + = + = =D D D D D D

cosP F v F v = =r r

1 1 2 2 3 3cm

1 2 3

1x i ii

m x m x m xm x

M m m m+ + += = + + + ))

1 1 2 2 3 3

cm1 2 3

1 i ii

m y m y m yy m y

M m m m+ + += = + + + ))

cm cm1 1and x x dm y y dmM M

= =# #

2i i

iI m r=

2I r dm=

2cmI I Md= +

2mech cm

12

E I Mgy= +v

objv R=

obja R=

cmv R= v

2 2cm cm

1 12 2

K I M v= +v

sinr F=t f

grav cmM gx=t 2

net

I= ta

B A A B = r rr r

r F= rrrt 3 L r p=r r r3

sinL mrv= b

ii net

i i

dLdLdt dt

= = =rr

r rt t

L I=r rv

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Final Exam Formulas

max2 2Av fA AT

= = =p p v

( ) ( )0cosx t A t= +v f ( ) ( ) ( )0 max 0sin sin xv t A t v t= + = +2v v f 2 v f

1 22

k k mf Tm m k

= = =v pp

( )2 2 2 2max1 1 1 12 2 2 2xE mv kx kA m v= + = =

2 gfL

= =v p

( ) ( )0max cos += tt

IMgl=

0p p gd= + r 1 1 2 2v A v A=

MV

=r

343

V r= 21 constant

2p v gy+ + =r r

s s = Tv

= f v

v k=v

2=k

Tf 22 ==

Fall 2008 Page 5 of 5

( ) ( )0, siny x t A kx t= +v f

211

22 ghAFA

AF =

( ) 221 dAAgF +=

24 rPI =

( )

=

010logdB10 I

I

0

s1 /ffv v

= 1

0

s1 /ffv v

= +2

( )o 01 /f v v f= +1 ( )o 01 /f v v f= 2

011

cvcv

s

s

+=

011

cvcv

s

s

+=+

Fg = Gm1m2 /r2