BOBOdHHHHHH H b  -ZxHHHV,(hh hd'0F  ?0?l/j""BO`H?"BHBMP `0?AA!j 1H  $4(| DSETb mxL|_! $  h   ' ( F G b c 3d,\_a :\]^a19mn,9AwMN`m   7 m n   i k  j  * v    < Hd,M D t   3 s   $   5 : F G b c d  g !h  i "k  n o  r #t  u $v "w  | }   #   $ "       "    "     !   "      !       "        "      "           !   "   !   "   !   "   !                # !   $ "  " "%  ) !*  + ",  0 1 !2  < !=  @ "B  O !Z  [ "c  n !t  u "{   !   " $ "       !   "   "   "      # &   $ "       "   "   "    "   "   "   "   "     "   "   !   "    "   " !   "    "    "    !   "    "   " !    "!  $ % "&  * "+  , -  4 "5  6 7  B !C  F "H $I "J  Y Z  ] "^  d "e  l "m  t "u  { "|   "     ' ) * ) )--/-1-/-1-1-/-1-1-1-/-4-1- /!-.1/-416-718-L1M-N/O-748-:/;-?/@-A4B/C-R1S-X1Z-i1j-y6{-6-:/;-?/@-B/C-G/H-I4J/K-Z1[-]4^/_-n1o-u/v-w4x/y-1-1-1-/---R1X-Y/i1j-k/1-1-1-1-1-1-1-/--/--1-1-/-7- 1 - 4 - 4 !- &/ '- +/ ,- 0/ 1- 5/ 6- 7- @9 A1 B- C/ E- H1 N- O/ T- W1 [- \/ _- j1 l- r1 x- y/ - 1 - / - - 1 - - < 4 < > < iA k< < C A A F A C A F A C A A F A H C A F A H A H A C A A F A H C A F A H A H A < < < J < *< +< /J 5< ^L _< cL d< h< jC kA mA nF oA qH rC tA vF wA {H |A H A C A A F A H C A F A H A H A C A A F A C A F A A H A C A A F A C A F A A H A C A A F A C A F A A H A C A A F A C A F A A H A C A A F A C A #H $A (H )A +H ,A 0H 1A 3H 4C 5A 7A 8F 9A BC CA FH GC HA MA UC VA WA `C aA hC iA jH kA lA vF wA A F A C A H A A A A < < < < A H A C A H A H A C A H A H ACA C A H A<4L5<;<<A=H>ABHCAH<ILJ<eLf<jLo<qLv<w4x<yL~<><L<<L<L<<><L<<L<<><L<L<<<L<L<OQO<L<L<L<4<L<L<<L<L<L<4<L<L<<><L<>< > < L <(>)<*L/<;L<<B<C<DSsOtVuXvVZVXVXV<L<><L<L<J<<<AHAHACAHAHA%C&A'H)A,H-A;C<A=H?ABHCAOCPAQHSAVHXAzC{A|H~AHAHACAHAHA_M// ?Q^ndd ?Q_n:: ?Q iu<f j g%#| Physics 1150 Exam #3 November 6, 1995 Name: _______K E Y___________ Possibly useful equations: q = s/r , w = Dq/Dt , a = Dw/Dt q = qi + wi t + ( 1/2 ) a t2 w = wi + a t vt = r w , at = r a I = S m r2 Iring = M r2 , Idisk = (1/2) M r2 L = I w , t = I a , t = DL / Dt KErot = (1/2) I w2 stress = F / A , strain = deformation/original modulus = stress/strain , Y = [(F/A) / (Dl/lo)] P = F/A , Ph = Patm + r g h Dm/Dt = r A v , r1 A1 v1 = r2 A2 v2 , A1 v1 = A2 v2 (1/2) r1 v12 + P1 + r1 g y1 = (1/2) r2 v22 + P2 + r2 g y2 DL = a Lo DT , c = Q / m DT , Q = c m DT Qf = m Lf, Qv = m Lv , Q1 + Q2 = 0 Note for Fridays hand-out: Some of the posted homework has severe, silly, ridiculous errors. Pleased double-check the posted solutions to ensure that you are working with the latest version. If you print out the solutions, please check the prited version against the screen version. Some documents have printed with strangevery strangeomissions.1. A solid disk with mass of 3.0 kg and radius of 15 cm rotates with an angular velocity of 2 radians per second.  a) What is the moment of inertia of the disk? Idisk = (1/2) M r2 I = (1/2) (3.0 kg) (0.15 m)2 = 0.0338 kg m2 b) What is the kinetic energy of the rotating disk? KE = (1/2) I w2 = (1/2)(0.0338 kg m2)(2 s-1)2 = 0.0675 kg m2/s2 = 0.0675 J  A second, identical disk, initially at rest is dropped onto the rotating disk. It sticks to the lower disk and the two rotate as a common unit. c) What is the final angular speed of the two rotating disks? L = I w Li = Ii wi = (0.0338 kg m2)(2 s-1) = 0.0675 kg m2/s This is an inelastic collision. Even in an inelastic collision, the angular momentum is still conserved (just as with linear momentum and inelasticf collisions on the air track. That is, L = constant Lf = Li Lf = If wf = (0.0675 kg m2)(wf) = 0.0675 kg m2/s = Li wf = 1 s-1 = 1 rad s-1 = 1 rad/s2. A telephone wire 125.00 m long a 1.25 mm in radius is stretched to a length of 125.30 m when a force of 1 kN is applied. What is Youngs modulus for the material of this wire? Y = stress/strain stress = F/A F = 1 kN = 1,000 N A = r2 = (0.00125 m)2 = (1.25 x 103 m)2 = 4.91 x 106 m2 stress = 1,000 N/4.91 x 106 m2 = 2.04 x 108 N/m2 = 2.04 x 108 Pa D means difference; Dl = lf li = lf lo strain = Dl/lo = 0.30 m/125 m = 0.30/124 = 2.4 x 103 Y = stress/strain Y = 2.04 x 108 Pa/2.4 x 103 = 8.5 x 1010 Pa3. Air (r = 1.3 kg/m3) blows past a 1.0 m x 2.5 m window with a speed of 20 m/s. What is the difference in pressure on the two sides of the window? What is the net force on the window?  We can immediately apply Bernouliis Equation, 1/2 r v2 + r g h + p = constant or 1/2 r v12 + r g h1 + p1 = 1/2 r v22 + r g h2 + p2 In our case, position 1 is outside the window and position 2 is inside the window. The height is the same so h1 = h2 = h, 1/2 r v12 + r g h1 + p1 = 1/2 r v22 + r g h2 + p2 1/2 r (20 m/s)2 + r g h + p1 = 1/2 r (0)2 + r g h + p2 1/2 r (20 m/s)2 + [r g h] + p1 = 1/2 r (0)2 + [r g h] + p2 1/2 r (20 m/s)2 = p2 p1 p2 p1 = 1/2 r (20 m/s)2 = 1/2 (1.3 kg/m3) (20 m/s)2 = 260 N/m2 = 260 Pa Dp = 260 Pa F = Dp A = (260 N/m2)(1.0 m x 2.5 m) = 650 N F = 650 N 4. A 0.050-kg ice cube, initially at 5.0C, is placed in 0.30 kg of water at 25C. What is the final temperature of the water? Or, if melting is not complete, how mu%ch ice remains unmelted at thermal equilibrium? Assume no heat is lost to the environment. cice = 2090 J/kg C , cwater = 4186 J/kg C , Lf = 3.33 x 105 J/kg First, assume all the ice melts, so Tf > 0C Q1 + Q2 = 0 Q1 = heat lost by the water Q1 = cwater mwater DTwater = (4186 J/kg C)(0.30 kg)(Tf 25C) Q1 = (4186 J/kg C)(0.30 kg)(Tf 25C) = 1,256 (J/C) Tf 31,395 J Q2 = heat gained by ice Q2 = heat gained in raising ice to 0C + + heat gained in melting ice + + heat gained in raising the melted ice (now water) to tempe#rature Tf Q2 = cice mice DT1 + Lf,ice mice + cwater mice DT2 Q2 = [2090 J/kg C][0.05 kg][0C ( 5C)] + + [3.33 x 105 J/kg][0.05 kg] + + [4186 J/kg C][0.05 kg][Tf 0C] Be very careful with these temperature changes! Q2 = 522.5 J + 16,650 J + 209.3 (J/C) Tf 0 Q2 = 17,172.5 J + 209.3 (J/C) Tf Now we are ready to go back to Q1 + Q2 = 0 1,256 (J/C) Tf 31,395 J + 17,172.5 J + 209.3 (J/C) Tf = 0 1,256 (J/C) Tf + 209.3 (J/C) Tf = 31,395 J 17,172.5 J 1,465 (J/C) Tf = 14,222 J Tf = [14,222/1,465]C Tf = 9.7CZNDSET.HH-j 6*??O|nd SPNT @"% P2-v15 - Copyright 1988 Silicon Beach Software, Inc. userdict/md known{currentdict md eq}{false}ifelse{bu}if currentdict/P2_d known not{/P2_b{P2_d begin}bind def/P2_d 27 dict def userdict/md known{currentdict md eq}{false}ifelse P2_b dup dup /mk exch def{md/pat known md/sg known md/gr known and and}{false}ifelse/pk exch def{md /setTxMode known}{false}ifelse/sk exch def/b{bind def}bind def/sa{matrix currentmatrix P2_tp concat aload pop}b/sb{matrix currentmatrix exch concat P2_tp matrix invertmatrix concat aload pop}b/se{matrix astore setmatrix}b/bb{gsave P2_tp concat newpath moveto}b/bc{curveto}b/bl {lineto}b/bx{closepath}b/bp{gsave eofill grestore}b/bf{scale 1 setlinewidth stroke}b/be {grestore}b/p{/gf false def}b/g{/gf true def}b g pk{/_pat/pat load def/_gr/gr load def}{/_gr {64.0 div setgray}b}ifelse sk{/_sTM/setTxMode load def}if/gx{/tg exch def}b 0 gx/x6{av 68 gt {false}if}b end P2_b pk end{/pat{P2_b gf{end pop sg av 68 gt{pop}if}{/_pat load end exec} ifelse}bind def}{/pat{P2_b pop _gr end}bind def}ifelse P2_b sk end{/setTxMode{P2_b/_sTM load end exec P2_b tg/_gr load end exec}bind def}{/setTxMode{pop P2_b tg/_gr load end exec}bind def}ifelse}if "Ph198 335 1 index neg 1 index neg matrix translate 3 1 roll currentpoint 2 copy matrix translate 6 1 roll "{m366 380 currentpoint 1 index 6 index sub 4 index 9 index sub div 1 index 6 index sub 4 index 9 index sub div matrix scale 11 1 roll o[ 9 1 roll cleartomark 3 2 roll matrix concatmatrix exch matrix concatmatrix /P2_tp exch def P2_b mk end{bn}if "d SPNT d SPNT QTjnXd SPNT  UUUUQOen Xd SPNT d SPNT `PvfZd SPNT `iu"Zd SPNT `u#Zd SPNT d SPNT dSPNTDSET.Hbj 6* l l|od SPNT @"% P2-v15 - Copyright 1988 Silicon Beach Software, Inc. userdict/md known{currentdict md eq}{false}ifelse{bu}if currentdict/P2_d known not{/P2_b{P2_d begin}bind def/P2_d 27 dict def userdict/md known{currentdict md eq}{false}ifelse P2_b dup dup /mk exch def{md/pat known md/sg known md/gr known and and}{false}ifelse/pk exch def{md /setTxMode known}{false}ifelse/sk exch def/b{bind def}bind def/sa{matrix currentmatrix P2_tp concat aload pop}b/sb{matrix currentmatrix exch concat P2_tp matrix invertmatrix concat aload pop}b/se{matrix astore setmatrix}b/bb{gsave P2_tp concat newpath moveto}b/bc{curveto}b/bl {lineto}b/bx{closepath}b/bp{gsave eofill grestore}b/bf{scale 1 setlinewidth stroke}b/be {grestore}b/p{/gf false def}b/g{/gf true def}b g pk{/_pat/pat load def/_gr/gr load def}{/_gr {64.0 div setgray}b}ifelse sk{/_sTM/setTxMode load def}if/gx{/tg exch def}b 0 gx/x6{av 68 gt {false}if}b end P2_b pk end{/pat{P2_b gf{end pop sg av 68 gt{pop}if}{/_pat load end exec} ifelse}bind def}{/pat{P2_b pop _gr end}bind def}ifelse P2_b sk end{/setTxMode{P2_b/_sTM load end exec P2_b tg/_gr load end exec}bind def}{/setTxMode{pop P2_b tg/_gr load end exec}bind def}ifelse}if "h198 282 1 index neg 1 index neg matrix translate 3 1 roll currentpoint 2 copy matrix translate 6 1 roll "{n367 380 currentpoint 1 index 6 index sub 4 index 9 index sub div 1 index 6 index sub 4 index 9 index sub div matrix scale 11 1 roll o[ 9 1 roll cleartomark 3 2 roll matrix concatmatrix exch matrix concatmatrix /P2_tp exch def P2_b mk end{bn}if "d SPNT dSPNT 0HHz4d SPNT camz8z4z4d SPNT d SPNT QTjnXd SPNT  UUUUQOen Xd SPNT d SPNT `PvfZd SPNT `iu"Zd SPNT `u#Zd SPNT d SPNT d SPNT d SPNT Q!7oXd SPNT  UUUUQ1o Xd SPNT d"SPNT V&Vd SPNT "6#"IdSPNTDSET.H8j 6*Ayod SPNT @"% P2-v15 - Copyright 1988 Silicon Beach Software, Inc. userdict/md known{currentdict md eq}{false}ifelse{bu}if currentdict/P2_d known not{/P2_b{P2_d begin}bind def/P2_d 27 dict def userdict/md known{currentdict md eq}{false}ifelse P2_b dup dup /mk exch def{md/pat known md/sg known md/gr known and and}{false}ifelse/pk exch def{md /setTxMode known}{false}ifelse/sk exch def/b{bind def}bind def/sa{matrix currentmatrix P2_tp concat aload pop}b/sb{matrix currentmatrix exch concat P2_tp matrix invertmatrix concat aload pop}b/se{matrix astore setmatrix}b/bb{gsave P2_tp concat newpath moveto}b/bc{curveto}b/bl {lineto}b/bx{closepath}b/bp{gsave eofill grestore}b/bf{scale 1 setlinewidth stroke}b/be {grestore}b/p{/gf false def}b/g{/gf true def}b g pk{/_pat/pat load def/_gr/gr load def}{/_gr {64.0 div setgray}b}ifelse sk{/_sTM/setTxMode load def}if/gx{/tg exch def}b 0 gx/x6{av 68 gt {false}if}b end P2_b pk end{/pat{P2_b gf{end pop sg av 68 gt{pop}if}{/_pat load end exec} ifelse}bind def}{/pat{P2_b pop _gr end}bind def}ifelse P2_b sk end{/setTxMode{P2_b/_sTM load end exec P2_b tg/_gr load end exec}bind def}{/setTxMode{pop P2_b tg/_gr load end exec}bind def}ifelse}if "Bh197 321 1 index neg 1 index neg matrix translate 3 1 roll currentpoint 2 copy matrix translate 6 1 roll "xn367 377 currentpoint 1 index 6 index sub 4 index 9 index sub div 1 index 6 index sub 4 index 9 index sub div matrix scale 11 1 roll o[ 9 1 roll cleartomark 3 2 roll matrix concatmatrix exch matrix concatmatrix /P2_tp exch def P2_b mk end{bn}if "d SPNT dSPNT 0HHAw9d SPNT camAw@Aw9Aw9d SPNT d SPNT QTjnXd SPNT  UUUUQOen Xd SPNT d SPNT d SPNT `Us Zd SPNT d SPNT `frZd SPNT `rZd SPNT d SPNT d SPNT d SPNT QJ`oXd SPNT  UUUUQDZo Xd SPNT dSPNTDSET.H 6*DSETh.Hd0x@[!:W\H3j~]Y|{]] ]9F* ]6*t@$H$H$H@HHH@uuu@DSETT ` K" " < _ ` _  ` _ v1 = 20 m/s p1 = ?ZNDSETT 4t$l""  < _ ` _  `  _ \v2 = 0 p2 = atmosphericZNDSETT p(#    _ 1.0 mZNDSETT dD*    _ l2.5 mZNDSET.H l  xUF1р 6*77 S @ X S SXSS0 60 6P05`05`P0_0_P00P00P  (+1 (N2++3(4 (TotDSET:.H !l        6*FNTMCUTSDSUMHDNISTYL:@STYL|X\                 c                d  !  7"  #  $ & ' )* T - 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