finalExamSolutions_p7b_fall2010-1

finalExamSolutions_p7b_fall2010-1 - 4' Final Exam DLSecm...

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Unformatted text preview: 4' Final Exam DLSecm Name (last) 0 (firm m J StudentlD firstalettersoflastname l Rubric Codes: 1. (30 points) A mass is attached to a spring and is aliowed to slide back and forth in the x-direction on a smooth surface without friction. The mass is 20 Kg, and the spring has a stiffness constant k=350 N/m. A student pulls the mass from its equilibrium position out to x = +0.25 meters, and then releases it at t=0 seconds. a) (10 pts) Find the solution for the position as a function of time for this case. A: At. 6'; 0/ K: : 0-}g5‘./‘(0 f Sihé = l lXL+)-:O.Z,‘)’S[n 77¢:3L E m imaym. MW’STMW‘W‘WHEE’K" Wéwfié—fiowdmof‘th 9:; :Lmz c) (10 pts) Find the solution for the velocity as a function of time. Give the numerical function and draw a figure of the function. Also clearly mark the amplitude and period in the figure. d) (5 pts) What is the maximum velocity, and at what time does it occur? ' Max Weed acct/us at 1‘} T, icy ii: 0.}63, 0-749 first 3 letters oi last name P73 Final Exam DI. Sec_____Namemm \é L Rubric Codes: m I Student ID (""0 5%... M. a... 2. (10 points) ’Lindsey,’ a clever cat, has arranged a piece of cardboard to hang out from a table over the floor below where she waits. She has weighed one end of the cardboard down with a 0.04kg paperweight, 15cm from the Center. The center of the cardboard sits right above the edge of the table. She has placed a delicious piece of cheese (0.01kg) only 10cm from the same edge. a. Will 'Charles,’ a 0.02kg mouse, be able to walk all the way out to the cheese and eat it without tipping the cardboard and falling to his doom? You must show the relevant work to justify your answer. Qjm‘w 4W3“ 6’; triage) {LL J0f &m_£4 p) Yg‘ P7,th 2 J“? I W“), , 14m MAA. 4 filté-zflwte ' .2 ALML : ’ ({MAML 6? (O h“) (0.10“) z (0.0%?)(m“gr/WINK”) 7: *0. {Lb luff)“ Java, I» 0‘14. Y‘if‘i'W-QL"! ’3 grail” {n f’zflfiowfl'kwég \ £141 QEngigfi M 313,, DP flu. (WA/DUEL + (Acme )) 50/ ['4 law/Adi; Mme-5(1) ‘hrwl ole mg} « vlc {7,1151%}, C} #9:, MD JD( (Dread/L I 3*? g‘tf W1 at; l”? (A A’égfmi’l‘i JD" [O'K‘ivlv . v J l/ P7B Final Exam DLSec~ Name am) K 2: l [‘RubricCodes: . . |__i._|_| first 3 letters of last name (first) Student ID (10 points) A steel rod spans a length of 3.5 meters and has a circular cross-section with a diameter of 0.04 meters. On one end a Bunsen burner heats the rod to 850 Kelvin, and the other is placed in contact with an ice-water bath, which remains at 273 Kelvin. The thermal conductivity of steel is 25 [W/m k]. What is the heat current density flowing through the rod? a) (Spts) k 7 "-35 Vt: (mob/m ‘59.. 17:1...“ ., j . _ : cogs. r L g z .— N k ) ' 3", M : W41, - {In What is the total heat current flowing in the rod? LI IN ‘2‘) (“n toamf ’ b) (5 pts) EH:'QHA ll .1 g. l 8’ w “mum-m"- first 3 letters of last name P78 Final Exam DLSec _ _____ Nameumi K Y «in» Student ID [ Rubric Codes: . , _ ___ 4. Hal and Mario sit on a Merry-Go-Round (MGR) while Orin stands on the ground and pushes the MGR around. Hal, mass in” = 60 kg, sits at radius rH = 0.6 m from the center. Mario, mass mM = 40 kg, sits near the edge at rM = 1.6 m. The radius of the MGR is also R=1.6m, but the MGR is virtually massless, so Mzo. They're all having a great time until Orin pushes so fast that Mario is about to slip and fall", at an angular velocity of around 25 rpm’s. Orin is merciless and will not stop the MGR, but he now stands away and watches. a), ; 3,555,“; Misfit"— : l. 6} WWI/g mm Ii V 60 5 a) (15 points) Hal would like to help Mario if he could, but he can’t get off the MGR. What can Hal do to slow down the MGR (he can‘t run because the handle-bars are in the way, and he can't touch the ground or any external object)? Explain. 3;! H“! may“ 40 “Ha. DW’Lr (I’JL/ W3 moms/14' ofl I‘M—flirt [kncrefije’s/ ADI/ml 156604455; ‘lLL‘L afljwlar Mowen‘fum 52f _’ ,1) gygltm :3 can grad, A) WI“ 0€CC.(CA$:SQ. L 3 J/LJ =tdnrll. I 7 A) WV b) (15 points) Hal, a math whiz, quickly calculates the total angular momentum of Hal and Mario together, before he moves, to be 324.6 kg m2 rad/s. He thinks he should move either inwards towards the center or outwards towards the edge to slow the angular velocity of the system, but is not sure which, so he flips a coin and decides to move outwards to r=1.6m. What is the new rotational velocity (of? ,2 Li : t animal/r 7 ‘,S}‘ir6 = mill/1w; ’r 714144pr P‘Zfifla‘ljggly DL Sec Name {mo KL If mm) l_|_|_| , ~ l StUdent low first 3 letters of last name 5. (20 points) Check out the circuit to the right. The battery is 5V and each of the light-bulbs in the circuit has a resistance of 20. As drawn. the circuit has a 3,99? place for another light-bulb to be added and there is a 4' choice of two different bulbs. One is the same as the bulbs in the circuit (20) while the other is 60. a. Consider the effect on Bulb #1 that adding the 20 bulb to the circuit has. In particular, when you do this, wfl Bulb #1 shine a little. bri hter or a littl dimmer or not, change at all? For credit you need to exglain your choice. (no calculations are needed!) (fig, abrasiv'flrl‘znl’ ((SI3iL4AC-L c”); lZz-S 3965 pguwn éAJLen 1",»: A Eh A* (Ki lAIL!‘(Gl‘-w( Whiting; £4CMQJ¢§ Aalflwgu _ M (“4+ prim/{M 53 m éq/k/y/ W a I Al“ 0‘1 39:; (L093 1. mew-2,! b. Now consider adding the 60 bulb to the circuit, instearly of filé Calcalalt‘gt‘hr‘mtee t ingslffgllfltllefi ‘0 7f ’lg” equivalent resistance of the entire circuit, 2. the current through Bulb #1, and 3. the v0 drop across Bulb #2. You must show the relevant work for credit. Eguivalent Resistance of Current throu h Bulb #1 9529.1! ,. Vim}; lzvcg Voltage Drop across Bulb #2 Vlyifi- : A VI "l A V1 ...
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