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DOC010 - FINAL EXAM PHYS 125 18 DECEMBER 2006 Name i5 yifl...

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Unformatted text preview: FINAL EXAM PHYS 125 18 DECEMBER 2006 Name: i5 yifl H (it: {A (17‘56 ( please print legib ) "i7 ,/ Student ID #: 50 2 C? ‘2: 31; a3 Part Score Part Score ’5/“i . Short answer El (7 (3/4! Problem #3 r (,1 CL Problem #1 fl 55g PM Egg x A: & Problem #2 L5 933% Problem #5 )2 U 7 ~ ~. Tot Honor Code Exams must be completed within the allotted time and with no outside assistance. Instructors will periodically enter the classroom, and you are permitted to ask questions of them. However, remember that your instructor is limited in the amount of information he can give. There should be no communication with any other persons (verbal, electronic, etc.) other than the instructor. The use of calculators on the exam is permitted, but is limited to numerical calculation. Any other uses (unit conversion, formulas, graphing, symbolic manipulation, etc.) are not allowed. Please Sign the honor code below as confirmation that you have complied with this policy: “On my honor, I have neither given nor received any unauthorized aid on this exam.” PHYS 125 Final Exam 18 December 2006 Short Answer (40 points) Each of the ten questions below is worth 4 points. 1. Three balls of equal mass and size start from rest and roll down different ramps. All ramps have the same height Which ball has the greater speed at the bottom of the ramp? (3) 1 ,/ 2 (c) 3 /""‘T‘\ (E1) ame speed for all balls Which ball will take the longest time to reach the bottom? (a) 1 (b) 2 (d) Same time for all balls 2. Paul and Todd are at the top of a building. Paul drops a ball to the ground whereas Todd throws a brick with the same weight in the hori— zontal direction (i. e parallel to the surface of the earth). On which object J does gravity do the most work during their Journeys to the ground? (a) the ball (b the brick (c) it is the same for both _____ “My” ,. M”, (d) it depends on the speeds at which the objects are thrown. 3 A child throws a ball up into the air and then it returns to the ground At its maximum height above the ground, what is the acceleration on the ball? , , ' / PHYS 125 Final Exam 18 December 2006 4. Paul is at the park swinging on a swing at its resonant frequency just before thanksgiving After a very festive holiday season he returns to the same park 1n January, 20 lbs heavier than before, He swings on the same swing. What happens to the resonant frequency of the swing when the heavier version of Paul is on it? (You can regard the swing—paul system as a simple pendulum.) (a) The resonant frequency increases. (b) The resonant frequency decreases. ”'m'l‘he resonant frequency remains constant. )/ \.,.,./ 5. Two blocks one of mass m and the other of mass 3m are connected by a rope and are resting on a frictionless horizontal surface. You connect a second rope to the 3m mass and pull with a tension T as shown in the figure below. I 7"» “'3‘ 9, é}? What is the tension in the rope that connects mass 3m with mass m? (b) [Tl/:51 7:”; z 45;; 51, , ®)FV2 :2 a, t-a I; i, / l r: x“ . ,I<é>"2lfl A“ T 2/ x53|fl ?;s:(¢§“§ a. a ;§gl4lTl 1;»; W 6 A 25— —g ice cube floats 1n a 250—g glass of water because of an upward bu0y~ ant force of the water on the me What IS the approximate magnitude of the normal force due to the table on the glass of water? 6"“in A16? Jay (a) 0.245 N (b) 2.20 N c 2.45 N k (d) 2.70 N (e) There is not enough information to an— swer this question. M<azoyra . 5 firm ’ _, f2 ~i \‘\ N's. M / ,2»: V/eez5/ 2/7.; ,A (6 PHYS 125 Final Exam 18 December 2006 7. Below is a graph of a tire’s angular velocity as a function of time. At which point is the torque on the tire the greatest? 8. Consider the situation depicted here. A gun is accurately aimed at a dan- gerous criminal hanging from the gutter of a building. The target is well within the gun’s range, but the instant the gun is fired and the bullet moves with a speed no, the criminal lets go and drops to the ground. The dotted line indicates the direction in which the bullet was aimed. What ha pens? The bullet f/(aghits the criminal regardless of p i the value of '00. (b) hits the criminal only if 1/0 is large enough. / (c) misses the criminal. / PHYS 125 Final Exam 18 December 2006 9. Suppose the entire population of the world gathers in one spot and, at the sound of a prearranged signal, everyone jumps up. About a second later, 6 billion people land back on the ground. After the people have landed, the magnitude of Earth’s momentum is (a) much greater than \/ (b slightly greater than (d) slightly less than the same as (e) much less than it was before the people jumped, 10. Friction between the wheels and the road forces the car around the corner as shown. If the coefficients of static and kinetic friction are 10 and 0.5, respectively, and the 1500-kg car is traveling at a constant speed of 10 m/s around a curve of radius 4 In, how much work has been done by friction? W F Vase/£36 4 MO/M’zbhe My A K If)”; ”a"! K ~41 a: .\ Q We m My / K /: t w M / Q A ”L m V A / ,x ‘ U 5! z: E E "V‘ 7 E L’ J / ,, ~x LU “fig; , 0 if] 2“,, 5:) "(r11 PHYS 125 Final Exam 18 December 2006 Problems (60 points) You must work problem #1. Furthermore, you may choose to work any three of the four remaining problems (#2~#5). Please put an “X” through the number of the problem you DO NOT want graded both here and on the front of the test. 1, (30 points) This problem extends over two pages. You are left an- swering Archimedes’ e—mail while he is away. The following very important e—mail comes that you must answer. Dear Archimedes, I hope this letter finds you well and that you are enjoying your time away from Syracuse. I’m trying to determine if the crown given to me is made of pure gold. I remember you told me to suspend it from a scale and measure its weight in air and then take another reading with itfully submerged in water. I did that. The scale read 10. 00 N in air and 9.35 N in water. However, I don’t remember how to solve for the density. Please calculate the density and show your work so that I can repeat it in the future. Sincerely, , {I ”‘4 King Hiero II /«jg/ ,‘f “fifty/g (a) (15 points) Draw a free—body diagram for the crown in water and solve for the buoyant force on the crown. “-5 “"““>' ? ,_.x fi _ "> w; a 2 [5,; , i W ”3.. T 2*" F é WQCLfi/rr £0 6‘} I :1? {5‘ PHYS 125 Final Exam 18 December 2006 (b) (5 points) What is the volume of the crown? ' :3 / ~33 r V ~.= z. w? "” 5 ‘ t ‘ f r «>3 ? ffljglm Cjitgéé y/i) m/ .1 19, 300 kg/m3)? If not, has it been laced with silver (pAg = 10, 500 kg/mB), or with platinum (ppt : 21,400 kg/m3)? (c) (10 points) What is the density of the crown? Is it pure gold (pp.u * I "MW .......... M V" I V 4/ at ”/3ch éj/mf / / rm" 1/ PHYS 125 Final Exam 18 December 2006 2. (30 points) James Bond has parachuted out of a plane and is now falling to the ground at the safe speed of 5.00 m/Sr At a height of 100 m above the ground, James aims his gun along the horizontal and fires a grappling hook at a. speed of 30.0 m/s toward a building that that is 50.0 In away in the horizontal direction. How far above the ground [1 will the grappling hook hit the building? 5”: ’5 g. 7:) 5:”; yxéflyarxf "ff/x: 0"” "‘61" PHYS 125 Final Exam 18 December 2006 PHYS 125 Final Exam 18 December 2006 3. (30 points) On your first trip to Planet X you happen to take along a 100 g mass, a 20~crn long spring, a meter stick, and a stopwatch, You’re curious about the acceleration due to gravity on Planet X, where ordinary tasks seem easier than on earth, but you can’t find this information in your Visitor’s Guide. One night you suspend the spring from the ceiling in your room and hang the mass from it. You find that the mass stretches the spring by 15 cm. You then pull the mass down 500 cm and release it. With the stopwatch you find that 10 oscillations take 8.0 s. What is the acceleration due to gravity? PHYS 125 Final Exam 18 December 2006 11 , *2 ~ 7 at ’7’” ‘9 “Mu- ” f ? kl.) {3! a ti; 2,4,2» J; PHYS 125 Final Exam 18 December 2006 / / Elli/(30 points) A painter leaves his 2—m long ladder leaning against a friction— /”2 less wall such that ladder makes an angle of 60° with the ground. What minimum coefficient of static friction is needed between the ladder and \‘the ground in order to keep it from slipping? 12 PHYS 125 Final Exam 18 December 2006 13 PHYS 125 Final Exam 18 December 2006 5. (30 points) This problem extends over two pages. Skateboarding legend, Tony Hawk, has designed an amazing skate ramp. Tony will start atop a ramp of height h, roll down, then complete a loop—the—loop with radius R = 3.00 m. Throughout the problem you should model Tony as a. point particle with mass m = 80.0 kg. (a) (15 points) What is the minimum speed Tony must be traveling at the top of the loop in order to complete it safely? " 5 , r « r r '1»rfl”"fl’~/" I ‘15, » V“ “is. Y“ e if 3 M: 7 ’/ (r “Al/1M ”4""?L‘W5 K affrwégé'r f; 14 PHYS 125 Final Exam 18 December 2006 (b) (15 points) Tony finds that in order to complete the loop, he has to leave from a height h = 80 mi How much work is being done by friction between the top of the ramp and the top of the loop if he is traveling at the minimum speed at the top of the loop? RN L10“ 5% i'\ 4* g . 04a f gwtéé w“ ’ f “”7 4% If M " W 5': 3 t a “k ’0’ h f “a! ., ‘ifli. {)jf‘vl W e a! “f ‘4 f: A ,L {€90 5.:3/‘(18/[ém/ A; floggesfla M; , ,,,,, 5 _, , “ii " at“?! w 4;” "‘1: 33’; Tm abfwga a; A 5' W1 Ll! (I _ ,2 a. z 7 .. WM , m : ‘1‘? M" f f 48 7- ,, . - ._ , 11,2» ,fy‘gfrgzrr 2/ : J ~ v « i W; ,’ g; ‘3’ is; 1441/ W’x’ 55 {)3 J ”‘ ”g PHYS 125 Final Exam 18 December 2006 Name: Ki/q! Hgfgga"(j ID: 450/ch 3/ Q’ 5 Exercise Steps Max Score 1 Three ramps 4 (d) Same speed for all balls 2 (c) Ramp 3 takes the longest time. 2 2 (c) It is the same for both. 4 3 Acceleration at max height 4 Magnitude is 9.8 111/52 3 Direction given as minus sign, “down,” 1 etc. Wrong units —1 4 (c) The resonant frequency remains 4 constant. 5 (a) If. /4 4 6 (d) 2.70 N 4 7 Torque is greatest at B 4 8 (:1) Bullet hits the criminal regard- 4 less. 9 (c) Momentum is same 4 10 Work of Friction 4 Full credit for saying “no work” or “zero work” or for identifying that the car can- not make the curve at this speed. Total 40 H g 2 PHYS 125 Final Exam 18 December 2006 MM Problem Steps Max Score 1a FBD and Buoyant Force 15 Free—Body Diagram 8 Weight points down 2 __~ A tension/scale force points up 2 __ Buoyant force points up 2 __ No other forces present 2 __ Buoyant Force 7 Apply Ff“ : may = 0 or, equivalently, 2 __ Fup = Fdown t0 FBD. Use 1000 N for weight. 1 ___ Use 9.35 N for tension/scale force. 1 _ Accurately solve for buoyant force 2 _‘ FB = W—T:0.65N Correct units 1 a 1b Volume of crown 5 $9; Archimedes principle F3 = pf Mg 1 __ Use F3 from part (a). 1 __ Use p; = pnzo = 1000 kg/ma. 1 “ Accurately solve for volume 1 __~ V = FB/(pg) : 6.6 x 10‘5 m3. Correct units 1 __ 1c Density 10 Use weight of 10.00 N to accurately find mass 3 m = W/g 21.02 kg Use mass and volume from part (b) to ac- 3 ___ curately find density p = m/V 2 1.54 X 104 kg/ma. Correct units on density ' 1 __ Use density to accurately deduce whether it 3 __ has been laced with platinum (p > 1.93 x 104 kg/ma) or silver (,0 < 1.93 x 104 kg/ms) Total 30 (IO Final Exam Problem 2 PHYS 125 18 December 2006 Steps Use horizontal direction to find At Apply Ax : vi‘rAt + %azAt2 Use um = 30.0 m/s Use a.I = 0 m/s2 Use Ax =2 50.0 m Accurately find At 5: 1.67 s Use vertical direction to find h Apply Ay = vi,yAt + éayAt2 or, equiva- lently, both 'Uf‘y : UM, + ayAt and 2ayAy : 2 2 ”fly ‘ ”Ly Use v1.3, = —5.00 m/s Use (1,, = ~9.8 rn/s2 Use Ay = h — 100.00 In Use At from above Accurately find h z 78 m Correct units Total Max Score 13 #000000 Hill 03 l l—l—‘OOCOCDOJ Hill! 30 l PHYS 125 Final Exam 18 December 2006 Mm Problem Steps Max Score 3 Find period/frequency 5 Trying to find period/frequency 2 ;_ Doing it correctly T = At/N 2 0.8 s or, 3 __j_ equivalently, the frequency f = N/At 2 1.25 Hz Find spring constant 10 / Q5314): wk/m or 27rf: y/k/m orT= 5 __:1_ 27m / m/lc Use m = 0.1 kg 2 _‘__ Use calculated T/f/w 2 _;__ Doing it correctly to find k 2 wzm = 1 _L 41r2m/T2 2 6.2 N/m Find acceleration due to gravity g 15 W, Apply Fnet = 0 or, equivalently, mg = kAy 5 1 Use [C from above 2 A Use Ay = 0.15 m 5 ‘7} Correctly find 9 = IcAy m 2 9.25 In 82 2 '3' Correct units / / 1 I “/u Total 30 *’ ‘0 Final Exam Problem 4 PHYS 125 18 December 2006 Steps Partial credit for FBD Wall’s normal force / points away from wall / located at the point where ladder meets wall Floor’s normal force / points upward / lo— cated at the point where ladder meets floor Weight / points downward / located at the center of the ladder Friction / points toward the wall / located at the point where ladder meets floor No other forces Newton’s 2nd Law Apply in horizontal direction Nwall = Ffriction Apply in vertical direction Nground = W Apply torques in rotational direction about ONE axis bottom: (L/2)W sin 30° = LNwau sin 60° center: (L/2)F{, sin 60° + (L/2)Nw sin 60° = (L/2)Ng sin 30° top: (L/2)W sin 30° + LN;r sin 60° 2 LNg sin 30° Solving Use Ffriction S ,UsNground Accurate algebraic solution for coefficient of friction ,us 2 1/ (2 tan 60°) 2, 0.29 No units Total Max Score 10 N 30 l l Final Exam PHYS 125 8 December 2006 MM Problem Steps 5a 5b Find minimum speed at top Apply Newton’s 2nd law to object at top of loop: F58: : ma.- Use a, = 112/7" Only force is weight Fur“ = mg Accurately solve for speed 1; 2 m 2, 544 m /s Correct units Work of Friction Find change in kinetic energy AK No initial kinetic energy K: = 0 J Use speed from part (a) to find final kinetic energy K; = $171.1)?” 9: 1200 J Find change in gravitational work Wg or change in gravitational potential energy AUg Height difference is [Ayl = I2R — h] = 2 in Change in potential energy is AUg 2 —-W9 2 mg(2R — h) 2 —1600 J Apply form of work—energy theorem, Wnet = AK or Wext 2 AE to find work by friction me = AK + AUg : AK — W9 2 ~390 J Correct Sign Correct units Total Max 15 4 0: 15 [\D 30 Score _/_r [\i ’ > l l l l :\J. ...
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