Exam1_solutions - Physics 2210 NAME Fall Semester 2015 UID NUMBER Midterm 1 Version A TA NAME Wednesday Discussion Day(circle one Academic Integrity

Exam1_solutions - Physics 2210 NAME Fall Semester 2015 UID...

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Unformatted text preview: Physics 2210 NAME: Fall Semester 2015 UID NUMBER: Midterm 1, Version A TA NAME: Wednesday, September 23, 2015 Discussion Day (circle one): Academic Integrity: Giving assistance to or receiving assistance from another student or using unauthorized materials during a University Examination can be grounds for disciplinary action, up to and including dismissal from the University. ' Honor pledge: On my honor as a University of Utah Student, I have neither given nor received unauthorized assistance on any part ofthis exam. Name (please print) Signature Date Instructions 1) Use a pencil to fill in the circles corresponding to your name and UID on the answer sheet. 2) In the space above, write your name, UID#, TA name, and circle your discussion days. 3) Sign and date the honor pledge above. 4) Use a pencil to fill in the circles on the answer sheet that match your answer choices. 5) Each problem has only one correct answer, but you can select more than one answer for partial credit on questions that have 5 choices (MCS): see the grading scheme below. 6) Circle your answers in the exam booklet ALSO as a backup to the answer sheet. 7) Use the space provided in the exam booklet to work out your problems. If you need more space, we can provide scratch paper. 8) Bring your completed exam booklet and answer sheet to the front of the classroom along with your UID card. Your UID card must match your face and the name on your exam to receive a grade. Grading Scheme MCS: multiple—choice-fiveanswer questions, each worth 8 points. Partial credit will be granted as follows: (a) If you mark only one answer and it is the correct answer, you earn 8 points. (b) If you mark two answers, one of which is the correct answer, you earn 4 points. (c) If you mark no answers, or more than two, you earn 0 points. MC3: multiple—ch0ice-three-answer questions, each worth 4 points. No partial credit. Choose only one answer! T/F: true orfaise questions, each worth 3 points. No partial credit. Choose only one answer! True/False Section: each question worth 3 points. 1. if two ends of a rope are pulled with forces of equal magnitude and opposite direction, the tension at the center of the rope must be zero. a.” True {2; F alseflj”j 2. Two springs of equal length have two different spring constants, k1 > k2. Both springs are compressed by the same amount, AL. The amount of force required to compress the springs is the same for both. agflIrge Q Fals§3 3. Two identical balls are thrown from the edge of the same cliff, each with the same initial speed. Ball 1 is thrown directly upward. Ball 2 is thrown directly downward. Neglect air resistance. Just before hitting the rgroundfllgoth balls have the same velocity. (ta. _ True .l b. False 4. The magnitude of an object ’s velocity must change ifthe magnitude of its acceleration is a constant. a .1399 b False) 5. Two balls are the same size, but one weighs twice as much as the other. The halls are dropped from the roof of a building at the same instant oftime. Assume forces from the air are negligible. T he balls will reach the grwounduat the same time. (fa: True b.‘ False 6. During a hailstorm, a small piece of ice falls from the sky and hits the windshield of a large truck that is traveling down the highway at high speed. During the collision, theforcefi'om the truck on the piece of ice is larger in magnitude than the force from the ice on the truck. a. Irue .‘b. False?" 7. A boy throws a small stone straight up. When the stone reaches its peak height, its acceleration is momentarily zero. a: True... False?“ 8. A car has lost power and a truck is pushing the car up a hill. While in contact, both vehicles are traveling at constant speed in a straight line up the hill. For these conditions, the netforce on the car is zero during its motion up the hill. a. True it "False 9. A car has lost power and a truck is pushing the car up a hill. While in contact, both vehicles are speeding up as they travel up the hill. For these conditions, theforce on the carfiom the truck is equal in magnitude to [theforce on the truck from the car. (a. True “bi “False 10. A car travels around a circular track at constant speed. The netforce on the car is zero. await ’5’; False “l K.-. Scenario 1 (20 points): Two blocks of mass m1 and m2 are placed on a frictionless plane inclined at an angle 9 relative to the horizontal. Block m2 is connected to a wall by a massless spring with spring constant R. Block m1 is connected to block m2 with a massless rope. The direction of gravity is indicated by g. For the following questions, use: m1 = 2 kg m2 = 4 kg 6 = 30° k = 120 N/m. 11. [MCS — select up to 2 answers] When the blocks are initially connected to the spring, the spring stretches relative to its natural (unstretched) length, L0. How much does the spring stretch, AL, for the values given? a. 98.1cm {M b. 42.5 cm i M t/ d. 16.3 cm _ e. cm 7 ’ [MA 17-, ,2"; s. ’7— ~_ > 2 mm “gm 4-‘V‘ALJKA #7 fl L ~‘ " ., .__ s ,. F , é é -f 0 ,4, '12. [MC3 — select only 1 answer] When the system IS 1n equilibrium (no acceleration), what 15 the netyforce on “u block m2 ? b. ngsine c. kAL //——‘\ 13. [MCS — select up to 2 answers] You pull block m1 downhill thereby guitc‘hing the spring) When the spring is stretched by an amount AL = 32.7 cm, the rope is cut, separating the twoblocks. At the moment just after the rope is cut, what is the acceleration ofblock mg? I . M- e c. 4.91 m/s?) / d. smith/32 _ I gyms-w mgr we M2,, 6'2, 2 MAIL? fjr an??? ( e. 1.31 m/s > t/\/\ r ’3"? “ I i 2‘ , 3 ’/ / Scenario 2 (20 points): A block of mass m slides along the inside of a frictionless circular track of radius R. The block slides freely and is not attached to the track. The circle lies in a vertical plane with the direction of gravity indicated by g. B 14. [MCS — select up to 2 answers] What is minimum speed of the block, 12mm, required to maintain contact with the track at the top of the circle (the location it has in the figure)? a. 17min 2 2R9 b. 17mm =fi3Rg/2 KM” - - f — 5 r" “\ i n *£;_1’3a__.:rx/_fifl~ K f K ( Wire—W a .31, ~' d. vmm = t/ZRg/B V fl 1’" r r’ 6- vmin : VRg/Z d ff :x 1 .' -. -. ‘ ' 'Si' 15. [MCS — select up to 2 answers] What is the normal force (support force) on the block at point B if the speed of the block at that point is 1{5g}? ? V ’2. a. mg upward if 3 * ,_ W \/ km If ,3,» if? b. mg downward ) W“ 1 t- pf I ~ c,- c. 4mg upward .. r " d. 5mg upward ‘ ‘ ' .15" "i Q. i ‘1" _ /“"”“‘"___“"‘f\ @6771 g upward r 16. [MC3 — select only 1 answer] What is the direction of the block’s acceleration when it is at point A? a —> fl“ mm \ rt 1"” mm“ ‘ b' / i “flew; J ////—\ \L x}; {I C. \d/r ¥41/ '" Mira Scenario 3 (20 points): Sarah is demonstrating her jumping abilities to a group of PHYS 2210 students. For her first stunt (stunt #1), she steps off the top of a building from rest and lands on a cushion directly below. it takes a time At for her to hit the ground. For her second stunt (stunt #2), Sarah goes back to the top of the same building and takes a running leap offof it. Her initial velocity is in the horizontal direction (i.e. there is no vertical component to her leap). She lands on some cushions a horizontal distance D from the base of the building, as shown in the figure. taxi t O Stunt #1 O | | I I | I y I D I 17. [MCS — select up to 2 answers] In stunt #1, it takes exactly 2 seconds for Sarah to hit the ground (At = 2 s). What is the height, H , of the building? (Note: the diagram above is not to scale.) flakim -* ’ | :7 '2 F l K L’ t" L, ‘ l I " . . am; 2- < b. ___>' n f? V f/h/{ifligui l’; \L‘RJ-r/‘fl-yr I 1: x | 7‘ '\ c. 24.1 m _ L I M f t if :4. f- . d. 32.8 m ‘ ‘ c. 37.3 m j 18. [MCS — select up to 2 answers] In stunt #2, Sarah’s initial velocity is purely horizontal. Sarah lands D = 20 meters from the base of the building. What is the angle 9 that her velocity vector makes with the horizontal at the moment she hits the cushions? (Note: the diagram above is not to scale.) a. 27'0 __-« i. I b. 43" :1 ‘ " C. 550 " it“; I” 0 ,tri ' .1 .1- fir; .. I' _ I , e. 75° (7 it"— (7' . , ' " ,/ \i . <3“ 5 f3 19. [MC3 — select only 1 answer] Suppose Sarah had taken exactly the same running [cap off a taller building. How wouldtheangle in the above problem change? .\ . ultwould be bigger?“ \ l I 5, b. It would be smaller. ( ‘9 r ‘ ii. " ‘ ' 4‘ f x t5 x c. It would be the same. .4‘ m5? x Q" '" ‘ k" a}, Scenario 4 (20 points): Imagine a tower built so high that its top extends above the earth’s atmosphere where air resistance (drag) can be neglected. The top of the tower is at a height H above the surface of the earth. A projectile of mass mp is fired off the top of the tower with speed 110. The initial direction of the projectile is tangential to a circular orbit, as shown in the figure. Some useful computations: G - Mmm = 3.98x1o14 ms2 6 : 6.67X10”“ m3/kg/s2 G'Mertrth Rearth = 6.25><107 mZ/s2 Mam = 5.97x1024 kg Rmm : 6.37x106 m G'Mearth _ 2 Rearth. 9.81 m/s,2 For the following questions, use H = Regal/3. 20. [MCS — select up to 2 answers] What is the gravitational force exerted by the projectile on the earth when the projectile is first launched from the tower? 1 a. “m g ‘i/‘Lw\‘,.;3 fifth“ ‘ 6H1_'.“\I :0 a... ... .. ,. r. . . 9 I if“. ,1 It ‘7 r r? W 0 1 i“? K it I} ‘ . ' ‘7 b' £me " 56": x - . A 7 m.“ ' A \ rr i \\j ’2 {’1' Md. W K M I 7 C_ ‘I. _/_,. ___..—|r—’ (I fl. -- I r), if: \ a 7. J l 4' *- 3 7. A d. "m g - (r 4 P .._. a"? 3' mpg ” -|. «w Ev?” {‘1 f r; I" r? 21. [MCS — select up to 2 answers] For the given value of H, there is only one projectile speed, 190, that leads to a closed circular orbit. What is this value of 120? a. 1.6 km/s if: mf M 2 b. 5.9 km/s :"V t/b ~ For" Gf’ag j-s 2; r I “M d. 10.5 km/s j/p‘ V I [’4 e. l4.lkm/s t. , I ¢- Z}. 5" gens“: J]: 22. [MC3 — select only 1 answer] If the height of the tower is increased, how must the projectile speed change to maintain a circular orbit? a. 120 must increase , _—‘\_ Q 120 must decrease ) c. 120 must stay the same Scenario 5 (20 points): Two cars approach an intersection traveling at different speeds along two perpendicular streets as shown. Alice’s car approaches the intersection traveling East, and Bob’s car approaches traveling North. Alice’s velocity relative to the ground is {7:413 (speed VAIG) and Bob’s is 173,6 (speed VB’G). I y For the following questions, use: VA‘G = 4-0 miles per hour (MPH) 3 l , x VB'G : Also, use the coordinate system shown in the figure: 7 = (Vx, V3,). 13%?» ‘ ' ' ‘ 23. [MCS — select up to 2 answers] What is Alice’s velocity relative to Bob, 9:413? § § i f——_______K—x¥_i_ (I r \ @0,—30)__M13H:? b, (40,30) MPH _, 1/ i i i if m e. (10,0) MPH d. 0,50 MPH ,4 ‘ , i < ) ,7- _ .7 a < 0 ‘i. if; ., . if} 1 rug) e. (0, —30) MPH at: i 9 ‘ ' 24. [MCS — select up to 2 answers] What is Bob’s speed relative to Alice, V3.14? a. 10 MPH b. 30 MPH J r. t C- 401541114 ’ ‘ ,«srl-MI/P- 7 ‘fir “3‘50 MPH__. e. 70 MPH 25. [MC3 — select only 1 answer] After passing through the intersection, Bob stops his car (VBJG = 0) but Alice continues as before. After Bob stops, what is Bob’s velocity relative to Alice, 1731,]? a. 0 c. , , ‘- fl/fi L”; _:;--r- r) ; ("I {'0‘} it? :9 b. (40,9),Mizn 14‘4"} « c J {:40 0) MPH X A * " -- ' 1/514 if ’5- ‘- “""\>A if»; "'- ‘f/Zz/ 65") 541‘ > 3" 7 of «g: a "> ...
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