Physics 218: Exam 1. Sections: , , , 544, , 557,569, 572 September 28 th, 2016

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1 Physics 218: Exam 1 Secions: , , , 544, , 557,569, 572 Sepember 28 h, 2016 Please read he insrucions below, bu do no open he exam unil old o do so. Rules of he Exam: 1. You have 90 minues o complee he exam. 2. Formulae are provided on he las page. You may NOT use any oher formula shee. 3. You may use any ype of handheld calculaor. However, you MUST show your work. If you do no show HOW you inegraed or HOW you ook he derivaive or HOW you solved a quadraic or sysem of equaions, ec. you will NOT ge credi. 4. Cell phone use during he exam is sricly prohibied. 5. Be sure o pu a box around your final answers and clearly indicae your work. 6. Credi can be given ONLY if your work is clearly explained and labeled. No credi will be given unless we can deermine which answer you are choosing, or which answer you wish us o consider. If he answer marked does no follow from he work shown, even if he answer is correc, you will no ge credi for he answer. 7. You are required o show work for he shor answer quesions. 8. Have your TAMU ID ready when submiing your exam o he procor. 9. Check o see ha here are 8 numbered pages. 10. If you need exra space, use he reverse side o complee your work and indicae/ mark on he main page of he problem ha you are coninuing on he reverse side. Sign below o indicae your undersanding of he above rules. 11. DO NOT REMOVE ANY PAGES FROM THIS BOOKLET (excep he formula shee). Name (prined): Insrucor s Name: Secion Number: Your Signaure: 1

2 Blank page for work 2

3 Shor answer quesions: 1. Find he angle beween wo vecors if raio of he magniude of heir vecor produc o heir scalar produc is You hrow a ball sraigh up and cach i a he same poin on is reurn. During he ball s fligh i reaches a maximum heigh, H, above he release poin. In erms of H, a wha heigh above he release poin will he insananeous velociy be he same as he average velociy over he enire pah? 3. A block is pushed up a fricionless ramp wih an iniial velociy and released a =0. The incline makes a 30 degree angle o he horizonal. Afer reaching some disance up he ramp, he block slides back down. Skech qualiaively he v x- and a x- graphs, assuming x-axis is along he ramp poining down. Be sure o show hese quaniies for he enire round rip of he block v x a x

4 4. A ypical garden hose aached o a fauce has a waer flow rae of 100 liers per minue. Wha is he flow rae of his hose in SI unis? (1 lier is a volume of a cube wih 10 cm sides). 5. A ypical DVD player spins is disk a a consan 1600 rpm (revoluions per minue). If he diameer of a ypical disk is 12.0 cm, find he acceleraion of a poin on he rim during his roaion. (Be sure o give boh magniude and direcion.)

5 Problem 1. A 5000 lb. SpaceX rocke blass off verically from he launch pad a Cape Kennedy Space Cener wih a ne consan upward acceleraion of 2 m/s 2. Unforunaely, he engine suddenly and compleely fails when he rocke is a a heigh of 500 m, a which poin he rocke coninues is fligh now unpowered. Ignoring air resisance, answer he following: a. Wha is he maximum heigh his rocke will reach? b. How long is he rocke s fligh from lif off o jus before i crashes back on earh? c. Skech y-, v y- and a y- graphs of he rocke s moion from he insan of blas-off o he insan jus before i srikes he launch pad. LO a Pass Fail y v y a y b c

6 Problem 2. Robin Hood is siing on a ree and wishes o hi a small arge (consider i a poin arge) ha is below him a 1.7 meers above he ground. An arrow released from Robin Hood s bow has velociy of 65 m/s and iniially makes a 5 degree angle below he horizonal. The arrow is released a a heigh of 5 m above he ground. Ignore effecs of wind and air resisance. a. How far away, in he horizonal direcion, mus he arge be if he sho is successful? b. Find he angle ha he arrow makes wih he horizonal when i his he arge. c. Wha is he average velociy of he arrow during his fligh (make sure o provide boh direcion and magniude)? a b 13.5 c

7 Problem 3. A railcar is moving along in he x-direcion a a consan velociy, v rail = 0.5 m/s, relaive o a bicyclis sanding on he side of he railroad racks. A =0 he origins of boh reference frames coincide. In he railcar frame he coordinae reference frame is siing on a pool able. A =0 a pool ball is rolled along he surface of he pool able wih a consan velociy, v y = 1.0 m/s in he direcion perpendicular o he railcar s moion. a) Find he velociy (magniude and direcion) of his rolling ball in he frame of he bicyclis sanding on he ground ouside he moving railcar. b) Find he displacemen (magniude and direcion) of he ball measured in each of he wo frames afer he ball has been rolling for 5 seconds. (displacemen in railcar frame and displacemen in saionary bicyclis frame) c) In wha direcion mus we roll he ball relaive o he pool able wih his same speed, for he saionary bicyclis o see he ball roll only in he y-direcion of heir reference frame? a b 12.5 c

8 Problem 4. We ie a small model airplane o he end of a wire and ie o oher end of he wire o a pos, allowing he airplane o move in a horizonal circle of consan radius L. The airplane is iniially a res when he moor is urned on a =0. The airplane experiences a ime-dependen angenial acceleraion while he moor is spinning, a() = a o + b 1/2, where a o and b are posiive consans. In erms of he quaniies given, a o, b,, and L, answer he following: a) Find an expression for he speed of he airplane for any ime afer he moor is fired. b) Wha disance along his circular pah will he airplane have raveled in his same ime,? c) Find he angle ha he oal acceleraion vecor makes wih he angen o he pah of he airplane a his ime,. a b c