PHYSICS 218 (517-520)recitation 1• In recitation,– We shall discuss exercises and problems. They may include homework problems.– Quiz: you are supposed to solve a quiz at each recitation. – Make a group so that each group contains 3 (or 4) students.Take a seat as in your Lab. – You should collaborate with your partners to solve quiz problems. You work as teams on the quiz problem. One group has one answer paper. The answer paper should have names and UIN of all group members. The group members will have the same credit for recitation quiz. One of you may serve as a focused peer mentor.• There is no Lab today (Sep.1).• There is no quiz today (Sep.1).• Unit– An equation must always be dimensionally consistent.– You cannot add length and time.• Unit conversion• Eg. The official world land speed record is 1228.0 km/h. Express this speed in m/s.31km = 10 m, 1 h = 3600 skm 1000m1228.0km/h = 1228.0 1228.0 341.11m/sh 3600 skm km 1000m 1 h = 1228.0 1228.0h h km 3600 s⎛⎞⎛ ⎞⎟⎟⎜⎜=× =⎟⎟⎜⎜⎟⎟⎜⎜⎝⎠⎝ ⎠⎛⎞⎛ ⎞⎟⎟⎜⎜=××⎟⎟⎜⎜⎟⎟⎜⎜⎝⎠⎝ ⎠=1 =1Unites are treated just like algebraic symbols.DO NOT forget to give your answers with correct units.Ex. The inhabitants of a small island begin exporting beautiful cloth made from a rare plant that grows only on their island. Seeing how popular the small quantity that they export has been, they steadily raise their prices. A clothing maker from New York, thinking that he can save money by "cutting out the middleman," decides to travel to the small island and buy the cloth himself. Ignorant of the local custom of offering strangers outrageous prices and then negotiating down, the clothing maker accepts (much to everyone's surprise) the initial price of 400 tepizes/m2. The price of this cloth in New York is 120 dollars/yard2.If he bought 500 m2of this fabric, how much money did he lose? (1 tepiz = 0.625 dollar and 1 yard = 0.9144 m.)StrategyHow much money he spent?How much he would spent in NY?22400 tepizes 0.625dollarin the island, 500 m 125,000dollars1 m 1 tepiz×× =222120dollars 1 yardin NY, 500 m 71,800dollars1 yard 0.9144 m⎛⎞⎟⎜×× ≈⎟⎜⎟⎜⎝⎠He lost 125,000 71,800 53,200 dollars∴−=Problem 1.67(a)• Approximately how many atoms make up our planet? For simplicity,assume the average atomic mass of the atoms is 14 g/mol. Avogadro's number gives the number of atoms in a mole.2727 2350mass of the earth = 5.97 10 g (Appendix F of the textbook)5.97 10 g 6.02 10 atoms number of atoms in the earth = 14g/mol 1mol2.6 10 atoms×××∴ ×=×xyAGIn Cartesian coordinate system,is represented by and .In polar coordinate system,is represented by ( ) and .xyAAAAAAθ=GGGθ22 1cos , sin ,,tan .xyyxyxAA AAAAAAAθθθ−==⎛⎞⎟⎜⎟=+ =⎜⎟⎜⎟⎜⎝⎠• θ is defined from the positive x-axis to the direction of a vector toward the positive y-axis, i.e., counterclockwise.• arctan function has two solutions in the range of (0, 2π).yAGθVector calculusˆkxzyˆiˆjˆˆˆ( , , ) or xyz x y zAAAA A A A A==++GGijkˆˆ ˆˆ ˆ ˆ1ˆˆ ˆˆ ˆˆ0⋅ = ⋅ = ⋅ =⋅ = ⋅ = ⋅ =ii jj kkij ik jkˆˆˆˆ ˆˆ()()ˆˆˆ ˆˆ ˆˆˆˆ ˆˆ ˆˆˆˆˆˆˆxy z xy zxx xy xzyx yy yzzx zy zzABAiAjAkBiBjBkABi i ABi j ABi kAB ji AB j j ABj kABk i ABk j ABk k⋅ =++⋅ ++= ⋅ + ⋅ + ⋅+ ⋅ + ⋅ + ⋅+ ⋅ + ⋅ + ⋅GGxxyyzzABABAB=++2222xyzAAAAA A⋅ =++=GGGScalar product (dot product, inner product)cos: angle between the two vectors (if , then 02if , th0en )02AB ABABABθθπππθθθ < ⋅⋅ =≤≤>> ⋅ <GGGGGGGG. (1,2,3), (3,2,1). Calculate the angle between the two vectors.Ex A B==GG222222123 14321 1413 22 31 10cos 14cos10 5cos , 44.414 7xx yy zzABAB AB AB ABAB θθθθ=++==++=⋅ =++=×+×+×===∴ == =DGGExerciseA particle is moving from the point A to the point B.Define the displacement of the particle , where 360and 880.= − ==RBA ABGGGGGWe write ( , ) and ( , ).xzxzAABB==ABGGcos 360 cos40 276sin 360 sin 40 231cos 880 cos163 842sin 880 sin163 257xzxzAAAABBBBθθφφ==×===×===×=−==×=DDDDThen A 360, =40 and B 880, =163θφ==DD(,),842 276 1118,257 231 26xzxxxzzzRRRBARBA== − = −− = −= − = − =RGRGProblem 1.71You are to program a robotic arm on an assembly line to move in the xy-plane. Its first displacement is ; its second displacement is , of magnitude and direction 63.2 measured 6.4 in 2 cm the sensABDGGe . The resultant of the two displacements should also have a magnitude of , but a direction 22.2 mefroasum the -axis toward tred in the senshe -axisfrom the +x-axis toward 6.42 th c e m e +yxyCAB=− ++DGGG.What is-axis ?AG()()cos , sin , 6.42, 360 63.2 296.8cos , sin , , 22.2,cos cos 6.42 (cos22.2 cos296.8 ) 3.05sin sin 6.42 (s(3.05, 8.16)in 22.2 sin 296.8 ) 8.16xyxyxyBB BB BCC CC CBAACBABABββ βγγ γγβγβ== ==− === === −= − =× − === − =× − =DD DDDDDDGGGProblem 1.99At Enormous State University (ESU), the football team records its plays using vector displacements, with the origin taken to be the position of the ball before the play starts. In a certain pass play, ˆˆ ˆ ˆthe receiver starts at 2.0 4.5 , where the units are yards, is to the right, and is downfield. ˆˆSubsequent displacements of the receiver are +8.5 (in motion before the snap), +11 (breaks ij i jij+ −downfield), ˆˆ ˆ ˆ6.0 4.0 (zigs), and +12.0 18.0 (zags). Meanwhile, the quarterback has dropped How far and in whicstraight ˆbac h direction mk to a posit ust the quation erb 7.0 . ack throw th e bij i jj− ++− all?receiver's final position ˆˆ ˆ ˆ ˆˆ ˆ ˆ( 2.0 4.5 ) (+8.5 ) (+11 ) ( 6.0 4.0 ) (+12.0 18.0 )ˆˆ16.5 28.5 quarterback's position ˆ7.0 ˆThe relative distance between the two: 16.5RRij i j ij i jijQQjRQ=+ − +++− ++ +=+= −− =GGGGGGˆ35.5 ij+221How far?16.5 35.5 38yardsWhich direction?35.5tan 65 (Both x and y components are positive.)16.565 from the right line, 25 to the right of downfieldRQ−−
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