05/05/04 PHYSICS 3 Exa #1 NAME Please wite down you nae also on the back side of this exa 1. Hee ae thee sets of values fo the sping constant k, daping constant b, and ass fo thee daped oscillatos: Set 1: 80 N/ 0.050 units 0.5 Kg Equation fo a daped oscillato d x b dx k Set : 40 N/ 0.500 units 1.00 Kg + + x = 0 t t Set 3: 10 N/ 0.05 units 0.5 Kg 1A The unit of the daping constant is a) Kg/s b) N/ c) N d) Joule/s e) NA 1B Rank the sets accoding to the tie fo the aplitude to decease to half its initial value, geatest fist. a) 1,,3 b) 1,3, c) 3,1, d),3,1 e) NA. A A polaized electoagnetic wave popagates in the negative z-diection. If at a given instant of tie the electic field points in the positive y-diection, what is the diection of the coesponding agnetic field? a) +X b) +Y c) -Z d) -X e) -Y B A electoagnetic wave is popagating though space. Its electic field is given by E = E COS( k z ωt) i, whee i is the unit vecto pointing in the X-diection, z is o the vaiable fo the Z-diection, and t is tie. The agnetic field is: E o a) B = ceocos( k x ωt) i b) B = COS( k y ωt) i c E o c) B = COS( k z ωt) j d) E = EoCOS( k z cωt) i e) NA c 3 A block of ass M= 1 Kg, at est on a hoizontal fictionless table, is attached to a igid suppot by a sping of constant k=5 N/c. Anothe block of k ass =50 gas is fied into the 1 Kg block with a speed of 10 /s and becoes attached to the block. M 3A The speed of the block iediately afte the collision is equal to (in /s). a) 0.1 b) 5 c) 0.5 d) e) NA
3B The aplitude of the esulting siple haonic otion (in etes). a) 0.1 b) 0.5 c) 0.5 d) 0. e) NA 4 In a hoizontal table a ass of 0.5 Kg is attached to a sping ( k = 50 N/). The ass is stetched 5 c fo its equilibiu position and eleased with zeo speed at t=0. 4A Indicate which of the following function(s) descibes coectly the position of the ass. 1 x ( t) = 5c COS( 10s t + / 9 ) ANSWER: Yes No x 1 π t ( t) = 5c COS(0π s ) ANSWER: Yes No. x ( t) = 10c COS(0π s ) ANSWER: Yes No. 3 4B Indicate which of the following functions descibes coectly the velocity of the ass. c 1 t s v ( t) = 50 COS(10s ) ANSWER: Yes No c t s v ( t) = 100π COS(0π s ) ANSWER: Yes No. 5. 5A A tansvese wave popagates along a sting. Cicle ALL the expession that ae coect: a) The paticles in the sting ove pependicula to the diection of popagation b) The paticles in the sting ove paallel to the diection of popagation c) The speed of the wave depends on the aplitude of the wave d) if the fequency of oscillations wee to incease, the velocity of the wave would also incease. e) All the above expessions ae incoect 5B. A nylon guita sting has a linea density of 10 g/ and is unde a tension of 145 N. The fixed suppots ae 90 c apat. The sting is oscillating in the standing wave patten shown in the 90 c figue. Calculate the fequency of the taveling waves whose supeposition gives this standing wave. a) 40 Hz b) 100 Hz c) 00 Hz d)3 Hz e) NA 6. 6A A sting is fixed a both end. The following list is issing soe of its esonance fequencies: 150Hz, 5 Hz, 300 Hz, 375 Hz, 55 Hz. One of the issing fequencies is: a) 100 Hz b) 50 Hz c) 450 Hz d) 400 Hz e) NA 6B The A sting of a violin is a little too tight stetched. Six beats pe second ae head when the sting is sounded togethe with a tuning fok that is oscillating accuately at concet A (440 Hz). What is the fequency of the violin sting oscillation? a) 446 Hz b) 3 Hz c) 45 Hz d) 437 Hz e) NA
7. 7A A unifo thin stick of ass M = 0.6 Kg and length L = 100 c is pivoted at one end. The peiod of oscillation fo sall angula displaceents is equal to (in seconds) a) 0.01 b) 6.8 c) 4. d) 1.63 e) NA 7B If an additional ass = 0.1 Kg is attached to one end of the stick (see figue below), the peiod of oscillation is equal to (in seconds) a) 4. b) 1.73 c) 1.6 d) 0. e) NA P L=100 c P L=100 c M=0.6 Kg M=0.6 Kg QUESTION 7A =0.1 Kg QUESTION 7B 8. A sting of length 3 and linea ass density 0.005 kg/ is fixed at both ends. One of its esonance fequencies is 5 Hz. The next highe esonance fequency is 336 Hz 8A Sketch in the space povided the fist, second, thid and fouth esonance wave pattens (see gaphs in the coesponding lectue notes) 1st nd 3d 4th 8B The fundaental fequency f 1 is equal to (in Hz) a) 5 b) 84 c) 336 d) 53 e) NA
9. 9A. Choose the coect answe to indicate if the following 3 dawings show physically possible efaction. (F = false, T = tue.) 1.1 a) F T F b) F F T 1. 1.6 1.1 1.3 1.4 c) T F F d) F F T e) NA 9B. Choose the coect answe to indicate if the following 3 dawings show physically possible efaction. (F = false, T = tue.) white light blue ed 1.3 1.5 1.5 1.1 white light ed blue a) F F T b) F T T c) T F F d) T T F e) NA 10. 10A In the figue povided at the ight, ight down the angle on incidence that will ake the eflected light linealy polaized. Indicate also the oientation of the electic field of the eflected wave. tan θ Β =1.33, θ Β =53 o λ = 500 n n=1 θ Β E.. n=1.33 10B. Light taveling in wate has a fequency equal to: a) 388 Hz b) 60 Hz c) 575 Hz d) 500 Hz e) NA BONUS QUESTION (3 exta points) A disk of adius R=0.1 and ass M =0.5 Kg is suspended fo a peg, as illustated in the figue below. The peiod of oscillations is equal to: 0.77 sec Suppot R
FORMULAS THAT MIGHT HELP ω = π f Siple Pendulu: Peiod T = π L Use g= 10 /s g in this exa Physical Pendulu: Peiod T I = π Use g= 10 /s in this exa gh Moentu of inetia: 1 Thin ba of length L I CM = ML (Axis pependicula to the ba) 1 1 Disk of adius R ICM = MR (Axis pependicula to the plane of the disk) d x b d x k Daped siple haonic oscillato + + x = 0 t t αt x( t) = Ae COS( ωt + φ) b whee ( b ) α = ω = ω 0 k ω 0 = natual fequency of the oscillato Quality facto: Q = ω0 b Whee ω 0 is the natual fequency of the oscillato ω ( 0 t) Q In tes of Q, the solution is expessed as: x( t) = A COS( t + ) e ω φ
Waves taveling along a sting: speed T v =, whee T is the tension and µ is the µ linea ass density. Y 1 Y Wave Equation = 0 x v t Electoagnetic waves E = c B Snell s law n SIN q ) = n SIN( 1 ( 1 q )