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WMU PHYS 1150 - Final Exam

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XF.4a 115PHYS-115(4) (Kaldon-26364) Name __________S O L U T I O N_________WMU - Spring 2005Final Exam - 200,000 points Rev. 04/19/05 Tu.A5State Any Assumptions You Need To Make – Show All Work – Circle Any Final AnswersUse Your Time Wisely – Work on What You Can – Be Sure to Write Down EquationsShort Answers Should Be Short! – Feel Free to Ask Any QuestionsFINAL EXAM [FORM - A]PHYS-115 (KALDON-4)SPRING 2005WMUThe Future Ends Thursday19 May 2005 at 12:01am…· STAR WARS EPISODE III: REVENGE OF THE SITH ·(Dr. Phil has his tickets. Do you?)Physics 115 / Final Exam Spring 2005 Page 2Getting a Charge Out of Physics (50,000 points)1.) Four charges, |q| = 6.00 x 10-6 C, are rigidly arranged in a square (L = 10.0 cm = 0.100 m) as shown. (a)Find the electric field vector, rEtotal, at the center of the square of charges at point P.E-fields cancel at center pairwise, so: rEtotal= 0(b) Another charge +q is placed in the center (point P). Find the force vector, rFtotal, on the center charge due tothe other four charges.FE cancel at center pairwise, too:The Stanford Linear Accelerator, SLAC, is a real machine that takes electrons and accelerates them for most ofa mile in vacuum up to speeds as great as 99.99% the speed of light. Consider an electron (me = 9.11 × 10 -31kg) in a constant electric field that starts from rest and ends up only at 1.00 × 108 m/s† after traveling in the +xdirection a distance of 1150 meters in 23.0 msec. Using our old friend from the kinematic equations, TheEquation Without Time, we find that avd=22 or a = 4.35 × 1012 m/s². (c) What is the magnitude and directionof the force on the electron?Fma kg msN== ´ ´=´--911 10 435 103963 1031 12 219../.chc hFE points in the same direction the electron accelerates: +x(d) What is the magnitude and direction of the constant E-field required in part (c)?Fma kg msNFqE eEEFeNCNCEE== ´ ´=´==-=-=´-´=-----911 10 435 103963 103963 101602 10247431 12 2191919../..../chc hE points in the opposite direction the electron accelerates: -x(e) What potential difference V would create the constant E in part (d)?V Ed N C m volts== =2 474 1150 2845./bgbg † This is only one-third the speed of light, well below the threshold of where we have to worry about using Relativity.rrrrEFORFqEtotaltotaltotal total====000Physics 115 / Final Exam Spring 2005 Page 3An Initial Resistance to Measuring Your Capacity for Physics (50,000 points)2.) All of the resistors in the circuit shown are R = 100. W. Consider thethree resistors along the right hand side (R2 , R5 , R7 ) which, for the record,are not in parallel with each other. (a) Which of the three resistors sees thelargest current? Why?R5 and R7 are in series leading back to thebattery, so they see the largest current.(b) Which of these three resistors generates the most heat? Why?P = I2 R ; Since R5 and R7 see the most current and all theR’s are identical then R5 and R7 generate the most heat.(c) Find the equivalent resistance of this circuit. Note: you don’t have to do part (c) first to answer (a) or (b).1 and 2, 3 and 4, and 5-6-7 are in Series12 and 34 are in ParallelRRRRRRRRRR12 1 234 3 4567 5 6 7100 100 200100 100 200300=+=+==+= + ==++=.. ... ..WW WWW WW111 120012002200100 01234 12 341234RRRR=+= + ==.. ..WW WW1-2-3-4 and 5-6-7 are in SeriesRRRtotal=+= + =1234 567100 300 400 0...WW WPhysics 115 / Final Exam Spring 2005 Page 4(d) A certain cylindrical resistor has a resistance R, a length L, a radius r, and a resistivity r. If we were todouble the length, radius and resistivity, how would the new resistance R’ differ from the original resistance R ?Express your answer as R’ = m R, where m is some multiplier which you will find.RLAArA r r ARLALAR==¢===¢===rppprr;;22224 4224bg (e) A parallel plate capacitor consists of plates that are 0.100 m × 0.275 m, separated by 0.0350 m of air andconnected to a 12.0 V car battery. If we doubled all the numbers given in this problem, would the new capacitorhold more charge Q on the plates, or less?CAdlwdClwdAdCQCVQCV CV CV Q==¢====¢=¢¢===eeee000022242222 4 4()bgbgA Little Light Diversion (50,000 points)3.) (a) Find the critical angle qc for glass with an n = 1.57.qcn=FHGIKJ=FHGIKJ=°--sin sin..1211115739 6Physics 115 / Final Exam Spring 2005 Page 5(b) Consider a 45°-45°-90° glass prism with an index of refraction n = 1.57, surrounded by air. A light raycomes in perpendicular to the long side, as shown. Follow the light ray, sketching it as it goes through the glassprism until it emerges back into the air. Calculate any of the angles which need to be calculated.Incoming ray comes down normal line, 0°, so intersects angledside at 45° > 39.6°, so Total Internal Reflection… twice.(c) Consider two flat mirrors placed together at right angles as shown. A light ray comes in to the top mirror atan angle 45° to the normal. Follow the light ray, sketching it as it bounces off both mirrors. Calculate any of theangles which need to be calculated.Gee – this corner reflector made from mirrors looks “just like”the mirror made from the T.I.R. inside the 45° prism.Physics 115 / Final Exam Spring 2005 Page 6(d) Suppose the light in part (b) comes from a little red LED laser pointer with a wavelength l = 656 nm and wehave placed an anti-reflection coating (n2 = 1.42) on the glass (n3 = 1.57). Find the thickness t of the anti-reflection coating.Both reflections are low-to-high, so both are phase-shifted halfa wavelength, and therefore doesn’t change the problem.(e) A shiny new rounded cylindrical Cow Magnet is dropped into a coil as shown. As the magnet enters thecoil, indicate whether the induced magnetic field in the coil is pointing UP or DOWN and whether the inducedcurrent in the wire at the top of the coil is going to the LEFT or the RIGHT.B-field from cow magnet is pointing down and increasing.The coil’s response is to create an induced B-field pointing UPto try to cancel the increasing magnetic field. From the R.H.R.the induced current must be going to the RIGHT.llllmmmmnnmnmdttnmnm== ===== =656142462 0224462 041155....Physics 115 / Final Exam Spring 2005 Page 7Relatively Speaking, This is The End (50,000 points)4.) (a) We’ve already established in class what b corresponds to about a 10% difference between classical andrelativistic physics. What if we were pickier and wanted to work at the 1% difference level? Determine the b,and find the speed v that g = 1.01 corresponds


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