PHYSICS 102 FINAL EXAMINATION

Transcription

1 PRINTED NAME: Circle your Class Section 1 9:00am Sohn 2 10:00am Klebanov 3 11:00am Galbiati 4 12:30pm Muthukumar 5 12:30pm Nappi Problem Score 1 /30 2 /20 3 /20 4 /20 5 /15 6 /15 Total /120 PHYSICS 102 FINAL EXAMINATION May 20, :30 10:30 pm McDonnell A02 When you are told to begin, check that this examination booklet contains all the numbered pages from 2 through 21. The exam contains 6 problems with unequal point values as listed above. Do not panic or be discouraged if you cannot do every problem; there are both easy and hard parts in this exam. Keep moving and finish as much as you can! Read each problem carefully. With the exception of problem 1, you must show your work the grade you get depends on how well the grader can understand your solution even when you write down the correct answer. Partial credit is given for relevant material only if it is in a comprehensive context. Please BOX your answers. DO ALL THE WORK YOU WANT GRADED IN THIS EXAMINATION BOOKLET! Rewrite and sign the Honor Pledge: I pledge my honor that I have not violated the Honor Code during this examination. Signature

2 Physics 102 Final Exam 20-May-2002 Page 2 *** Possibly useful constants and equations *** You may remove this page and use it as a reference, if you wish. ɛ 0 = C 2 N 1 m 2 µ 0 = 4π 10 7 TmA 1 k = 1/4πɛ 0 = Nm 2 C 2 e = C h = Js c = m/s 1 yr = s 1 hr = 3600 s hc = 1240eVnm 1u = 931.5MeV/c 2 m p = kg = 938.2MeV/c 2 m e = kg = 511keV/c 2 F =kq 1 Q 2 /r 2 F =qe V =kq/r U =qv U = 1 2 CV 2 E =σ/ɛ 0 R =ρl/a B =µ 0 I/2πr V =IR P =IV ; P =I rms V rms N s Φ s =MI p NΦ =LI B =µ 0 IN/L X C = 1/ωC X L =ωl Z = R 2 + (X L X C ) 2 P rms =I rms V rms cosφ F =IL B E A =Q/ɛ 0 f r = 1/2π LC F =ILB sinθ B l =µ 0 I N =N 0 exp( λt) λ =ln(2)/t 1/2 1/f = 1/d i + 1/d 0 m = d i /d 0 E= 13.6Z 2 /n 2 ev R= A 1/3 m r n = n 2 /Z m E =hf S =cɛ 0 E 2 E =cb t = t 0 / 1 (v/c) 2 E =mc 2 / 1 (v/c) 2 p =mv/ 1 (v/c) 2 v AB =v AC +v CB /(1 +v AC v CB /c 2 ) L =L 0 1 (v/c) 2 sin(θ) = 1.22λ/d Q =CV sin(θ) =λ/d C =ɛ 0 A/d λ =h/p

3 Physics 102 Final Exam 20-May-2002 Page 3 1. In the following there are 15 multiple choice questions. Circle the correct choice. There are 2 points for each correct answer. Circling more than one is considered a wrong answer. There is no partial credit. (a) Two uniformly charged spheres are shown in the diagrams below. The right sphere contains three times the charge as the left sphere. Which diagram correctly represents the magnitudes and directions of the electric forces acting on the spheres due to the charges on the spheres? (b) A uniform electric field points to the right as shown. A charge enters the region of uniform field with an initial velocity upwards as shown. If the charge is negative, which of the trajectories are possible? A. 1 and 2 B. 3 C. 4 D. 2 E. 6.

4 Physics 102 Final Exam 20-May-2002 Page 4 Problem 1. Continued (c) If a parallel plate capacitor is charged up with a dielectric nearby, what will happen? A. Nothing, dielectrics are electrically neutral. B. The dielectric is blown away. C. The dielectric is sucked in. (d) In the circuits shown, all four light bulbs are identical and the two batteries are identical. Which circuit puts out more light? A. Circuit 1. B. They re the same. C. Circuit 2.

5 Physics 102 Final Exam 20-May-2002 Page 5 Problem 1. Continued (e) The figures below show three regions of uniform magnetic field, each containing a different object. All vectors are in the plane of the paper. In which case(s) is there a net force on the object? A. 1 and 2. B. 3 only. C. 2 and 3. D. No Cases. (f) The long parallel wires shown to the right carry equal currents in the same direction. Which of the following is true? A. The magnetic field from the left wire cancels the field from the right wire at the position of the right wire. B. The wires are attracted to each other. C. The wires repel each other. D. The magnetic forces must cancel, otherwise wires would move whenever we put a current through them.

6 Physics 102 Final Exam 20-May-2002 Page 6 Problem 1. Continued (g) The diagrams show two regions of uniform, vertical magnetic field. In case 1, a coil of wire is spun around a vertical axis. In case 2, a coil of wire is spun around a horizontal axis. Which of the following is true? A. An EMF is generated in the coil in case 1. B. An EMF is generated in the coil in case 2. C. An EMF is generated in the coil in both cases. D. An EMF is not generated in either case, because the magnetic field and the loop area are fixed. (h) A long straight wire carries a steady current I in the vertical direction as shown. A rectangular conducting loop lies in the same plane as the wire, with two sides parallel to the wire and two sides perpendicular to the wire. Suppose the loop is pushed towards the wire as shown. The direction of the induced current in the loop is A. clockwise. B. counterclockwise. C. indeterminant with the given information.

7 Physics 102 Final Exam 20-May-2002 Page 7 Problem 1. Continued (i) A light bulb and capacitor are connected in series and powered by a variable frequency AC generator. Which of the following is true? A. The light is brightest at low frequencies. B. The light never lights up. C. The light is brightest at high frequencies. D. The intensity is the same at both high and low frequencies. (j) In the circuit shown, switchs has been open for a long time. It is closed, after which: A. First light B comes on followed by light A. B. Lights A and B come on at the same time. C. Light A never comes on because the inductor impedes the current. D. Light B goes out because the inductor acts just like a wire if one waits long enough.

8 Physics 102 Final Exam 20-May-2002 Page 8 Problem 1. Continued (k) A fish swims below the surface of the water. An observer above the water sees the fish at A. a greater depth than it really is. B. its true depth. C. a smaller depth than it really is. (l) A diffraction grating is illuminated with red light at normal incidence. The pattern seen on a screen behind the grating consists of three spots, one at zero degrees (straight through) and one each at ±45. Now, green light of equal intensity and coming from the same direction is added. The new pattern consists of: A. Red spots at 0 and ±45. B. Green spots at 0 and ±45. C. Yellow spots at 0 and ±45. D. A yellow spot at 0, red spots at ±45, and green spots slightly farther out. E. A yellow spot at 0, red spots at ±45, and green spots slightly closer in.

9 Physics 102 Final Exam 20-May-2002 Page 9 Problem 1. Continued (m) Muons are created at the top of the atmosphere (altitude 10 km) by cosmic rays. The lifetime of a muon isτ = s. Even though they are travelling with v = 0.999c, they can only travel about 0.6 km in one lifetime before they decay. Yet muons still manage to reach sea level. Why? A. Muons decay into different particles than can make it to the Earth s surface. B. When moving at the speed of light the distance covered is no longer given by d =vt. C. In the muon s frame our clock runs faster so the distance is shorter. D. In our frame, the muon s clock runs slower and it has longer to traverse the atmosphere before it decays. (n) A beam of electrons hits a crystal with an interatomic spacing of 0.1nm. Diffraction spots are seen with a regular spacing of 0.1 radians. The wavelength of the electrons is about A. 100 nanometers. B. 1 nanometer. C nanometers. D nanometers.

10 Physics 102 Final Exam 20-May-2002 Page 10 Problem 1. Continued (o) A radioactive source next to a Geiger counter produces clicks. When a lead shield is placed between the source and the counter, as shown in the figure, the clicks stop. If a uniform magnetic field out of the page is turned on below the shield (as shown in the figure), clicks are heard again. If the field points into the page, no clicks are heard. What is the sign of the particles emitted in the decay of the radioactive source? A. Positive. B. Negative. C. Not enough information to tell.

11 Physics 102 Final Exam 20-May-2002 Page Imagine that you are living in the distant future when technology has advanced to the point that it s feasible to contemplate a trip to a star cluster which is 250 light years away. Even though you realize you ll never again be able to see the friends and family you leave behind, you volunteer to be one of the astronauts on the first mission to a distant star cluster. (a) Naturally, you want to get there in a reasonable amount of time, so you still have some of your life left for exploration. How fast must you be travelling (relative to the Earth) in order to get there in 10 years by your clock? Give your answer as a number times the speed of light. Be sure that you get enough digits from your calculator to see that the number is not 1! (5 points) (b) What is the Earth to star cluster distance as it appears to you as you are travelling to the star cluster at the speed calculated in part (a)? (4 points)

12 Physics 102 Final Exam 20-May-2002 Page 12 Problem 2. Continued (c) The mass of you and your space ship is 30,000kg. What is the kinetic energy of you and your ship travelling at the speed calculated in part (a) as reckoned by an observer on Earth? (5 points) (d) How much mass must be converted into energy to provide the energy of part (c)? (3 points) (e) Of course you are expected to send back reports once you arrive at the star cluster. Immediately on arrival, you send back an I ve arrived safely radio message. How long after you left the Earth do residents of the Earth receive this message (according to their clocks)? (3 points)

13 Physics 102 Final Exam 20-May-2002 Page In the lab you observe the light from a discharge lamp with a crossbow spectrometer as indicated in the diagram. Some data: distance from grating to meter stick,d=0.60m, grating containsn=400 slits per millimeter. When you look through the grating, you see the light source directly in front; to one side, you see a blue, a blue-green, and a red line. You measure their positions along the meter stick (from the 0 order image of the lamp) asx 1 = 0.106m, x 2 = 0.119m, andx 3 = 0.163m, for the blue, bluegreen, and red lines, respectively. (a) What are the wavelengths (in nanometers) of the light in the three lines? (5 points) (b) What gas is in the discharge lamp? (3 points)

14 Physics 102 Final Exam 20-May-2002 Page 14 Problem 3. Continued (c) You notice the same set of lines appears on the other side of the lamp (at negative x). You decide to improve the accuracy of your measurements by averaging the two distances you can measure for each line. (Of course, you ignore the sign ofx while averaging.) Give at least two reasons why this improves the accuracy of your measurements. (4 points) (d) You have several filters, one of which transmits only the red line (and absorbs the blue-green and blue lines). Another transmits only the blue-green line and a third transmits only the blue line. You have an unknown metal. Using these filters, you find that there is no photo-electric effect when the metal is illuminated by the red line, a strong photo-electric effect when the metal is illuminated by the blue line, and a feeble photo-electric effect when the metal is illuminated by the blue-green line. Feeble means the ejected electrons have almost no kinetic energy, not more than K = 0.05eV. What can you say about the work function (in electron volts) of the unknown metal? (Be as quantitative as you can!) (5 points) (e) You crank up the lamp intensity to see if you can observe a photoelectric effect with the same metal and the red line. Do you succeed? Why or why not? (3 points)

15 Physics 102 Final Exam 20-May-2002 Page An apparatus consists of two long concentric, conducting cylinders, sketched in cross section to the right. Each cylinder is very thin. The inner cylinder has radiusa and the outer cylinder has radiusb. Spread uniformly over the inner cylinder is a chargeλ>0 per unit length. (That is, each meter of the inner cylinder going into or out of the page contains a chargeλ.) Similarly, a charge λ per unit length is spread uniformly over the outer cylinder. In addition, the inner cylinder carries a currenti> 0 coming out of the page and a currenti flows into the page on the outer cylinder. The currents are uniformly spread over the cylinders. (a) What is the magnitude of the electric field in the region inside the inner cylinder,r<a, between the cylinders,a<r<b, and outside the outer cylinder, b < r? Give your answers as formulae which may include physical or mathematical constants (such as µ 0,ɛ 0,π, etc., and the variables defined in the problem such asa, b,λ,i, andr, the distance from the centerline of the two cylinders. Sketch some representative electric field lines on the diagram to the right. Be sure to show in which direction the field points on each line! (6 points)

16 Physics 102 Final Exam 20-May-2002 Page 16 Problem 4. Continued (b) What is the magnitude of the magnetic field in the region inside the inner cylinder,r < a, between the cylinders,a<r<b, and outside the outer cylinder,b<r? Again, you should give your answers in terms of formulae. Sketch some representative magnetic field lines on the diagram to the right. Be sure to show in which direction the field points on each line! (6 points)

17 Physics 102 Final Exam 20-May-2002 Page 17 Problem 4. Continued (c) A charged particle is moving in the region between the inner and outer cylinders parallel to the axis of the cylinders. In other words, it s travelling into or out of the page. Suppose its charge isq> 0 and its speed isv. Show that if the particle is moving in the correct direction (either into or out of the page) with the correct speed, it will travel in a straight line, undeflected by the combined electric and magnetic fields between the cylinders. Find the direction and find an expression for the speed. Show that the speed doesn t depend on where the particle is (as long as it s between the cylinders), nor on the particle s charge (as long as it s positive). If you were unable to do parts (a) and (b), then for partial credit, you may take the electric field to point to the right and have magnitudee and the magnetic field to point up and have magnitude B. (6 points) (d) Suppose the region between the cylinders is filled with teflon which has a dielectric constantκ=2.1. Nothing else is changed. What is the magnitude of the electric field between the cylinders in terms of the magnitudee 0 without the dielectric? (2 points)

18 Physics 102 Final Exam 20-May-2002 Page Radium decays by emitting an alpha particle according to Ra X +α, with a half life of 1600 years. Mass data: m Ra = u,m X = u,m α = u. (a) Identify the nucleusx by giving its atomic mass number,a, and its atomic number, Z. (3 points) (b) How much energy (in MeV) is released by this decay? (3 points)

19 Physics 102 Final Exam 20-May-2002 Page 19 Problem 5. Continued (c) If all this energy is carried away by the alpha particle, what is its de Broglie wavelength? (Hint: the alpha particle may be treated non-relativistically.) (4 points) (d) How many decays per second occur in one gram of radium? (5 points)

20 Physics 102 Final Exam 20-May-2002 Page The diagram below shows an object (the arrow) which is locatedd o = 12units (each tick mark on the horizontal line is a unit) in front of a lens. The lens is a converging lens with a focal lengthf = 3units. The focal points are indicated on the diagram. (a) Algebraically determine the location of the image. Specify the location by determining its distance from the lens in units and stating whether it is to the left or right of the lens. (5 points) (b) On the diagram above, carefully trace at least two rays that allow you to geometrically determine the location of the image of the tip of the arrow. (5 points)

21 Physics 102 Final Exam 20-May-2002 Page 21 Problem 6. Continued (c) What is the magnification? (3 points) (d) Is the image real or virtual? Is it erect or inverted? (2 points)

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