Final Fall 2002 - Physics 171.102 Final Exam Dec 17 2002...

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Unformatted text preview: Physics 171.102 Final Exam Dec. 17, 2002 Prof. Barnett h = 6.6 ><1O‘34 J sec 0 = 3 ><108 m/sec 16V : 1.6 X 10-19 J mezemn = 9 x 10'31 kg 60 = 8.854 x 10-12 02/(N m2) MM 2 2 x 1030 k9 Mearth Z 6 X 1024 kg Msun :— 2 X 1030 kg Rearth = 6 X 106 m Rmm orbit: 1.5 x 108 km G = 6.7 x 10‘11 N - 7712/ng .U'o = 47r x 10-7 T - m/A Do all 9 problems. Use a pen. An exam written with pencil or a pen with snow paint is not subject to regrading. Show and explain your work CLEARLY to get maximum partial credit. You g1_ay use material written on both sides of four 3 x 5 index cards. . A point charge of 10—10 C is at the center of a hollow conducting sphere with inner radius of Rim.” 2 1.0 cm and outer radius Router : 2.0 cm. There is a net charge, Q, on this conducting sphere. An electron sits outside the sphere a total distance of d = 3.0 cm from the charge at the center of the sphere. This electron feels no force due to the combination of the point charge and charge Q. A s l). (10 pts) What is the value of Q? ) (5 pts) What is the surface charge density dinner on the inner surface of the sphere? ) l ) ( U3 '1 C 5 pts) What is the surface charge density (router on the outer surface of the sphere? D 10 pts) Find the electric field E(R) for the region 0 < R < 5 cm. Draw a NEAT graph of EU?) for this region. E) (15 pts) Find the electric potential V(R) for the region 0 < R < 5 cm with the constraint that V : 0 at R : 00. Draw a NEAT graph of V(R) for this region 0 < R < 5 cm. . A neutral particle is at (0, 0, 0) in a two Tesla uniform magnetic field aligned in the Zdirection, B = 2.0 T It. At t 2 0 it decays into two particles, called A and B. The masses of the two daughter particles are mA : 10—25 kg and m3 2 3 X 10"25 kg. Particle A has charge QA = +10‘18 C and initially has a velocity in the :5 direction 17A : 106 m/s 2'. A) (10 pts) What is the charge and initial velocity of particle B? B) (15 pts) The two particles travel paths such that at a later time t 2 to they collide with one another. What are the (ct, y, z) coordinates of the collision point? C) (15 pts) At what time t0 do the two particles collide? 3. The adjacent drawing shows a resistance R and inductance L in parallel connected to switch which is closed at t : 0. Thereafter, a constant currentsource, by varying its emf, maintains a constant current Io out of its upper terminal, through the switch and circuit. A) (15 pts) Derive an equation relating the time rate of change of the current in the inductor, dIL/dt, to the current in the resistor, I R. B) (15 pts) Derive expressions for the ~eurrent through the resistor I R(t) and the current through the inductor I L (t) as functions of time. C) (10 pts) Find the time, in terms of R and L, when the two currents, I R(t) and 1;,(t), are ' equal. 400 4. An object is placed against the center of a thin lens and then moved away, from it along the central axis as _ SI the position of the image is measured. The adjacent figure shows the image position 5’ and the object position S, 118ng the Reese definitions, out to S = 60 cm. —-400 A) (150 pts)-What is the focal length of the lens? ‘1 B) (10 pts) What is‘the image position 5’ when the object is at S = 100 cm? . 2 C) (10 pts) For what? region of object positions will the image be real? I0 25 W/mx b) (10 pts) For' what region of object positions will the image be upright? +50° 5. Unpolarized light travels in the z direction with an intensity of 10 i 25 W/mz. It passes through three polarizing sheets as shown. The sheets have polarization orientations of +50°, +20° and —70° relative to the x axis. 3 A) (10 pts) What is the intensity of the light beam after passing through the first polarizer? - B) (10 pts) What is the intensity of the light beam after passing through the second polarizer? C) (10 pts) What is the intensity of the light beam after passing through the third polarizer? ' 6. The earth receives photons ffom the sun at a rate of about 2.5 X 1021 per second per meter2 for a portion of the earth’s surface perpendicular to the sunlight rays. Assume all sunlight has wavelength 500 nm. A) (15 pts) What is the total energy received by earth from the sun per second? B) (10 pts) What momentum per second is transfered to the earth by all of this sunlight? C) (15 pts) How big a force does this sunlight exert upon the earth compared to the regular gravitational force between the earth and sun? 7. The Standard Model of Particle Physics includes a variety of particles and forces. A) (10 pts) Name two distinctions between a “fermion” and a “boson”. Give one example of each. B) (5 pts) Write down the names of the different types of quarks and their electric charges relative to the charge on a proton. C) (5 pts) Write down the names of the different types of leptons and their electric charges relative to the charge on a proton. D) (5 pts) What is the quark substructure of a proton, a neutron and a 7r+ meson? 8. Schrodinger discovered a non—relativistic time independent equation that describes atoms and molecules. This equation is fii¥¢@) _ 2m dx2 + Wadi/1&3) = EWII?) A particle is in a rigid box potential, or infinite square well potential, given by V(a:) : oo 2: < 0 . V(x) : oo V(zr) : 0 V00 2 00 V(x) = 0 0 < :c < a V(:r) : oo a<x. ‘ x=0 - ' 11::a The “boundary conditions” for 112(5r) at :r 2 0 and :1: = a are 1p(x) = 0. A) (15 pts) A possible solution to this equation is was) : 1/2/a sin(mrx/a) where n is a positive integer. Prove that this function is a solution to the Schrodinger equation for 0 < :r < a and that it meets the boundary conditions stated above. B) (10 pts) Find the energy E in eV for the state with n = 3 if the mass of the particle is 10‘30 kg and the width of the well is a = 10"9 m. C) (5 pts) Draw a NEAT graph of M33) for O < (E < a and n : 3. D) (15 pts) Write down the function that describes the probability of experimentally finding- the particle between (t and r + dx in the region 0 < x < a for n = 3. Draw a NEAT graph of this probability for 0 < a: < a. 9. An armada of Star Trek space ships is 1.0 light—years long as measured in its rest frame. The entire armada is moving with respect to the Star Trek headquarters ground station at a uniform speed of 60% the speed of light. A messenger makes a trip from the back of the armada to the front of the armada at a speed of 80% the speed of light relative to the Star Trek headquarters ground station. A) (15 pts) How long does it take the messenger to make the trip according to the commander at rest in the Star Trek headquarters ground station? B) (15 pts) How long does it take the messenger to make the trip according to a space ship pilot at rest with respect to the armada? C) (15 pts) How long does it take the messenger to make the trip according to the messenger? ...
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