Fall 07 Phys 143l Practice Final Solutions

Fall 07 Phys 143l Practice Final Solutions - Duke...

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Unformatted text preview: Duke University Department of Physics Physics 143 Fall Term 2007 PRACTICE FINAL EXAM I will abide by the Duke Honor Code. Name: This is a closed book exam, with two sides of one page cheat sheet allowed. Calculators are allowed, but only for basic calculations: you may not use special memory, graphing etc. functions. You must always show your work for credit. Each problem is worth 10 points. You must hand in your cheat sheet with your exam. Problem 1: Two events occur at the same point x ′ at times t ′ 1 and t ′ 2 in an inertial frame of reference S ′ , which moves with speed v relative to S . What is the spatial separation of these events measured in S ? According to the Lorentz transformation, in S , Δ x = γ ( x ′ + vt ′ 2 ) − γ ( x ′ + vt ′ 1 ) = γv Δ t ′ , where Δ t ′ = t ′ 2 − t ′ 1 . Problem 2: Two spaceships approach each other. They are each viewed from Earth as having a speed half that of light. What is their speed relative to each other? Relativistic addition of velocities can be used for this problem. One space- ship is in the S frame, and it sees Earth approach at u = 0 . 5 c . The other is in the S ′ frame and it sees Earth approach at u ′ = − . 5 c . We now want to find v , the velocity of S ′ with respect to S , which is the speed of the spaceships relative to each other. u ′ = u − v 1 − vu/c 2 Solving for v gives v = u − u ′ 1 − uu ′ /c 2 Plugging in gives v = 4 c/ 5. Problem 3: If you could convert 1 g of dirt directly into energy and you could sell the energy for 10 cents per kilowatt-hour, how much money would you get? E = mc 2 = (10 − 3 )(3 × 10 8 ) 2 = 9 × 10 13 J. 1 kilowatt-hour is (10 3 J/s)(3600 s) = 3 . 6 × 10 6 J. This comes out to $2.5 million. Problem 4: Describe the Michelson-Morley experiment, and explain how its result is relevant to Einstein’s theory of special relativity. The Michelson-Morley experiment consists of a beam of light that is split by a half-silvered mirror and travels down two perpendicular “arms”; the light is then reflected off mirrors and recombined at the beam splitter (see diagram). Because light along each of the two paths has traveled a different distance, the two beams will interfere and produce “fringes”. If we assume that the Earth is hurtling through the ether (a hypothesized medium in which light propagates), there will be an effective ether “wind” which will change the time of flight of light in each arm, depending on the orientation of the apparatus with respect to the ether wind. This will change the interference fringe pattern. The fringe pattern will therefore shift as the apparatus rotates, if there is such a thing as the ether....
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This note was uploaded on 04/27/2008 for the course PHYSICS 143L taught by Professor Scholberg during the Fall '07 term at Duke.

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Fall 07 Phys 143l Practice Final Solutions - Duke...

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