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phy190_midterm_2007_sols

phy190_midterm_2007_sols - PHY190 Special Relativity...

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PHY190 – Special Relativity – Midterm Exam Thursday November 15, 2007 Duration - 50 minutes (Solutions: November 14) (Additional notes: November 16) 1. Draw a spacetime diagram that shows the following worldlines. Label which is which! (a) A particle traveling at a constant speed of 0.5 in the ˆ x direction, passing x = 0 at t = - 2 s. (b) A particle that at t = 0 is at rest at x = +3 s, but accelerates in the - ˆ x direction and approaches the speed of light as time passes. (c) A light flash that originates from well before t = 0 but passes the position x = 2 s at t = 2 s as it travels in the ˆ x direction. Parts a) and c) were worth [3 points], part b) was worth [4], for a total of 10 points on this ques- tion. Axes had to be clearly labeled so that the speed of the object could be read-off the graph. If you didn’t do this you lost 1 point right off the bat for each part (or as many as 2 points for the whole question). For a) and c) the particle or light pulse “passes” the specified coordinate so the worldline should not just start or stop there. For b) the worldline should never get flatter than a 45-degree angle (ie. correspond to something traveling faster than the speed of light). It seems almost no one got less than 5 or 6 on this question though a ’large’ number lost two points for not indicating any units. We were actually pretty liberal about how you indicated the approach to v = c for part b) but it had to be ’graphical’; just saying that v never exceeds c wasn’t enough – what did this mean graphi- cally?
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PAGE 2 2. At t = 0 , an alien spaceship passes by the earth: let this be event A . At t = 13 minutes (according to synchronised clocks on earth and Mars) the spaceship passes by Mars, which is 5 light-minutes from earth at the time: let this be event B . Radar tracking indicates that
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