Exam 3 practice problems solutions

# Exam 3 practice - Exam#3 practice problems solutions Physics 204 1 NASA makes an announcement that the Hubble Space Telescope has detected a signal

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Exam #3 practice problems solutions Physics 204 1. NASA makes an announcement that the Hubble Space Telescope has detected a signal from an alien probe. When the probe sent the signal it was 0.20 ly (light years 1 ) away and headed towards Earth at 0.75 c . a. By the time the signal reaches Earth how far away is the probe? How much time will pass on earth between the signal being received and the probe arriving? b. At the moment the probe sends the signal, how far away does the probe detect the earth to be? c. From the moment the probe sends the signal, how long will the probe take to reach the earth according to its own clock? Since the speed of light is finite, the light that was emitted by the probe when it was 0.20 ly away took 0.20 yr to arrive. During that time the probe traveled    0.75 0.20 0.15 d vt c yr ly . By the time the light reaches Earth the probe will be only 0.05 ly away. This means the probe will arrive at Earth in     0.05 0.75 0.067 t d v ly c yr Because of length contraction, from the probe’s point of view the earth is only       22 1 1 0.75 0.20 0.132 p x v c x ly ly   away. At 0.75 c it will take the probe     0.132 0.75 0.176 t d v ly c yr to reach Earth. 2. In order to investigate the alien probe featured in the previous problem NASA launches a probe of its own. It speeds away from Earth at 0.60 c . a. How fast is the alien probe moving relative to NASA’s probe? b. Unfortunately the alien probe is highly maneuverable and slips past NASA’s probe. NASA’s probe turns around and pursues the alien probe but can’t keep up due to its slower speed. How fast is the alien probe moving relative to NASA’s probe now?        2 0.75 0.60 0.93 0.75 0.60 11 1 AE EN AE NE AN AE EN AE NE cc v v v v vc v v v v c     The result was negative because of the coordinate system I used. The alien probe is moving to the left from the point of view of NASA’s probe. Once the alien probe slips past NASA’s probe… 1 A light year is the distance that light travels in 1 year. Earth x NASA's probe Alien probe 0.60 NE  0.75 AE Earth x 0.60 NE 0.75 AE

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       22 2 0.75 0.60 0.27 0.75 0.60 11 1 AE EN AE NE AN AE EN AE NE cc v v v v vc v v v v c       3. A diffraction pattern is being created by an electron beam being sent through a rectangular gap of width 20.0 nm . A detector located 2.00 m from the gap measures the first minimums of the pattern to be at 0.01 m . a. How is this possible? Electrons aren’t the same as light. Why should they create any sort of diffraction pattern at all? b. What is the speed of the electrons in the beam? Light isn’t the only thing that shows wavelike behavior. Electrons will as well provided their De Broglie wavelength is comparable to the size of the gap. This is single slit diffraction, and since the first minimums are so close the small angle approximation is reasonable. I’ll use the low-speed approximation for momentum since it’s easier to work with.
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## This note was uploaded on 01/31/2011 for the course PHYS 204 taught by Professor Brahmia during the Spring '10 term at Rutgers.

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Exam 3 practice - Exam#3 practice problems solutions Physics 204 1 NASA makes an announcement that the Hubble Space Telescope has detected a signal

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