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# Unit 1 - Physics 225 Relativity and Math Applications...

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Physics 225 Relativity and Math Applications Spring 2010 Unit 1 Special Relativity I: Do you c what I c ? N.C.R. Makins, G. Gollin University of Illinois at Urbana-Champaign © 2010

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Physics 225 1.2 1.2
Physics 225 1.3 1.3 Unit 1: Special relativity-- time dilation and Lorentz contraction Introduction: the speed of light is finite, and constant. You're going to love this: its consequences are the weirdest things you'll see in physics before you learn about quantum mechanics. All the strange features of special relativity come from the fact that the speed of light is exactly 2.9972458 × 10 8 meters per second. It doesn't matter whether the source of light moves with respect to the measuring apparatus: any device measuring c (the speed of light) will obtain, within experimental error, this value. Nothing else works this way: sound travels at fixed speed with respect to the air, for example. The value 2.9972458 × 10 8 meters per second really is exact: it serves as a definition, along with some time standard, of the length of one meter. The speed of light is very close to 1 foot per nanosecond, so we'll use that as a convenient approximation this week and next week. Here’s what you’ll discover today: Events which are simultaneous in one frame of reference are not necessarily simultaneous in another frame. The rate at which time passes in a moving frame of reference is slowed down. Moving objects become shorter along their direction of motion. Exercise 1.1: Constant c and simultaneity Mr. Urkin, sociopathic co-proprietor of Urkin's Deli and Hardware Emporium, is capable of throwing a snowball at 50 miles per hour. While riding as a passenger in a delivery truck traveling 40 miles per hour, he hurls snowballs at stationary pedestrians ahead of, and behind, the moving truck. (a) Calculate the speeds of the snowballs from the perspectives of the two pedestrians shown in the diagram. 40 mph foward victim rearward victim Urkin's Deli and Hardware Emporium

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Physics 225 1.4 1.4 (b) The starship Nostromo, drifting in deep space, passes a large interstellar recreational facility which is also adrift, as shown in the figure. Observers on the recreational facility see the Nostromo as moving to the right, with speed 0.8 c . While the ship is between the ends of the rec facility, it fires its communications lasers to send signal pulses in the forward and aft directions to receivers built into the ends of the rec facility. According to technicians on the recreation facility , how fast are the two light pulses traveling as they pass through the receiver hardware built into each end of the rec facility? Note that (slowly moving) snowballs do not behave the same way as bursts of light!
Physics 225 1.5 1.5 The Sulaco, another fast ship, glides past the same drifting interstellar recreational facility. As before, observers on the recreational facility see the ship moving to the right with speed 0.8 c . Unfortunately, Sulaco's X-band antenna strikes the rec facility's TV parabola, interrupting the final episode of Pride and Prejudice. Sulaco's

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Unit 1 - Physics 225 Relativity and Math Applications...

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