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HW Chapter 15 - t t v lsvsc I For ordinary s peeds vap 1 1...

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PHYS4102 HOMEWORK CHAPTER 15 Assigned Tuesday, April 19, Thursday, April 28 These problems are taken from Griffiths. Problem 1. This problem deals with the relativistic velocity addition for- mula. It is composed of two problems from Griffiths. t I vlsvsc t- "' For "ordinary" speeds (vap 11 c, vsg 11 c), the denominator is so close to I thr discrepancy between Galileo's formula and Einstein's is negligible. On the hand, (10.7) has the desired property thatif vnp consistent with (10.6): c*vsg | + cvs-c c' But how can Galileo's rule, which relies on nothing but the most primitiw metrical inference, possibly be wrong? And if it rs wrong, what doesthis do to classical physics? (As a matter of fact, I used this very rule in equation (10-ll support the principle of relativity itself!) The answer is that specialrelativity us to alter our notions of spaceand time themselves, and therefore also of sucl rived quantities as velocity, momentum, and energy. Although it developed cally out of Einstein's contemplation of electrodynamics, the special theorl'- limited to any particular class of phenomena-rather, it is a description of the time "arena" in which c// physical phenomena take place. And in spite of the ence to the speed of light in the secondpostulate, relativity has nothing to do light: c is evidently a fundamental velocity, and it happensthat light (also and, presumably, gravitons) travel at that speed, but it is possibleto conceirc universe in which there are no electric charges, and hence no electromagnetk or waves, and yet relativity would still prevail. Because relativity defines the of space and time, it claims authority not merely over all presently known ena, but over those yet to be discovered. It is, asKant would say, a any future physics." Problem l0.l (a) What's the percent error introduced when you use Galileo's rule, instead d stein's, with r,a3 : 5 milh and vss : 60 mi/h? (b) Suppose you could run at half the speed of light down the corridor of a tni three-quarters the speed of light. What would your speed be relative to ground! (c) Prove, using equation (10.7), thatif uts < c and vBs 1 c then us ( c. In result.
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