p38_042 - 42. (a) Squaring Eq. 38-44 gives E 2 = mc2 2 +...

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42. (a) Squaring Eq. 38-44 gives E 2 = ( mc 2 ) 2 +2 mc 2 K + K 2 which we set equal to Eq. 38-52. Thus, ( mc 2 ) 2 +2 mc 2 K + K 2 =( pc ) 2 + ( mc 2 ) 2 = m = ( pc ) 2 K 2 2 Kc 2 . (b) At low speeds, the pre-Einsteinian expressions p = mv and K = 1 2 mv 2 apply. We note that pc À K at low speeds since c À v in this regime. Thus, m ( mvc ) 2 ( 1 2 mv 2 ) 2 2 ( 1 2 mv 2 ) c 2 ( mvc ) 2 2 ( 1 2 mv 2 ) c 2 = m. (c) Here,
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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