p38_054 - 54. (a) The strategy is to find the γ factor...

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Unformatted text preview: 54. (a) The strategy is to find the γ factor from E = 14.24 × 10−9 J and mp c2 = 1.5033 × 10−10 J and from that find the contracted length. From the energy relation (Eq. 38-45), we obtain γ= E = 94.73 . mc2 Consequently, Eq. 38-13 yields L= L0 = 0.222 cm = 2.22 × 10−3 m . γ (b) and (c) From the γ factor, we find the speed: v=c 1− 1 γ 2 = 0.99994c . Therefore, the trip (according to the proton) took ∆t0 = 2.22 × 10−3 /0.99994c = 7.40 × 10−12 s. Finally, the time dilation formula (Eq. 38-7) leads to ∆t = γ ∆t0 = 7.01 × 10−10 s which can be checked using ∆t = L0 /v in our frame of reference. ...
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