ch37-p065 - 65. (a) From the length contraction equation,...

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65. (a) From the length contraction equation, the length L c of the car according to Garageman is == −= = L L L c c c γ β 1 305 0 9980 193 22 (. ( . ) . m) 1 m. (b) Since the x g axis is fixed to the garage x g 2 = L g = 6.00 m. (c) As for t g 2 , note from Fig. 37-31 (b) that, at t g = t g 1 = 0 the coordinate of the front bumper of the limo in the x g frame is L c , meaning that the front of the limo is still a distance LL gc from the back door of the garage. Since the limo travels at a speed v , the time it takes for the front of the limo to reach the back door of the garage is given by tt t v gg g =−= = × 21 8 8 600 0 9980 2 998 10 136 10 .. .( . . mm m/s) s. Thus t g 2 = t g 1 + t g = 0 + 1.36 × 10 –8 s = 1.36 × 10 –8 s. (d) The limo is inside the garage between times t g 1 and t g 2 , so the time duration is t g 2 t g 1 = 1.36 × 10 –8 s. (e) Again from Eq. 37-13, the length L g of the garage according to Carman is = L L L g g g 1 6 00 0 9980 0 379 ) .
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ch37-p065 - 65. (a) From the length contraction equation,...

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