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One Universe: At Home in the Cosmos


Solutions to Exercise 22

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(a) The vehicle has mass m = 1000 kg.  The observer sees the vehicle with a mass

m' = m / sqrt(1 - (v/c)^2) = 1000 / sqrt(1 - (0.5c/c)^2) = 1000 / sqrt(0.75)
   = 1000 kg / 0.866 = 1150 kg.

(b) for v = 0.7 * c, 

m' = 1000 / sqrt(1 - (0.7c/c)^2) = 1000 / sqrt(0.51) = 1400 kg.

(c) for v = 0.999995 * c,

m' = 1000 / sqrt(1 - (0.999995c/c)^2) = 1000 / sqrt(0.000009999975)
   = 1000 / 0.00316 = 316000 kg.