Building a Starship. Eventually we might like to build a starship to send a mann

Question

Building a Starship. Eventually we might like to build a starship to send a manned mission to the nearest star. The distances are really far and so we will have to travel very fast to get there in human lifetime, even if it takes 50 years. The starship will have to be very large to bring all the crew and supplies for such a long mission, so let’s make it the size of large ocean liner. Although we don’t know what technology we will have to drive the starship we can calculate how much kinetic energy it must have for such a journey. A large cruise ship has a mass of 60 million kg (6 x 107 kg). The speed of light is v = 3 x 108 m/s. The starship must travel with a velocity one-tenth the speed of light to get there in less than 50 years. a) How much kinetic energy this starship have in order to make the trip at that speed?

Explanation / Answer

c = speed of light = 3 x 108

v = speed of spaceship = 3 x 107 m/s

m = mass of spaceship = 6 x 107 kg

kinetic energy is given as

KE = mc2 (1/sqrt(1 - (v/c)2) - 1)

KE = (6 x 107) (3 x 108)2 (1/sqrt(1 - (0.1)2) - 1)

KE = 2.72 x 1022 J

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