a 2000kg ship initially at rest in an inertial system is accelerated along a str

Question

a 2000kg ship initially at rest in an inertial system is accelerated along a straight line for (3.16E7 seconds) by means of a photon rocket of 300MW power. If this is accomplised using a series of He-Ne lasers with wavelength=633 nm,

b) what is the speed of the spaceship after one year?
c)what distance does it travel
d) what fraction of energy released is in the kinetic energy of the spaceship
e) what is the wavelength of light observed in the initial inertial reference frame after 1 year?
(doppler effect)

Explanation / Answer

(b) The total momentum of the photons emitted by the rocket is p = E / c = Pt / c This will be the final momentum of the rocket, p = (m - Dm)v where m = 2000 kg is the initial mass and v is the velocity. Solving for v, v = p / (m - Dm) = Pt / (m - Dm)c = (300 x 106 W)(3.1 x 107 s) / [(2000 kg - 0.1033 kg)(3 x 108 m/s)] = 15,500 m/s Note that the rocket is still nonrelativistic since b = v/c = (15,500 m/s) / (3 x 108 m/s) = 5.167 x 10-5

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