How much energy is required to accelerate a spaceship with a rest mass of 134 me
ID: 1610542 • Letter: H
Question
How much energy is required to accelerate a spaceship with a rest mass of 134 metric tons to a speed of 0.490 c? Hints: In the acceleration process the energy we have is converted to the kinetic energy of the spaceship. The classical kinetic energy of an object is half of the mass multiplied by the square of the velocity. What is the relativistic form of the kinetic energy?
Every day our Earth receives 1.55×1022 J energy from the Sun. If we were able to use 0.85 percent of this energy to accelerate spaceships, then how many missions would be possible in one year?
Explanation / Answer
A)
given
m = 134 mtric ton
= 1.34*10^5 kg
v = 0.49*c
KE_relativistic = mo*c^2/sqrt(1 - (v/c)^2) - mo*c^2
= mo*c^2*(1/sqrt(1 - 0.49^2) - 1)
= 0.14715*mo*c^2
= 0.14715*1.34*10^5*(3*10^8)^2
= 1.77*10^21 J
B) Energy received by the earth from the sun in one year, E = 365*1.55*10^22
= 5.66*10^24
no of spaceships that can be accelerated, N = 5.66*10^24/(1.77*10^21)
= 3.20*10^3
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