a. How much energy is required to accelerate a spaceship with a
rest mass of 115 metric tons to a speed of 0.489
c?
b. 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?
a) given
m = 115 metric ton
= 115000 kg
v = 0.489*c
we know,
relativistic kinetic energy = m*c^2*(1/sqrt(1 - (v/c)^2) -
1)
KE = 115000*(3*10^8)^2*(1/sqrt(1 - (0.489*c/c)^2) - 1)
= 1.515*10^21 J
so, Energy required = 1.515*10^21 J
b) Energy received from sun in one year =
365*1.55*10^22
= 5.6575*10^24
let N is the number mission possible in one year
0.85*5.6575*10^24 = N*1.515*10^21
==> N = 0.85*5.6575*10^24/(1.515*10^21)
= 3174 <<<<<<<<---------------------Answer
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