Question

How much energy is required to accelerate a spaceship with a rest mass of 110 metric tons to a speed of 0.490 c?

Tries 0/20

Every day our Earth receives 1.55×10²² J energy from the Sun. If we were able to use 0.95 percent of this energy to accelerate spaceships, then how many missions would be possible in one year?

Answer 1

(a)

Energy required to accelerate the spaceship,

E = (-1)mc^2

Here, = 1 / sqrt [1 - (v/c)^2]

=   1 / sqrt[(1 - (0.490)^2] = 1.147

m = 110000 kg

E = 147 * 110000 * (3*10^8)^2

E = 1.456*10^21 J

(b)

Energy received per day = 1.55*10^22 J

energy received in a year = 365 *  1.55*10^22 J = 565.75*10^22 J

As  we were able to use 0.95 percent of this energy,

Eyear = (0.95 / 100) *  565.75*10^22 = 5.37*10^22 J

Eyear / Espaceship =  5.37*10^22 /  1.456*10^21

Eyear / Espaceship = 36.89 37

37 missions would be possible in one year.