Many speculative plans for spaceships capable of interstellar travel have been d

Question

Many speculative plans for spaceships capable of interstellar travel have been developed over the years. Nearly all are powered by the fusion of light nuclei, one of a very few power sources capable of providing the incredibly large energies required. A typical design for a fusion-powered craft has a 1.2×10^6 kg ship brought up to a speed of 0.12c using using the energy from the fusion of 2/1H and 3/2He. Each fusion reaction produces a daughter nucleus and one free proton with a combined kinetic energy of 18 MeV; these high-speed particles are directed backward to create thrust.

Part A

What is the kinetic energy of the ship at the noted top speed? For the purposes of this problem you can do a nonrelativistic calculation.

K= ?

2 sig figs apropriate units

Part B

If we assume that 50% of the energy of the fusion reactions goes into the kinetic energy of the ship (a very generous assumption), how many fusion reactions are required to get the ship up to speed?

N = ?

2 sig figs

Part C

How many kilograms of 2/1H and 3/2He are required to produce the required number of reactions?

m2/1h,m3/2He = ? kg

2 sig figs seperated by comma

Explanation / Answer

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a)

K = 0.5 m v^2 = 0.5 * 1.2e6 * (0.12*3e8*0.12*3e8) = 7.776 x 10^20 = 7.8 x 10^20 J

b)

N = 2*(7.776e20)/(18e6*1.6e-19) = 5.4 x 10^32

c)

1H2:

m = 5.4e32*(2.0141017778) * 1.660538921e-27 = 1.8 x 10^6 Kg

2He3:

m = 5.4e32*(3.0160293191) * 1.660538921e-27 = 2.7 x 10^6 Kg

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