Question

Suppose that the starship Enterprise from Star Trek has a mass of 8.0 × 107 kg, about the same as the Queen Elizabeth 2. Suppose that it was moving at half the speed of light. Read its G off of the graph in figure l on p. 76, and use this to compute its energy. Compare with the total energy content of the world’s nuclear arsenals, which is about 1021 J.

Answer 1

Answer on question #53485, Physics / Relativity

Question Suppose that the starship Enterprise from Star Trek has a mass of $8.0\times 10^{7}$ kg, about the same as the Queen Elizabeth 2. Suppose that it was moving at half the speed of light. Read its G o of the graph in gure l on p. 76, and use this to compute its energy. Compare with the total energy content of the worlds nuclear arsenals, which is about $10^{21}$ J.

Solution Let us find gamma factor

$\gamma=\frac{1}{\sqrt{1-v^{2}/c^{2}}}=\frac{1}{\sqrt{1-0.5^{2}}}\approx 1.1547$

Total energy of the starship is

$E=\gamma mc^{2}=1.1547\cdot 8.0\times 10^{7}\cdot(3\cdot 10^{8})^{2}\approx 8.3\cdot 10^{24}\,J$

Thats much bigger, then worlds nuclear arsenals.

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