A space barge pushes on a spaceship with a rest mass of 15,000 kg and accelerates it from a speed of 0.600c to a speed of 0.700c.How much work does the barge have to do to accomplish this? (c = 3.00 × 10⁸ m/s) A)1.35 × 10²⁰ J B)2.03 × 10²⁰ J C)2.70 × 10²⁰ J D)5.42 × 10²⁰ J E)8.78 × 10¹⁹ J

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Quizplus · Accepted Answer

The work done on the spaceship can be calculated using the relativistic work-energy theorem, which states that the work done is equal to the change in relativistic kinetic energy. The relativistic kinetic energy (K) is given by $K = (\gamma - 1)mc^2$, where $\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ is the Lorentz factor, $m$ is the rest mass, and $c$ is the speed of light. For the initial speed $v_i = 0.600c$, the initial Lorentz factor $\gamma_i$ is calculated using $v_i$, and for the final speed $v_f = 0.700c$, the final Lorentz factor $\gamma_f$ is calculated using $v_f$. The change in kinetic energy ($\Delta K$) is then $\Delta K = (\gamma_f - \gamma_i)mc^2$.Plugging in the given values and calculating gives a result in the range of $2.03 \times 10^{20}$ Joules, which corresponds to choice B.

A Space Barge Pushes on a Spaceship with a Rest