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Suppose we have a spaceship about the size of a typical ocean cruise ship today, which means it has a mass of about 120 million kilograms, a
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Suppose we have a spaceship about the size of a typical ocean cruise ship today, which means it has a mass of about 120 million kilograms, and we want to accelerate the ship to a speed of 12 % of the speed of light. Suppose you want to generate the energy to get it to cruising speed using matter-antimatter annihilation.
Part A. How much energy would be required? (Hint: You can find the answer simply by calculating the kinetic energy of the ship when it reaches its cruising speed; because 12 % of the speed of light is still small compared to the speed of light, you can use the formula that tell us that kinetic energy = 12mv2.) Express your answer using two significant figures.
Part B. How does your answer compare to total world energy use at present, which is about 5×1022 joules per year? How does your answer compare to total world energy use at present, which is about joules per year? EspaceshipEworldenergyuse∼1 EspaceshipEworldenergyuse∼105 EspaceshipEworldenergyuse∼1020
Part C. The typical cost of energy today is roughly 5¢ per 1 million joules. Using this price, how much would it cost to generate the energy needed by this spaceship? Express your answer using two significant figures.
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Physics
3 years
2021-07-30T13:14:13+00:00
2021-07-30T13:14:13+00:00 1 Answers
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Answer: A 7.8 ·10^22 J B 1.6 times C 3.9 ·10^15 $
Explanation: A : Speed of light c = 3.0·10^8 m/s, 0.12·c = 3.6·10^7 m/s
Mass is 120·10^6 kg . Change of kinetic energy
E = ½mv² = 0.5 · 120·10^6 kg · (3.6·10^7 m/s)² = 7.776·10^22 J
B exponent is same , 7.776 / 5 = 1,55 times of energy use of Earth in year.
C Energy is 7.776·10^22 J / 10^6 = 7.776·10^16 MJ
Price is 0.05 $ · 7.776·10^16 MJ = 3.888·10^15 $