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Answer :
Final answer:
By considering the force applied by the ion drive engine and the necessary rest periods to avoid thermal breakdown, we can calculate the number of 'bursts' needed and the total time it would take for the engine to accelerate a spacecraft from 500,000 kg m/s to 900,000 kg m/s.
Explanation:
To answer this question, we need to consider both the consistent force from the ion drive engine and the time periods during which it is allowed to function to prevent thermal breakdown. The force exerted by the ion engine is given as 122 N, and the amount of time it can work continuously before needing a rest period is 0.125 seconds. Now, this force will work to change the momentum of the spacecraft. The change in momentum per burst (or impulse) is simply force multiplied by time (Impulse = Force x Time).
The total change in momentum required to get the spacecraft to reach 900,000 kg m/s from the initial 500,000 kg m/s (5000 kg * 100 m/s) is 800,000 kg m/s. To find the number of bursts required, divide the total needed momentum change by the momentum change per burst. Once you have the number of bursts required, remember that each burst requires 0.125 seconds of work time and 12 seconds of rest time. Multiplying the total bursts by the total time per burst will give you the total time necessary for the engine to achieve the needed momentum change.
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