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Spacecraft Speed Change in 1 Week with 0.09-N Thrust
Chapter 4, Problem 90(choose chapter or problem)
Questions & Answers
QUESTION: The mass of a spacecraft is about 480 kg. An engine designed to increase the speed of the spacecraft while in outer space provides 0.09-N thrust at maximum power. By how much does the engine cause the craft’s speed to change in 1 week of running at maximum power? Describe any assumptions you made.
ANSWER:Step 1 of 2
Consider the following provided data.
The spacecraft's thrust is \(T = 0.09\;N\), and its mass is \(\rm{m} = 480\;{\rm{kg}}\).
The time under consideration is t = 1 week, which translates to \(\left( {7 \times 24 \times 60 \times 60} \right)\;{\rm{s}}\).
When applying Newton's 2nd Law to the spacecraft's motion with the given thrust, we make a few assumptions.
First, we assume that no other external forces are acting on the spacecraft.
Second, we suppose that the thrust is applied uniformly.
Finally, we imagine the spacecraft is moving along a straight trajectory.
Under these conditions, we have T = ma.
Solving for acceleration gives us a = T/m.
Plugging in our given values, we have:
\(a= \frac{{0.09\;{\rm{N}}}}{{450\,{\rm{kg}}}} \)
\(a= 187.5 \times {10^{ - 6}}\;{\rm{m/}}{{\rm{s}}^2}\).
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Spacecraft Speed Change in 1 Week with 0.09-N Thrust
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Discover the impact of a 0.09-N thrust engine on a 480 kg spacecraft's speed during 1 week of maximum power operation. Uncover the assumptions involved in this space physics scenario.