Editing A bug in my high school physics intuition

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== "Answer 1 is also correct" ==
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== "Answer 1 is correct" ==
  
 
Wait, wait, wait. Answer 1 didn't say anything about work being force times time. You can't just substitute some other argument with the same conclusion. What's wrong with the reference frame argument? Nothing. It just doesn't apply to the bicycle problem we just thought about. If you're cruising along at 1 m/s, then when we shift to the reference frame in which you're stationary, it doesn't look at all the same as when you were going 0 m/s. The ground is now moving backwards underneath you at 1 m/s!
 
Wait, wait, wait. Answer 1 didn't say anything about work being force times time. You can't just substitute some other argument with the same conclusion. What's wrong with the reference frame argument? Nothing. It just doesn't apply to the bicycle problem we just thought about. If you're cruising along at 1 m/s, then when we shift to the reference frame in which you're stationary, it doesn't look at all the same as when you were going 0 m/s. The ground is now moving backwards underneath you at 1 m/s!
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If you're in the rocket, then the argument in Answer 1 is completely valid. Rocket ships are not the same as bicycles! To power a bicycle, you have to throw the Earth backwards relative to you however fast you want to go. The faster you want to go, the faster you have to throw the Earth. But to power a rocket ship, you just have to throw something backwards relative to you.
 
If you're in the rocket, then the argument in Answer 1 is completely valid. Rocket ships are not the same as bicycles! To power a bicycle, you have to throw the Earth backwards relative to you however fast you want to go. The faster you want to go, the faster you have to throw the Earth. But to power a rocket ship, you just have to throw something backwards relative to you.
  
== The thrilling conlusion ==
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So how am I going to update my intuition so that I'm less likely to make the same mistake in the future? By remembering that you can't just "apply a force" to something. You have to push off against something else. I don't think I could have been confused by Answers 1 and 2, or thought of the wrong one, if I'd kept in mind the thing you push against.
  
So how am I going to update my intuition so that I'm less likely to make the same mistake in the future? By remembering that you can't just "apply a force" to something. You have to push off against something else. I don't think I could have been confused by Answers 1 and 2, or thought of the wrong one, if I'd kept in mind the thing you push against. Another way to say it is that even though the total amount of work done is independent of reference frame, what that work is done '''on''' is not, so you have to keep track of everything that gets worked on.
 
  
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== Epilogue: what's right about Answer 1′? ==
 
== Epilogue: what's right about Answer 1′? ==
  
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As expected, the work depends on more than the impulse. It also depends on the ''difference'' between their speeds and on how much their speeds change (or equivalently, on their masses). Those things are agreed on by people in different reference frames (let's ignore relativistic speeds for now). So even though the amount of work you do ''on a given object'' depends on the reference frame, the total work done by exerting a fixed amount of impulse is independent of reference frame. Whew! It [[#"It depends on your reference frame"|would have been crazy if that weren't true]].
 
As expected, the work depends on more than the impulse. It also depends on the ''difference'' between their speeds and on how much their speeds change (or equivalently, on their masses). Those things are agreed on by people in different reference frames (let's ignore relativistic speeds for now). So even though the amount of work you do ''on a given object'' depends on the reference frame, the total work done by exerting a fixed amount of impulse is independent of reference frame. Whew! It [[#"It depends on your reference frame"|would have been crazy if that weren't true]].
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