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Roy E.
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Summary of contribution activity by day
Longest streak: 17 days
Roy E.
Roy E. joined Socratic
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karma
Activity
178 Answers
74 Edits
3 Asked
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@roy-e Roy E. updated the answer to What is the integral of #int ln x / x dx #? .
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@roy-e Roy E. wrote an answer to What is the integral of #int ln x / x dx #? .
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@roy-e Roy E. wrote an answer to How does calculus relate to physics? .
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@roy-e Roy E. wrote an answer to Can the ozone layer repair itself? .
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@roy-e Roy E. wrote an answer to How do you find the area of the parallelogram with vertices: p(0,0,0), q(-5,0,4), r(-5,1,2), s(-10,1,6)? .
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@roy-e Roy E. commented Adam: I think all the modulus stuff is misleading and have never met it before. In any particular answer you wouldn't need it and indeed it would be confusing* or even wrong. I think the mark scheme writer was trying to use a short-hand to show what answers were acceptable. The trap, if any, is muddling the signs on δm. It might seem "natural" to draw the diagram with "BEFORE" showing "m" and "AFTER" showing "m-δm" (or equivalently, "BEFORE" showing "m" and "AFTER" showing "m-δm", with the implication that δm is a positive quantity. However, you would then have to remember that dm/dt is the limit not of δm/δt but rather -δm/δt: dm/dt is negative however you approach the sign convention. That's why I prefer the convention in my diagram. It's not confusing, IMHO, provided you have at the back of your mind that δm is a negative number, so that m+δm is slightly smaller than m, -δm is the mass of exhaust gas, and δm/δt tends to dm/dt.
Small point: I was brought up to show forces with simple arrows, velocities with filled triangular arrowheads (doubled for acceleration), and impulses (and momentums) with open triangular arrowheads. Then to construct a careful "BEFORE" and "AFTER" diagram showing a SYSTEM before and after an IMPULSE. So BEFORE+IMPULSE=AFTER. It's easy to get muddled or baffled by rocket questions. The idea of a system helps, because Newton's Law applies to a collection of particles, even if they change shape (as here, into two parts: burnt fuel and unused fuel). (It's not useful to consider, say, the rocket casing as a system, as you know nothing about the innards and the pressure etc.)The subtle thing with rocket algebra that this is all instantaneous: in the next instant the system is slightly different (less mass). In GCSE mechanics (e.g. colliding snooker balls) this doesn't happen.
*PS: if the text book or your teacher is trying to get you to use the || stuff and then "explain" the change of sign I'd get a new book or teacher, or patiently explain how to do it easily. If concept of an "instantaneous frame of reference" worries you (e.g. the velocity at time t being zero) just add an mv on both sides of the equation, then cancel them! on Can somebody please explain to me the signs used for ∂m in this solution, with regard to the 'u'. I do not understand why '-|∂m|' is used, and then how it is later changed to a '+∂m'? Thanks in advance! - Show more activity
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