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# Roy E.

Roy E. joined Socratic 1 year ago. Roy E. hasn't written a biography yet.

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• @roy-e Roy E.
3 months ago
• @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 Î´m. &nbsp;It might seem "natural" to draw the diagram with "BEFORE" showing "m" and "AFTER" showing "m-Î´m" (or equivalently, "BEFORE" showing "m" and "AFTER" showing "m-Î´m", with the implication that&nbsp;Î´m is a positive quantity.&nbsp; However, you would then have&nbsp;to remember that dm/dt is the limit not of&nbsp;Î´m/Î´t but rather -Î´m/Î´t: 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&nbsp;Î´m is a negative number, so that m+Î´m is slightly smaller than m, -Î´m is the mass of exhaust gas, and&nbsp;Î´m/Î´t tends to dm/dt.&nbsp;

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. &nbsp;If concept of an "instantaneous frame of reference" worries you (e.g. the &nbsp;velocity at time t being zero) just add an &nbsp;mv on both sides of the equation, then cancel them!
on Can somebody please explain to me the signs used for âˆ‚m in this solution, with regard to the 'u'. I do not understand why '-|âˆ‚m|' is used, and then how it is later changed to a '+âˆ‚m'? Thanks in advance!
3 months ago