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Further Note on the Motion of a Body Whose Mass is Changing

Published online by Cambridge University Press:  03 November 2016

Extract

The note on this subject published in the Gazette of July 1941 was written in the hope that it might clear away a difficulty which I have good reason to know many students and teachers of dynamics find, when confronted by a problem of changing mass, where it is not obvious which, if indeed either, of the equations M dV/dt = F or d (MV)/dt = F applies. Among letters previously received on the subject I have found it asserted that the latter equation is “fundamental” and that results not in conformity with it must be wrong. I showed by three simple examples of changing mass that it is possible for one or other of these equations to be true or for neither to be true, and hoped that readers would feel satisfied to form the equation of motion for any such case directly, by the simple process of equating the change of momentum in time δt to the impulse of the force producing the change. Could there be a simpler procedure? Unfortunately readers in general are not so easily satisfied, and I seem to have stimulated an ambition to produce an equation of motion “of quite general validity” applicable to all such cases.

Type
Research Article
Copyright
Copyright © Mathematical Association 1942

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References

page 165 of note * It has been represented to me that the words “ejects it vertically” are capable of the meaning that after ejection the smoke and gas are moving vertically. I agree; but inasmuch as this would require a mechanical device whereby an engine, itself moving with variable acceleration, would be able to impart to its smoke a velocity equal and opposite to that of the atmosphere, I need hardly say that this was not the meaning I intended. My meaning, as shown in my solution, is that the engine ejects the smoke and gas through a vertical chimney and therefore they possess the horizontal velocity of the engine.