Research ArticleNo Access

The Rocket Equation and that Minus Sign: An Avoidable Pitfall in the Language of Physics

Defence Science and Technology Group, CEWD, 205 Labs, P.O. Box 1500, Edinburgh SA 5111, Australia

E-mail Address: don.koks@dst.defence.gov.au

https://doi.org/10.1142/S2661339522500093Cited by:0 (Source: Crossref)

Abstract

Derivations of the rocket equation that use a momentum-conservation argument are notorious for often encountering a problem that would produce an incorrect sign in their result, if it were not “fixed” in various ad hoc ways that can always be shown to be mathematically invalid. Here, we show that the problem of the unwanted minus sign typically (perhaps always) results from a misunderstanding of the language of calculus. When one adheres to a simple and fundamental rule of calculus notation, the derivation of the rocket equation becomes straightforward, and no unwanted minus sign appears.

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References

1. R. T. Weidner and R. L. Sells, Elementary Classical Physics, 2nd edn, Vol. 1, Section 5-8 (Allyn and Bacon, Inc., 1973). Google Scholar
2. P. A. Tipler, Physics, 2nd edn, Section 8-8 (Worth Publishers, Inc., 1982). Google Scholar
3. W. Chester, Mechanics (George Allen & Unwin, 1979). Google Scholar
4. B. P. Cowan, Classical Mechanics (Routledge & Kegan Paul, 1984). Crossref, Google Scholar
5. D. C. Giancoli, Physics for Scientists & Engineers with Modern Physics, 4th edn (Pearson, 2014). Google Scholar
6. K. W. Ford, Classical and Modern Physics (Xerox College Publishing, 1972). Google Scholar
7. D. Halliday and R. Resnick, Fundamentals of Physics (Wiley International Edition, 1974). Google Scholar
8. D. Halliday, R. Resnick and J. Walker, Fundamentals of Physics (Extended), 9th edn (Wiley, 2010). Google Scholar
9. J. B. Marion and W. F. Hornyak, Physics for Science and Engineering (CBS College Publishing, 1982). Google Scholar
10. F. J. Bueche, Introduction to Physics for Scientists and Engineers, 4th edn (McGraw-Hill, 1986). Google Scholar
11. W. Benenson, J. W. Harris, H. Stocker and H. Lutz (eds.), Handbook of Physics (Springer, 2002). Crossref, Google Scholar
12. C. Kittel et al., Mechanics, Berkeley Physics Course Volume 1, 2nd edn (McGraw-Hill Book Company, 1973). Google Scholar
13. H. C. Ohanian, Physics, 2nd edn (W.W. Norton & Co. 1989). Google Scholar
14. M. J. Pinheiro, Some remarks about variable mass systems, Eur. J. Phys. 25, L5 (2004). Crossref, Google Scholar
15. A. A. Blagonravov (Editor-in-Chief), Collected Works of K.E. Tsiolkovskiy. Vol. II — Reactive Flying Machines (NASA, 1954). Google Scholar
16. Tsiolkovsky Rocket Equation, https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation, Retrieved April 2022. Google Scholar
17. The Rocket Equation, https://www.narom.no/undervisningsressurser/sarepta/rocket-theory/rocket-engines/the-rocket-equation, Retrieved April 2022. Google Scholar
18. Ideal Rocket Equation, https://www.grc.nasa.gov/www/k-12/rocket/rktpow.html, Retrieved April 2022. Google Scholar
19. The Rocket Equation, https://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node103.html, Retrieved April 2022. Google Scholar
20. P. Blanco, Maximum momentum and kinetic energy of a rocket, The Phys. Teach. 58, 534 (2020). Crossref, Google Scholar