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Question Number 126603 by Ar Brandon last updated on 22/Dec/20

$$\mathrm{If}\mathrm{there}\mathrm{is}\mathrm{a}\mathrm{positive}\mathrm{error}\mathrm{in}\mathrm{the}\mathrm{measurement}$$$$\mathrm{of}\mathrm{velocity}\mathrm{of}\mathrm{a}\mathrm{body},\mathrm{then}\mathrm{the}\mathrm{error}\mathrm{in}\mathrm{the}\mathrm{measure}-$$$$\mathrm{ment}\mathrm{of}\mathrm{kinetic}\mathrm{energy}\mathrm{is}$$

Answered by Olaf last updated on 22/Dec/20

$$\mathrm{E}=\frac{1}{2}{mv}^2$$$$\mathrm{lnE}=\ln \frac{1}{2}+\ln m+2\ln v$$$$\frac{d\mathrm{E}}{\mathrm{E}}=2\frac{dv}{v}$$$$\frac{\mathrm{\Delta }\mathrm{E}}{\mathrm{E}}=2\frac{\mathrm{\Delta }v}{v}$$$$\mathrm{The}\mathrm{relative}\mathrm{error}\mathrm{in}\mathrm{the}\mathrm{measurement}$$$$\mathrm{of}\mathrm{the}\mathrm{kinetic}\mathrm{energy}\mathrm{is}\mathrm{the}\mathrm{double}\mathrm{of}$$$$\mathrm{the}\mathrm{relative}\mathrm{error}\mathrm{in}\mathrm{the}\mathrm{measurement}$$$$\mathrm{of}\mathrm{the}\mathrm{velocity}$$

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