6 Physics and MeasurementP1.15(a)This is incorrect since the units of axare ms22, while the units of vare ms.(b)This is correct since the units of yare m, and coskxafis dimensionless if kis in m−1.*P1.16(a)aFm∝∑or akFm=∑represents the proportionality of acceleration to resultant force andthe inverse proportionality of acceleration to mass. If khas no dimensions, we haveFm=, LT1FM2=, FMLT2=⋅.(b)In units, Tkg ms⋅=⋅, so 11newtonkg m s2=⋅.P1.17Inserting the proper units for everything except G,kg mskgm2LNMOQP=G22.Multiply both sides by m2and divide by kg2; the units of Gare mkg s32⋅.Section 1.5Conversion of Units*P1.18
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International System of Units, United States customary units, Conversion of units, Metre