Definition of the Erg

In the book's glossary, the definition of the erg is stated as "a small metric unit of energy in the centimeter-gram-second (CGS) system of units, amounting to the work required to lift 1 gram of mass 1 centimeter above the Earth's surface." The latter part of this statement is off by a factor of 980. Consider Newton's second law relating force (F) to acceleration (a), such that (F = ma), where m is the mass.

On the surface of the Earth, the acceleration of gravity (g) is equal to 980 cm/s/s in CGS units. The energy or work (W) required to to lift a mass (m) to some height (h) above the Earth's surface is calculable by integrating the gravitational force over the displacement. Near the Earth's surface, the force can be regarded as a constant (F = mg), so that the work becomes (W = mgh). Solving for the mass yields (m = W/gh). Setting (W = 1 erg), (h = 1 cm), and (g = 980 cm/s/s), the mass is computed to be (m = 1/980 gm) or (m = 1.02 milligrams). From these considerations, the work involved in lifting a mosquitito to a height of 1 cm comes close to being an erg's worth of energy.