Question

The S.I. unit of energy is the joule, J. 1 J = 1 kg·m2/s2. Another energy unit, the erg, was once in widespread use. 1 erg = 1 g·cm2/s2. Calculate the number of ergs in 1 J, showing all your work.

Answer 1

To convert joules to ergs, we change the units of kilograms to grams and meters to centimeters, revealing that 1 joule is equivalent to 10^7 ergs.

Step-by-step explanation:

The objective is to calculate the number of ergs in 1 joule (J). As stated, 1 J = 1 kg·m²/s² and 1 erg = 1 g·cm²/s². To convert joules to ergs, we need to express a joule in terms of grams and centimeters.

First, we convert kilograms to grams and meters to centimeters:

1 kilogram = 1000 grams1 meter = 100 centimeters

Therefore, 1 J = (1 kg)(100² cm²)/s² = (1000 g)(100² cm²)/s².

Now calculate the number of cm²:

1 J = 1000 g × 10000 cm²/s² = 10·· g·cm²/s².

So, 1 joule is equivalent to 10· ergs.