What formula can be used to determine the efficiency of a machine with an input of 100J and an output of 30J?

The efficiency of a machine is calculated to assess how well it converts input energy into useful output energy. The formula that accurately represents this relationship is given by the ratio of output energy to input energy, multiplied by 100% to express it as a percentage.

In this case, with an input of 100 joules (E_in) and an output of 30 joules (E_out), the efficiency can be determined using the formula:

η = (E_out / E_in) × 100%

This means you would take the output energy (30 J), divide it by the input energy (100 J), and then multiply by 100 to convert the fraction into a percentage. Thus, this calculation provides a clear measure of how efficiently the machine operates; specifically, it indicates what percentage of the input energy is successfully converted into output.

The other formulas misrepresent the relationship between input and output energy. Therefore, the correct approach is to directly compare the output to the input, which is precisely what the selected formula accomplishes.