Physics 101 problem

Question

The following formula estimates an average person’s lung

capacity V (in liters, where 1 L = 103 cm3): V = 4.1H - 0.018A - 2.7,

where H and A are the person’s height (in meters) and age (in years), respectively. In this formula, what are the units of the numbers 4.1, 0.018, and 2.7?

Answer 1

All equations must be "dimensionally homogeneous." This means that all terms in an equation have to have the same units. Analogously, you can't add apples and oranges, only apples and apples. The problem tells us that for this equation, our units are liters. Since 2.7 is alone, it has to be in liters. That was easy. Up next, since 4.1 multiplied by meters must give liters, that means its units must be [L/m]. (Checking the work, [L/m] * [m] = [L]. Good to go!)

The same reasoning can be used for the third term.

Hope this helps!