Question 1.CA.3: Consistency of units When an object moves through air, the a...
Consistency of units When an object moves through air, the air exerts a force on it. (You notice this force when you put your hand out the window of a moving car.) The strength of the force, which we denote by F, is related to the speed υ of the object by the equation F = bυ², where b is a constant. In SI units (kg, m, s), the units of force are kg · m/s² and the units of speed are m/s. For the preceding equation to have consistent units (the same units on both sides of the equation), the units of b must be
A. kg/m.
B. kg · m/s.
C. kg/m².
To solve this problem, we start with the equation F = bυ².
For each symbol whose units we know (in this case, F and υ), we replace the symbol with those units. For example, we replace υ with (m/s). We obtain
\left(\frac{kg\cdot m}{s\cdot} \right)=b\left(\frac{m}{s} \right)\left(\frac{m}{s} \right). (Algebraically, units are treated like numbers.)
We now solve this equation for b. When we multiply both sides of the equation by s², the seconds (s) cancel. Also, one of the meter units (m) cancels. We obtain b = kg/m, so the correct answer is A.