In physics equations, the numbers almost always have units attached to them (lengths are in meters, accelerations are in meters per second squared, and so on). When you either do a units conversion or the rearrangement of an equation to solve for an unknown, you should treat the units just like the numbers in the equations: you move them around by associative laws, dividing them out of both sides of the equation, cross-multiply, etc.
It takes a lot more patience and effort to carry out the algebra with both the numbers and the units; hence, many students don't... often paying the price in lost points on a test due to careless mistakes. Here is an example: a car decelerates uniformly from 25 kilometers per hour to rest over a distance of 30 m; what is its negative acceleration value in m/s2? You are taught to convert everything to SI units before plugging values into an equation but you might forget. Here is what you should do to catch your mistakes:
vf = 0 m/s, x-xo = 30 m. vf2 = vo2 + 2a(x-xo) 0 (m/s)2 = 252(km/h)2 + 2a(30 m) -625 km2/h2 = (60 m)a a = -10.4 km2/mh2 (not the correct ending units). |
Another very common example: forgetting to square a number in an equation. Suppose a 30 g ball is rolling at 2.0 m/s on a table 0.45 m above the floor; if the ball rolls off the edge how much kinetic energy will it have just before it strikes the floor, ignoring air friction? Here are the algebraic steps with one mistake, but the units don't agree at the end such that you know there was a mistake made somewhere:
1/2 (0.030 kg)(2.0 m/s) + (0.030 kg)(9.8 m/s2)(0.45 m) = KEf + 0 0.030 (kg m)/s + 0.132 (kg m2)/s2 = KEf hmmm... I can't add terms that don't have the same units. |