2.5 Freely Falling Bodies
This section’s pretty straightforward, but introduces a symbol you’ll use a lot: g.
g is usually pronounced “little gee” since there is the more important Big G, which we’ll get to when we talk about force.
Little g isn’t a fundamental constant of the universe – it’s the average acceleration something will experience if you drop it close to the surface of the Earth. Later, we’ll understand this through more basic principles. For now, think of it way: in your equations that contain an a for acceleration, if they deal with freely falling bodies, you can change a to g.
g is usually given as 9.8 meters per second per second. You’ll note the units are the same as acceleration, because little g is just a particular rate of acceleration that we humans care about.
For convenience, unless your teacher is anal about these things, you’re better off just saying g=10. It’ll save time on your calculations, and won’t make you any less intelligent. Remember, “9.8″ is bullshitty too. You’ll have a slightly different lower little g on Mount Everest than you will near the Dead Sea. We’ll get more into the specifics later, but here’s a simple way to think about it: You know if you drop something in space that it experiences almost no gravity. So, in space, little g=~0. It seems reasonable therefore to suppose that as you go higher up, little g will get lower, and this is indeed the case.
There are two other good takeaway facts here that are simple but important:
1) Little g itself is always positive. Let me be clear here, because I think the book might be a tad confusing: This DOES NOT mean you never put a minus sign in front of g. In fact, you often do. It means the value of g is 9.8 m/s^2, NOT -9.8 m/s^2. Students often screw this up because they know gravity usually “points down.” The way we handle that, by convention, is by writing “-g” for the acceleration. That keeps everything nice and clear.
2) The quadratic formula is your friend. If you don’t have it memorized, you should. It’s pretty simple, and you’ll need it any time you encounter a quadratic polynomial that doesn’t have obvious solutions. This is physics, not pure math, so your solutions are not going to have pretty answers unless the professor is being nice to you. So, you’re going to want the quadratic formula. If you don’t already know how to use it, learn.
Since this is not pure math, you should also be aware that you can just throw out answers to the quadratic formula that don’t make any sense. Because you’re dealing with quadratic roots, you’ll always get two answers. Sometimes you won’t understand why, and then later it’ll turn out the math is telling you something you didn’t realize. But, often, it’s just giving you answers that don’t make physical sense. Remember, the math is just a way to solve equations that are similar to reality – it doesn’t mean all answers are equal. If your math tells you the solution occurred at t=20 and t=-10, and the question doesn’t involve a time machine, you can be pretty certain t=20 is the correct solution.