4.6: Free Body Diagrams
Free body diagrams: MAKE’EM.
What is an FBD? Very simple – it’s a diagram in which you denote all the forces acting on a body. You may think to yourself “well, I’m a total badass, so I can just write out all the forces and add them up.” This is technically possible, but a good way to get confused. With an FBD you can look at an object, think for a sec, then figure out what’s going on.
The book then goes through three important things, which I’ll simplify here. I’ve combined 1 and 2 since I think they make more sense as one idea.
1 and 2) At the beginning, decide what body you’re referring to and then list ONLY the forces which are exerted on that body.
Obvious, but important. If you’re making an FBD of a person (you) who just got punched, the forces you care about are ONLY those of the person getting punched. Your face is delivering force back at that fast, but that isn’t relevant to the FBD of you as you get punched.
It’s an easy mistake to make. If you’re making the FBD of yourself getting punched in the face, you may be tempted to write “Force of face on fist” at the front of the face. However, that force is acting on the fist, not your face. If that force were present in the FBD of your face, your face would move forward when punched. As we all know, that only happens in old episodes of Star Trek.
3) The sense in which the body is “Free” is that we’ve extracted it from its surroundings. I’m currently sitting on a couch at equilibrium. If you drew an FBD of my ass, there’d be the downward force of gravity, the downward force of my upper body, clothes, and cheetoh crumbs pushing down on my ass, and the equivalent upward force of couch-on-ass. In the FBD, you don’t show the upper body or the couch. Because they are not the body in question. You would draw my ass, then hang the following vectors on it: 1) Torso on ass, 2) Gravity on ass, 3) Couch on ass.
The first two point down, the second points up.
The book then shows some samples, which I don’t loooove. For example (a), which depicts a runner springing off of a step is a lot more scrutable after we learn about energy. Physically, it’s easier to think about that situation like this: The woman pushes on the step, which causes it to bend but not break. Then it bends back due to internal forces, at which point she detaches from the step.
But, I’m really just grousing about idealizations, which are inevitable.
Next stop: Interesting or difficult problems in Chapter 4