Lessons · Engineering · the free-body diagram
The free-body diagram: the body alone, and every force on it
Cut the body free of everything touching it, and at every cut draw the force the removed thing was putting on the body. Nothing else goes on the page.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
Every statics mistake that reaches a site started as a force left off a sketch, or a force drawn on the wrong body. The diagram is the calculation; the equations only read it back.
How to think about it
Draw the body with nothing attached. Weight at its centre, straight down. Then walk round its edge: wherever something was touching, draw what that thing did to the body. Friction last, along the surface, opposing the slide.
Worked example
1. Draw the crate alone, nothing elseThe floor, the rope, the person pushing: gone. Only the crate.
2. W = m g, straight down through the centreGravity acts everywhere in the body; one arrow at the centre of gravity stands for all of it.
3. N from the floor, perpendicular to it, upThe floor was touching the bottom face, so the floor's push goes there.
4. P, the push, 40 N to the rightThe hand was touching the side. Its force goes on the crate, where the hand was.
5. f, friction, along the floor, to the leftThe floor can also resist sliding. It acts along the surface, against the direction the crate would move.
Your turn
A lamp hangs from one cord. Write the two forces on its diagram.
W down at the centre; up along the cord
Solve one, graded on the server
The trap
Drawing a force the body puts on something else. The crate pushes down on the floor, and that arrow belongs on the floor's diagram, never the crate's. A diagram with it on both is a diagram of nothing.