Appendix B: Free Body Diagram

During school examinations (but rarely in the A-levels), you are often asked to draw free body diagrams (FBD). School teachers often impose many “requirements” in these drawings. Let’s go through these requirements now.

Consider the scenario of a crate on a rough floor being pushed by a finger with a constant force. And we are told that the crate is accelerating at a constant rate.

Obviously, the FBD must include all the external forces acting on the “free body” (the crate!), like the one shown below. Notice that in this FBD, the crate is treated like a point mass. And we must be mindful that the lengths of the arrows should convey the relative magnitudes of the forces. E.g. N and mg must be drawn the same length since there is no vertical acceleration, whereas F is drawn longer than f since there is rightward acceleration.

In many schools, the above is still deemed inadequate. Because A-levels problems often involve moments, so the lines of action of the forces are important too. As such, the points of application of the forces should be shown in the FBD, like the one below.

Notice that we no longer simplify the crate as a point mass. As an elongated body, mg is drawn exactly where it is supposed to act i.e. at the CG. For simplicity, let’s assume that the finger is nudging the crate at the middle, so the line of action of F also passes through the CG. This means that F and mg both exert zero moment about the CG. But f exerts a CW moment about the CG. This means that N must provide an ACW moment to keep the crate in rotational equilibrium. For this reason, you are expected to draw N (and thus f also) to be acting somewhere on the right of the CG.

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