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1.22 Omitted Forces

In reading texts and drawing sketches to solve problems, one must be on the guard against carelessness. One critically important error to avoid is omission of forces. The style of this writing is to avoid using F in favor of using ΣF. The summation sign reminds us to be sure to include ALL of the forces relevant to the physical situation. These are forces of gravity and forces that act on the boundary of the system. Students and (authors) who use "f" for forces tend to omit relevant forces more often than those who use ΣF.

Below left is a copy of Figure 1-8 as printed in Cengel and Boles. This sketch (as published)is incomplete. The figure clearly indicates forces that are "unbalanced." As drawn, these unbalanced forces cause the man and all of his apples to accelerate toward the bottom of the page. Obviously the authors do not intend this acceleration. They simply forgot to apply ΣF properly.

Below right is a correction of the text figure. The "omitted" forces are included. Centers of mass are indicated and the distributed gravity force is summed and located there as Fg. With forces balanced, acceleration is zero.

It is likely in the actuality this sketch models that atmospheric air surrounds the man and his apples. The sum of ambient atmospheric pressure forces of air acting on the man and apples is small and (for simplicity) not included.

Sketches should be done carefully.

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