Chapter 11: Torque

11.4 Problem solving

The process for solving problems with torque is nearly identical to the process for solving problems with force (see section 9.4). However, instead of a free body diagram—which represents the system as a single point—we’ll use an extended free body diagram (E-FBD); with torque, the location where the force is applied is important.

Example

A plank of wood is resting on two sawhorses. A cat is sitting on the plank between the two sawhorses, closer to one than the other. The plank has a uniform mass distribution. Draw a free body diagram and an extended free body diagram for the plank of wood.

The plank has four forces acting on it: a normal force of each sawhorse pushing directly up on the plank, the weight of the plank pulling down, and the weight of the cat pushing down.

For the free body diagram, the plank is represented as a single point with the forces acting on it:

A dot has four arrows extending from it. Two arrows, slightly offset from one another, point directly up; one is labeled F superscript N subscript 1 and the other is labeled F superscript N subscript 2. The other two arrows, slightly offset from one another, point directly down; one is labeled F superscript G subscript c, and the other is labeled F superscript G subscript w.
Free body diagram for the plank

For the extended free body diagram, we show where the forces are exerted on the plank:

A long, narrow rectangle has four arrows extending from it. A short distance in from the left end of the rectangle is an arrow pointing straight up, labeled F superscript N subscript 1. A little bit farther to the right is an arrow pointing straight down, labeled F superscript G subscript c. Midway along the rectangle is an arrow pointing straight down labeled F superscript G subscript w. A short distance in from the right end is an arrow pointing straight up, labeled F superscript N subscript 2.
Extended free body diagram for the plank

Note the weight of the plank \(\left(F^G_w\right)\) is located at the center of the plank. Since the mass of the wood is uniformly distributed, the center of mass is in the center of the plank.