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Mechanics

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For equilibrium, all the horizontal components of the force must cancel one another, and all the vertical components must cancel one another as well. This condition is necessary for equilibrium, but not sufficient. For example, if a person stands a book up on a table and pushes on the book equally hard with one hand in one direction and with the other hand in the other direction, the book will remain motionless if the personís hands are opposite each other. (The net result is that the book is being squeezed). If, however, one hand is near the top of the book and the other hand near the bottom, a torque is produced, and the book will fall on its side. For equilibrium to exist it is also necessary that the sum of the torques about any axis be zero.

A torque is the product of a force and the perpendicular distance to a turning axis. When a force is applied to a heavy door to open it, the force is exerted perpendicularly to the door and at the greatest distance from the hinges. Thus, a maximum torque is created. If the door were shoved with the same force at a point halfway between handle and hinge, the torque would be only half of its previous magnitude. If the force were applied parallel to the door (that is, edge on), the torque would be zero. For an object to be in equilibrium, the clockwise torques about any axis must be canceled by the counterclockwise torques about that axis. Therefore, one could prove that if the torques cancel for any particular axis, they cancel for all axes.