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Mechanics

Equilibrium of Forces

Components of a Force

Force is a vector quantity. This means that it has its full effect in a particular direction but that it also has reduced effects in other directions.

The effect of a force in a direction not along its own line of action is called a component of the force.

The process of finding the magnitudes of the components of a force is called resolving the force into its components.

Resolving a force into vertical and horizontal components

The force, , in the diagram can be considered to be the sum of two forces as shown below. These forces are the vertical and horizontal components of .

The magnitude of the vertical component of is given by

Fv = Fcosa

The magnitude of the horizontal component of is given by

Fh = Fcosq

The magnitude of the component of a force in a direction at 90° to its own line of action is therefore always equal to zero. This is why it is often useful to resolve a force into its vertical and horizontal components: these two components can then be considered as two independent forces.

 

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