Sunday, 18 March 2012

Equilibrium of Particles

Equilibrium equations for a particle: 
A particle is in equilibrium if the resultant of ALL forces acting on the particle is equal to zero

Equilibrium equations in component form: 
In a rectangular coordinate system the equilibrium equations can be represented by three scalar equations:

Triangle of Forces
When 3 coplanar forces acting at a point are in equilibrium, they can be represented in magnitude and direction by the adjacent sides of a triangle taken in order.
triangle of forces

Using the results from the previous example, the three forces acting on the 2 kg mass can be represented by a scale diagram.
triangle forces problem
Our starting point is the 20N force acting downwards. One force acts at 45 deg. to this line and the other at 60 deg. So to find the magnitude of the two forces, draw lines at these angles at each end of the 20N force. Where the lines cross gives a vertex of the triangle. Measuring the lengths of the lines from this to the ends of the 20N force line will give the magnitudes of the required forces.

Polygon of Forces
For equilibrium, forces are represented in magnitude and direct to form a polygon shape.
If a number of forces are acting at a point, then the missing side in the polygon represents the resultant force. Note the arrow direction on this force is in the opposite direction to the rest.
polygon of forces


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