Resultant of coplanar concurrent force system, Mechanical Engineering

Resultant of coplanar concurrent force system:

The resultant force, of given system of forces can be found out by the resolution method, which is discussed below:

Assume the forces be P1P2P3P4, and P5 acting at 'o'. Let OX and OY be the two perpendicular directions. Let the forces subtend angle a1, a2, a3, a4, and a5 with Ox respectively. Let R be the resultant and inclined at the angle with OX.

Resolved part of 'R' along OX = Sum of the resolved parts of P1, P2, P3, P4, P5 along OX.

16_Resultant of coplanar concurrent force system.png

That is

Resolve all the forces horizontally and find algebraic sum of all horizontal components

(which is ∑H)

1683_Resultant of coplanar concurrent force system1.png 

Resolve all the forces in vertical direction and find the algebraic sum of all the vertical components (that is, ∑V)

1808_Resultant of coplanar concurrent force system2.png 

The resultant R of given forces can be given by equation:

769_Resultant of coplanar concurrent force system3.png  407_Resultant of coplanar concurrent force system4.png 

And the resultant force will be inclined at the angle 'θ' with the horizontal, so that

                                                               tanθ = ∑V/∑H 

 

Posted Date: 10/16/2012 1:42:26 AM | Location : United States







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