law of parallelogram of forces
If two forces, acting at a point, are represented in magnitude and direction by the two sides of a parallelogram drawn from one of its angular points, their resultant is represented both in magnitude and direction by the diagonal of the parallelogram passing through that angular point.
Magnitude and Direction of the Resultant of Two Forces:
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Let OA and OB represent the forces P and Q acting at a point O and inclined to each other at an angle α then the resultant R and direction ‘θ’ (shown in figure) will be given by
and Case (i): If P = Q, then tanθ = tan (α/2) ⇒ θ = α/2
Case (ii): If the forces act at right angles, so that |
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Example: If the line of action of the resultant of two forces P and Q divides the angle between them in the ratio 1 : 2 then the magnitude of resultant is
(A) 
(C)
Detail Explanation : Let 3θ be the angle between the forces P and Q. This means that the resultant make an angle θ with the direction of P and angle 2θ with the direction of Q
Therefore,
⇒ 
Also,
⇒ 
From (1) and (2), we get R = 
REDETAIL EXPLANATION OF A FORCE
A force may be resolved into two components in an infinite number of ways. The most important case of the reDetail Explanation of forces occurs when we resolve a force into two components at right angles to one another.
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Components of a Force in Two Directions: Let F be the given force represented in magnitude and direction by OC and let the directions of the two components be along OL and OM. Also ∠COL = α and ∠COM = β. Then
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Triangle of Forces:
If three forces, acting at a point, are represented in magnitude and direction by the sides of a triangle, taken in order, they will be in equilibrium.
Remark:
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In the triangle of forces it must be carefully noted that the forces must be parallel to the sides of a triangle taken in order, i.e. taken the same way round.
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