# Resultant of two forces

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Resultant of two forces
Learning objectives Resultant of parallel forces Resultant of perpendicular forces Resultant two forces at any angle

Resultant of two forces
A resultant force is a single force which can replace a set of forces acting on an object. It has exactly the same effect on the object as the original set. Parallel forces 7 N 4 N Resultant force = = 11 N 5 N 12 N Resultant force = = 7 N

Resultant of Perpendicular forces
4 N Resultant = = 5 N Angle  = tan-1(3/4) = 36.90

Two forces at any angle a2 = b2 + c2 – 2b c cos A
Resultant R 5 N 8 N 5 N 300 1500 300 8 N Using cosine rule : a2 = b2 + c2 – 2b c cos A R2 = – 28 5 cos 150 R = 12.6 N Use sine rule to find : Giving: sin  =  = 11.50

Example a2 = b2 + c2 – 2b c cos A Using cosine rule :
130° 15 N 25 N 15 N Resultant 50° 130° 25 N Using cosine rule : a2 = b2 + c2 – 2b c cos A R2 = – 225 15 cos 50 R = 19.2 N Use sine rule to find : Giving: sin  =  = 36.8°

Example Find the magnitude of the resultant of the forces shown in the sketch, and the angle it make with the larger force. 8 N 500 5 N 5 N Resultant 130° 50° 8 N By the cosine rule : R2 = – 2 x 8 x 5 x cos 1300 Gives R = 11.9 N By the sine rule : Gives  = 18.80

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