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

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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 N12 N Resultant force = = 7 N

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

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Two forces at any angle 8 N 5 N N 5 N 30 0 Resultant R Using cosine rule : a 2 = b 2 + c 2 – 2 b c cos A R 2 = – cos 150 R = 12.6 N Use sine rule to find : Giving: sin = =

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

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

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