Resultant of two forces

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

2. 4 N 7 N 5 N 12 N 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 Resultant force = 7 + 4 = 11 N Resultant force = 12 - 5 = 7 N

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

4. 5 N Resultant R 5 N  300 300 8 N 8 N Two forces at any angle 1500 a2 = b2 + c2 – 2b c cos A Using cosine rule : R2 = 82 + 52 – 28 5 cos 150 R = 12.6 N Use sine rule to find : Giving: sin  = 0.198712  = 11.50

5. 15 N Resultant 15 N 130°  50° 130° 25 N 25 N Example a2 = b2 + c2 – 2b c cos A Using cosine rule : R2 = 252 + 152 – 225 15 cos 50 R = 19.2 N Use sine rule to find : Giving: sin  = 0.5991  = 36.8°

6. 5 N 5 N Resultant 500 50° 8 N 8 N Example Find the magnitude of the resultant of the forces shown in the sketch, and the angle it make with the larger force.  130° By the cosine rule : R2 = 82 + 52 – 2 x 8 x 5 x cos 1300 Gives R = 11.9 N By the sine rule : Gives  = 18.80