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Replace the two parallel forces by single force:
Replace the two parallel forces acting on the control lever by a single equivalent force R.
Sol.: Since single equivalent force is resultant.
Let ΣH and ΣV be the horizontal and vertical component of the resultant. Resolving all the forces in horizontal direction
ΣH = 50 - 80 = -30N ...(i)
As there is no vertical force that is the resultant is horizontal. Now for finding out point of application of resultant, Let resultant is at distance of 'd' from the point 'O'. Apply varignon's theorem, and by taking moment about point 'O'
R.d = 50 × 80 - 80 × 50 = 0
But ΣR = ΣH = -30N, so d = 0
d = 0, means point of application of the resultant is 'O'
Therefore an equivalent force 30N acts in negative x-axis at point 'O' which replaces the given force system.
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