Force P, 2P and 3P are acting along three sides of an equilateral triangle ABC in cyclic order. Find the magnitude and direction of resultant.
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Rajdeep11111:
Is the answer zero?
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For an equilateral triangle, all angles are equal A=B=C=60 degree
Sum of forces acting in HORIZONTAL direction:
F1 = P + 2P (-cos60) + 3P (-cos60)
= P + 2P (-1/2) + 3P (-1/2)
= -1.5P
Sum of forces acting in VERTICAL direction:
F2 = 0 + 2P (Sin60) + 3P (-sin60)
= 2P (0.866) + 3P (-0.866)
= -0.866P
Magnitude of resultant force (R)= Square root (F1 + F2)
= square root ((-1.5)^2 + (-0.866)^2))
= square root (3)
Magnitude R = 1.732P
Let ϴ be the angle of the resultant force in direction x
Then ϴ = tan-1 [(-1.5P)/(-0.866P)]
Direction of resultant force:
ϴ = 60 degree
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