Concurrent forces 3p,7p and 5p act respectively along three directions which are parallel to side of an equilateral triangle taken in order determine the magnitude and direction of the resultant

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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 = 3P + 5P (-cos60) + 7P (-cos60)

= 3P + 5P (-1/2) + 7P (-1/2)

= -6P

Sum of forces acting in VERTICAL direction:

F2 = 0 + 5P (Sin60) + 7P (-sin60)

= 5P (0.866) + 7P (-0.866)

= -1.732P

Magnitude of resultant force (R)= Square root (F1 + F2)

= square root ((-6)^2 + (-1.732)^2))

= square root (39)

MagnitudeR = 6.24P

Let ϴ be the angle of the resultant force in direction x

Then ϴ = tan-1 [(-6P)/(-1.732P)]

Direction of resultant force:

ϴ = 73.89 degree

Askiitians expert
Ankit