A system of forces acting on a bell crank is as shown in fig. Determine the magnitude, direction and the point of application of the resultant w.r.t. O.[Figure: bell crank pivoted at O. A horizontal arm extends 300 mm to the left of O (two segments o…

Question

Q.3 (A) A system of forces acting on a bell crank is as shown in fig. Determine the magnitude, direction and the point of application of the resultant w.r.t. O. [Figure: bell crank pivoted at O. A horizontal arm extends 300 mm to the left of O (two segments of 150 mm). A 1000 N vertical downward load acts at 150 mm left of O; a 500 N force acts at the left end (300 mm from O), directed downward to the right at 60° to the horizontal. A second arm rises from O to the upper right at 60° to the horizontal, 300 mm long (two segments of 150 mm). A 1200 N vertical downward load acts at its mid-point (150 mm from O) and a 700 N horizontal force acts to the left at its upper end (300 mm from O).]

Doubtly AI · Accepted Answer

Axes: O origin, x right, y up; forces in N, distances in mm. ForcePoint (x, y) F_x F_y M_O = xF_y - yF_x 500 N(−300, 0)+250−433.01+129 904 1000 N(−150, 0)0−1000+150 000 1200 N(75, 129.90)0−1200−90 000 700 N(150, 259.81)−7000+181 865 Σ−450−2633.01+371 769 N·mm Magnitude: R = √(450² + 2633.01²) = 2671.2 N Direction: θ = tan⁻¹2633.01/450 = 80.30^° below the horizontal, towards the left (third quadrant). Position (Varignon): Σ M_O = 371 769 N·mm anticlockwise. Perpendicular distance d = 371769/2671.2 = 139.2 mm. Intercept on the x-axis: x R_y = Σ M_O ⇒ x = 371769/-2633.01 = -141.2 mm. Answer: R = 2671.2 N acting at 80.30° to the horizontal, down and to the left; its line of action cuts the horizontal arm 141.2 mm to the left of O (perpendicular distance 139.2 mm from O).

A system of forces acting on a bell crank is as shown in fig. Determine the magnitude, direction and the point of application of the resultant w.r.t. O.[Figure: bell crank pivoted at O. A horizontal arm extends 300 mm to the left of O (two segments o…

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Force	Point (x, y)	\(F_x\)	\(F_y\)	\(M_O = xF_y - yF_x\)
500 N	(−300, 0)	+250	−433.01	+129 904
1000 N	(−150, 0)	0	−1000	+150 000
1200 N	(75, 129.90)	0	−1200	−90 000
700 N	(150, 259.81)	−700	0	+181 865
Σ		−450	−2633.01	+371 769 N·mm