Meriam, Kraige & Bolton — Statics of Particles: Problem 2_67

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/67 Replace the two cable tensions which act on the pulley at of the beam trolley by two parallel forces which act at the track-wheel connections and . Given values from the diagram: Horizontal distance between track-wheel and the central vertical axis: Horizontal distance between track-wheel and the central vertical axis: Horizontal distance between the two vertical cables acting on the pulley: Force in the left cable: (vertically downward) Force in the right cable: (vertically downward) Problem 2/67 1. Analyze the original force system The original system consists of two vertical downward forces acting on the pulley at . We need to determine the resultant force and the resultant moment about the center point (which lies on the vertical centerline of the trolley). Resultant Vertical Force (): Resultant Moment about (): Assuming the pulley is symmetric about the vertical centerline, the left cable is at and the right cable is at (since the total spacing is ). Let counter-clockwise (CCW) be positive: 2. Establish the equivalent system at and O AB A200 mm B200 mm 180 mm 6.3 kN 4.1 kN O O R R=F = ∑ y 6.3 kN+4.1 kN=10.4 kN (downward) OM O x=−90 mmx= +90 mm180 mm M = O (6.3 kN)×(90 mm)−(4.1 kN)×(90 mm) M = O 567 kN⋅mm−369 kN⋅mm=198 kN⋅mm (CCW) AB We need to find two parallel (vertical) forces and acting at the track-wheel connections and such that they are statically equivalent to the original system. This means they must have the sam