Meriam, Kraige & Bolton — Statics of Particles: Problem 2_150

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/150 The blades of the portable fan generate a 1.2-lb thrust T as shown. Compute the moment of this force about the rear support point O. For comparison, determine the moment about O due to the weight of the motor–fan unit AB, whose weight of 9 lb acts at G. Problem 2/150 1. Analysis of Geometry and Given Data First, we establish a coordinate system with the origin at the rear support point . Based on the provided diagram, we can identify the following coordinates and vectors: Origin: Pivot point : The vertical support is located horizontally from and has a height of . Thus, . Fan Axis: The axis of the motor is inclined at above the horizontal. Center of Gravity : The diagram shows a perpendicular distance of from the pivot to the axis at point . Since the axis is tilted up, the perpendicular arm is directed at an angle of from the horizontal. Forces: Thrust : Magnitude . According to the "Air flow" direction (to the right) and the arrow in the diagram, it acts to the left-down along the axis. Weight : Magnitude . It acts vertically downward at point . Coordinates of point : 2. Moment of the Thrust Force about ● Calculation Process M O O O(0,0) P2 in.O 10 in.P=(2,10) ABθ=15 ∘ G4 in. PG15 ∘ PG 15+ ∘ 90= ∘ 105 ∘ TT=1.2 lb WW=9 lbG G x = G x − P 4sin15= ∘ 2−4(0.2588)=0.9647 in. y = G y + P 4cos15= ∘ 10+4(0.9659)=13.8637 in. TO 1. Present Final Formula: We use Varignon's Theorem relative to the pivot and then transfer to . The moment