Meriam, Kraige & Bolton — Statics of Particles: Problem 2_36

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/36 A man exerts a force F on the handle of the stationary wheelbarrow at A. The weight of the wheelbarrow along with its load of dirt is 185 lb with center of gravity at G. For the configuration shown, what force F must the man apply at A to make the net moment about the tire contact point B equal to zero? Problem 2/36 1. Geometry and Coordinate System Analysis First, we establish a coordinate system with the origin at the tire contact point . Based on the provided diagram, we identify the positions of the relevant points: Point G (Center of Gravity): Located to the left of . Position vector: . Point A (Handle): Located to the left of , making it to the left of . Its height is above the ground. Position vector: . Weight Force (): Acts vertically downward at . . Next, we determine the direction of the force applied at : The handle at makes an angle of with the horizontal (sloping down-right). The extension of the handle to the left of is at an angle of from the positive x-axis. The force is applied at an angle of clockwise from this handle extension. Angle of with the positive x-axis: . Force components: . 2. Moment Equilibrium about Point B ● Calculation Process For the net moment about point to be zero, the sum of moments created by the weight and the applied force must vanish: B(0,0) 8 in.Br = G −8i+y j G 37 in.G8+37=45 in. B26 in.r = A −45i+26j WGW=−185j lb FA A20 ∘ A180− ∘ 20= ∘ 160 ∘ F60 ∘ Fθ = F 160− ∘ 60= ∘ 100 ∘ F=F(cos1