Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_115

⚡ Mecademy AIENG정역학 · ch4  Problem Statement The elements of a stump grinder with a total mass (exclusive of the hydraulic cylinder and arm ) of 300 kg with mass center at are shown in the figure. The mechanism for articulation about a vertical axis is omitted, and the wheels at are free to turn. For the nominal position shown, link is horizontal and the teeth of the cutting wheel are even with the ground. If the magnitude of the force exerted by the cutter on the stump is 400 N, determine the force in the hydraulic cylinder and the magnitude of the force supported by the pin at . The problem is to be treated as two-dimensional. Problem 4/115 (a) Force in the hydraulic cylinder ● Calculation Process 1. Present Final Formula: We analyze the equilibrium of the cutting boom by taking the sum of moments about the pin . Where: The origin is at pin . mm (horizontal distance to is 500 mm, vertical distance is 600 mm). mm (horizontal distance to is 380 mm, vertical distance is 150 mm). The force on the cutter from the stump is N (directed up and to the left). The cylinder is assumed to be horizontal based on the provided geometry ( mm), so N (assuming tension). 2. Substitute Values: Substitute the known values into the moment equation about . DF CEG B CE F P C PDF ACF C M = ∑ C 0⇒(x )(F )− Ay (y )(F )+ Ax (x )(P )− Fy (y )(P)= Fx 0 C(0,0) A=(500,−600)CA F=(−380,150)CF F = A (−400cos20,400sin20) ∘∘ DF y = D y = F 150P=(−P,0) C (500)(400sin20)− ∘ (−600)(−400cos20)− ∘ (150)(P)=0 3. Par