Meriam, Kraige & Bolton — Statics of Particles: Problem 2_88

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/88 An exhaust system for a pickup truck is shown in the figure. The weights , , and of the head-pipe, muffler, and tailpipe are 10, 100, and 50 N, respectively, and act at the indicated points. If the exhaust-pipe hanger at point is adjusted so that its tension is 50 N, determine the required forces in the hangers at points , and so that the force–couple system at point is zero. Why is a zero force–couple system at desirable? Problem 2/88 1. Analysis of Forces and Geometry We establish a coordinate system with the origin at point . The -axis is horizontal to the right, and the -axis is vertical upward. Based on the provided dimensions (in meters), we identify the positions and magnitudes of all vertical forces: Origin: Weight of head-pipe: at Hanger force at A: at Weight of muffler: at Hanger force at B: at Weight of tailpipe: at Hanger forces at C and D: Their lines of action pass through a common center at on the -axis. The forces and are inclined at to the vertical: 2. Force Equilibrium Equations For the force-couple system at to be zero, the resultant force must be zero: Sum of forces in the x-direction: W h W m W t AF A B,CD OO Ox y O(0,0) W = h −10j Nx = h 0.5 m F = A 50j Nx = A 0.5+0.2=0.7 m W = m −100j Nx = m 0.7+0.65=1.35 m F = B F j B x = B 1.35+0.65=2.0 m W = t −50j Nx = t 2.0+0.5=2.5 m x = CD 2.5+0.4=2.9 mx F C F D 30 ∘ F = C F (−sin30i+ C ∘ cos30j) ∘ F = D F (sin30i+ D ∘ cos30j) ∘ OR Sum of forces in the y-direction