Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_45

⚡ Mecademy AIENG정역학 · ch3  Problem Statement During an engine test on the ground, a propeller thrust is generated on the airplane with mass center at . The main wheels at are locked and do not skid; the small tail wheel at has no brake. Compute the percent change in the normal forces at and as compared with their "engine-off" values. Problem 3/45 (a) Normal force at the tail wheel 1. Formula: First, the weight of the airplane is . In the "engine-off" state ( ), the normal force is found from the moment equilibrium about the main wheel : In the "engine-on" state (), the thrust acts at an angle . Assuming its line of action passes through , its components are and . The new normal force is found from: 2. Substitution: Given: , , , , , . Using : Engine-off: Engine-on: 3. Calculation: T=3000 N 1800-kgGB An AB A W=mg T=0N A0 B M = ∑ B 0⇒W⋅d − GB N ⋅ A0 d = AB 0 T=3000 Nθ=12 ∘ GT = x Tcosθ T = y TsinθN A M = ∑ B 0⇒W⋅d − GB N ⋅ A d − AB T ⋅ x h − G T ⋅ y d = GB 0 m=1800 kgd = GB 0.8 md = AB 4+0.8= 4.8 mh = G 1.4 mT=3000 Nθ=12 ∘ g= 9.81 m/s 2 W=1800⋅9.81=17658 N N = A0 = 4.8 17658⋅0.8 = 6 17658 2943 N 4.8N = A 17658(0.8)−3000(1.4cos12+ ∘ 0.8sin12) ∘ W⋅d = GB 17658⋅0.8=14126.4 N⋅m Percent change 4. Result: ● Final Conclusion: The normal force at the tail wheel decreases by approximately when the engine is running at full thrust. (b) Normal force at the main wheels 1. Formula: From vertical force equilibrium : Engine-off state: . Engine-on state: . Percent change: . 2. Substitution: En