exam02_soln

exam02_soln - ME 274 Summer 2011 Examination No. 2 PROBLEM...

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θ smooth A smooth G A G N G N A x y mg ME 274 – Summer 2011 SOLUTION Examination No. 2 PROBLEM NO. 1 Given : The system shown below is released from rest. The bar is homogeneous with a mass of m and a length of L . The center of the mass of the bar, G, is constrained to move within a smooth vertical guide. End A of the bar is constrained to move on a smooth horizontal surface. Find : Determine the angular acceleration of the bar on release. Use the following parameter values in your work: m = 100 kg , L = 2 meters and θ = 53.13 ° . Please clearly indicate the four steps in a neat and orderly presentation of your work. 1.FBD 2.Newton-Euler (1) F x = N G = ma Gx = 0 N G = 0 (2) F y = N A mg = ma Gy N A = m g + a Gy ( ) (3) M G = N A L 2 cos = I G α m g + a Gy ( ) L 2 cos = 1 12 mL 2 3.Kinematics a G = a A + × r G / A ω 2 r G / A a Gy ˆ j = a A ˆ i + ˆ k ( ) × L 2 cos ˆ i + sin ˆ j ( ) = a A L 2 sin ˆ i + L 2 cos ˆ j (4) ˆ j : a Gy = L 2 sin 4.Solve (3) and (4) give: gcos L 2 cos = 1 6 mL = 6 gcos / L 1 + 3 cos CCW ( )
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exam02_soln - ME 274 Summer 2011 Examination No. 2 PROBLEM...

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