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posted by  Dave2 on 10/2/2008 7:36:02 AM  |  status: Live  

More Three D Equilbrium using a force triangle to find reation forces

Course Textbook Chapter Problem
Classical Mechanics Vector Mechanics for Engineers: Statics (8th) by Johnston, Eisenberg, Beer 4 89
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Hi All,
 
I am not quite to sure with this problem. I need some assistance.
 
Here is the problem: A uniform slender rod 10 inches lonf and weighing 0.01 lb is balenced on a glass of inner diamerter 2.8 inches. Neglecting friction, determine the angle θ corresponding to equilibrium.
 
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posted by samuel(SME- Mech) on 10/3/2008 8:32:35 AM  |  status: Live
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Dave2's comment:
"Thanks for the solution!"
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From equilibrium equations,
 
∴ Σ Fx = 0
 
=> Ra - Rc sinθ = 0
 
=> Ra = Rc sinθ  ------> (1)
 
∴ Σ Fy = 0
 
=> Rc cosθ - W = 0
 
=> Rc cosθ = W ---> (2)
 
∴ Taking moments about A,
 
=> Σ Ma =0
 
=> (Rc cosθ) * AD + (Rc sinθ) * CD - (W*AG) = 0
 
 
 
 
 
=> cos θ = 0.824
 
=> θ = 34.48
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