A circular roller of weight 1000 N and radius 20 cm hangs by a tie rod AB = 40 cm and rests against a smooth vertical wall at C as shown in figure. Determine the tension in the rod and reaction at point C. Hint: Tie rod means rod subjected to tensile force as cable.
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Solution. Let us draw the free-body diagram of the circular roller.
Sin θ =20/40 =1/2 ; θ = 300
Applying conditions of equilibrium
Ʃ f x = 0
-f sin θ + R c =0
Ʃ f y = 0 => f cos θ -1000 = 0
From (2) f = 1000 /cos 300 = 1154 .7 N
From (1) RC =F sin 300 = 1154.7 sin 300 =577.35 N
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