Answer :
The force exerted on the post by the roller,
- A = D = 0
- B = 868 N ; C = 126.1 N
The equilibrium for bracket,
∑ [tex]F_{y}[/tex] = 0
T sin 20° - 270 = 0
T = 789.43 N
[tex]T_{x}[/tex] = ( 789.43 ) cos 20°
[tex]T_{x}[/tex] = 741.82 N
[tex]T_{y}[/tex] = ( 789.43 ) sin 20°
[tex]T_{y}[/tex] = 270 N
The 270 N force and [tex]T_{y}[/tex] forms a couple
τ = ( 270 ) 0.25
τ = 67.5 N m Clockwise
∑ [tex]M_{B}[/tex] = 0
( 741.82 * 0.125 ) - 67.5 + [tex]F_{CD}[/tex] ( 0.2 ) = 0
[tex]F_{CD}[/tex] = - 126.138 N
∑ [tex]F_{y}[/tex] = 0
[tex]F_{AB}[/tex] - 126.138 - 741.82 = 0
[tex]F_{AB}[/tex] = 867.96 N
The direction of force [tex]F_{CD}[/tex] is towards left and the direction of force [tex]F_{AB}[/tex] is towards right. The force [tex]F_{CD}[/tex] is exerted by roller B and the force [tex]F_{AB}[/tex] is exerted by roller C. Rollers A and D exert no force. The force exerted by the rollers exert oppositely on the post. So the force exerted by roller C is 126.1 N and the force exerted by roller B is 867.96 N.
Therefore, the force exerted on the post by the roller,
- A = 0
- B = 867.96 N
- C = 126.1 N
- D = 0
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