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The question is given in the image attached. Please I need full solution...

Kruthik , 6 Years ago
Grade 12
anser 1 Answers
Venkat

Last Activity: 6 Years ago

At A, at bottom with roller there will be only one reaction force pointing upwards. The roller is free to move in x direction, hence no x- reaction force. Only y-reaction force is present.
 
At B, the ladder is constrained to move in x and y direction. Hence, reaction force is present in x and y. The reaction force at x is leftwards and in y direcrtion upwards.
 
Note that W will act at midpoint of ladder.
 
From equilibrium of forces,
F_{y}_A+F_{y}_B = W \\F_{x}_B = 0
 
Assume ladder length of ‘l’. When resolved this will give you lcos30 as vertical distance, and lsin30 for horizontal distance.
Now apply moment equilibrium about B, Take anticlockwise moment due to force is +ve, then,
 
F_{y}_A(lcos30)+ W (l/2)\times(sin30)=0 \\0.866F_{y}_A=-0.25W \\F_{y}_A= -0.2886W
Negative y means, the force direction is opposite to our assumption of upwards, that is it acts downwards/
 
 Solve it to find B
F_{y}_A+F_{y}_B = W \\-0.2886W+F_{y}_B = W \\F_{y}_B=1.2886W
Hence, force at B acts upwards.
 
 

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