AQA A-level M2 help

[username01]

can anyone help with the following question?:

The diagram shows a uniform rod AB of weight W and length 2a. The rod rests with a on rough horizontal ground and leans against a rough fixed prism of semicircular cross-section of radius a. the coefficient of friction at both contacts is mu. When friction is limiting the rod makes an angle theta with the horizontal. show that

sin(theta)=sqrt((mu/(1+(mu squared)))

Question is from AQA A-level maths M2 textbook, ex 2D, Q9, where there is also a diagram (and the final line is formatted better and easier to read!) if anyone has this book and it helps.
thanks

 

[stapel]

can anyone help with the following question?:

The diagram shows a uniform rod AB of weight W and length 2a. The rod rests with a on rough horizontal ground and leans against a rough fixed prism of semicircular cross-section of radius a. the coefficient of friction at both contacts is mu. When friction is limiting the rod makes an angle theta with the horizontal. show that

sin(theta)=sqrt((mu/(1+(mu squared)))

Question is from AQA A-level maths M2 textbook, ex 2D, Q9, where there is also a diagram (and the final line is formatted better and easier to read!) if anyone has this book and it helps.
thanks

Please reply with a scan of the image, and a clear listing of what you have tried so far, so we can "see" where you're getting stuck. Thank you!

 

[username01]

I don't have scanning facilities at the moment, but have tried my best to draw out the diagram from the textbook in paint. N.B. the prism is supposed to be perfectly spherical. (the box at the bottom is the last line of the question). Whilst trying to work it out I've added normal reactions at both the floor and the point of contact with the prism, and frictional forces opposing what would otherwise be its direction of motion. I've tried taking moments about several points by resolving some of the forces; equation the frictional forces to (mu x reaction), and equating the reaction at the floor to Wsin(theta) and the reaction at the prism to Wcos (theta). Have also tried setting up simultaneous equations with these and using trig identities on them, but have been working on this for a couple of days now and not getting very far.