Mechanics Static Rigid Body Problem

[James10492]

Hi all, its me again with another mechanics problem I cannot solve.



"A uniform plank AB of 6m length and weight W Newtons rests on a smooth peg at point C. The plank rests in limiting equilibrium with one end A on rough horizontal ground where the coefficient of friction between it and the ground is .8. The plank is inclined at the angle alpha, where tan alpha = .75. Given that the magnitude of the normal reaction with the ground is 80 N, find the magnitude of the normal reaction with the peg and the plank, and the value of W."

As you can see in my notes I try to make an expression for the normal reaction at C by taking moments about A. I think you can work out W by resolving the forces vertically but I must be doing something wrong as my results do not lead to the correct solution. I am having a hard time seeing how to solve this problem when you are not given the distance AC.

*Edit: I realise that resolving vertically, it should be 80 + R(C) *.8 = W, not what I wrote.

 

[lex]

Just resolve vertically and resolve horizontally. The two equations will be sufficient to find the two missing forces of magnitude W and $R_c$.

 

[topsquark]

Hi all, its me again with another mechanics problem I cannot solve.

View attachment 32661

"A uniform plank AB of 6m length and weight W Newtons rests on a smooth peg at point C. The plank rests in limiting equilibrium with one end A on rough horizontal ground where the coefficient of friction between it and the ground is .8. The plank is inclined at the angle alpha, where tan alpha = .75. Given that the magnitude of the normal reaction with the ground is 80 N, find the magnitude of the normal reaction with the peg and the plank, and the value of W."

As you can see in my notes I try to make an expression for the normal reaction at C by taking moments about A. I think you can work out W by resolving the forces vertically but I must be doing something wrong as my results do not lead to the correct solution. I am having a hard time seeing how to solve this problem when you are not given the distance AC.

*Edit: I realise that resolving vertically, it should be 80 + R(C) *.8 = W, not what I wrote.

You can get another relation that will help. There is a friction force acting to the right at point A (due to the plank on the surface.) Do a sum of forces in the +x and that will give you another equation to work will.

If that isn't enough then take a new axis about point C.

-Dan

 

[James10492]

Thanks for your answers, I got the answer now.