# Moments And Friction

Hi, can anyone figure this out, I can almost do it, but my inequalities don't really make sense:

A uniform ladder, of mass m, leans against a vertical wall with its base on horizontal ground. The length of the ladder is 6metres. Assume that the wall is smooth and that ground is rough, with the coefficient of friction between the ladder and the ground equal to 0.5.

a)If the angle between the ladder and the ground is Theta, show that the ladder remains at rest if Theta is greater than or equal to 45 degs.

see attachment
Hi, nice solution. I'm still slightly confused. I think you've shown that if the ladder remains at rest, then theta>45. Which isn't the same as the question, if theta is greater than or equal to 45, then show the ladder will remain at rest.

Also, what happens if theta=45, then the frictional force is limiting, does that mean
the ladder may or maynot move???
In limiting equilibrium, f=µR holds true, and the forces are balanced. i.e. no acceleration.
C4>O7
In limiting equilibrium, f=µR holds true, and the forces are balanced. i.e. no acceleration.

So it may or maynot move then???
Basically, if f=mu*R then doesn't necessarily imply object is moving??
Well by no acceleration I mean if the ladder was moving then no net force is there to stop it, but if it wasn't initially moving, then it won't start to move either.
C4>O7
Well by no acceleration I mean if the ladder was moving then no net force is there to stop it, but if it wasn't initially moving, then it won't start to move either.

Ok, thats what I thought, thanks