Mechanics for Alevel
posted by Bob .
An object of mass 50kg rests on a rough plane inclined at an angle z to the horizontal. It is supported in this position by a light string parallel to the plane which is attached to the object and fixed to a point at the top of the plane. The string has a breaking strain of 200N and the coefficient of friction between the object and the plane is 0.2, Find the largest value of angle z which would allow the string to remain intact

as you increase the angle, the static friction increases up to a maximum value of mu*N.
you need to find the value of z for which the max force upward = force downward:
Tmax + fmax = mg sinz
200 + mu*mgcosz = mg sinz
200 + 0.2*50*9.8cosz = 50*9.8 sinz
z = 34.9 deg 
I'm sorry, but I'm stuck at 200 + 0.2*50*9.8cosz = 50*9.8sinz