Assume a small square block $m$ is sitting on a larger wedge-shaped block of mass $M$ at an upper angle $\theta$ such that the little block will slide on the big block if both are started from rest and no other forces are present. The large block is sitting on a frictionless table. The coefficient of static friction between the large and small blocks is µs. With what range of force $F$ can you push on the large block to the right such that the small block will remain motionless with respect to the large block and neither slide up nor down?
This question really is not too complicated without friction acting upon the small block (Preventing a block from sliding on a frictionless inclined plane)
But what happens when we add friction to the system? Why is it considered static, if at rest, the mass would slide down the plane?
Best Answer
I won't solve the question for you, but I guess a clue will help you better to grab the concepts rather than some complicated solutions.
Here you see we will have to apply the external force F if friction isn't enough to keep it from moving. So let the friction do the most it can, i.e. apply the maximum value of friction (coefficient of friction times normal reaction) and the rest is done by an external force F.
The force F results in motion of the whole system and the acceleration would be $\frac{force}{totalmass}$ which results to some pseudo force on the smaller body, if you are sitting on the larger block (to be complicated in the same frame as of the larger block) some component of this force adds to the frictional force and keeps the smaller block from motion.
Figure out the rest yourself.