Try this beautiful Problem, useful for Physics Olympiad based on Block on a Cart.

The Problem: Block on a Cart

A block is placed against the vertical front of a cart. What acceleration must the cart have so that block A does not fall? The coefficient of static friction between the block and the cart is (\mu_s).

Discussion: 

A block is placed against the vertical front of a cart. Let the mass of the block be (m) and the common acceleration of the system be (a).

The force equation can be written as
$$ F=ma$$

Now,

$$f-mg=0$$ Since the coefficient of static friction is (\mu_s),

$$f=\mu_s$$

Therefore,$$ \mu_s ma=mg$$  $$\Rightarrow a=\frac{g}{\mu_s}$$