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