A block of mass $m$ is in contact with the cart $C$ as shown in the figure. The coefficient of static friction between the block and the cart is $\mu$. The acceleration $\alpha$ of the cart that will prevent the block from falling satisfies:

For the block not to fall, the upward frictional force $f$ must balance the downward gravitational force $mg$.
$$f\ge mg$$
The frictional force $f$ is given by $\mu N$, where $N$ is the normal reaction. The normal reaction is provided by the pseudo-force due to the acceleration of the cart:
$$N=m\alpha$$
Substituting $N$:
$$\mu (m\alpha )\ge mg$$
$$\mu \alpha \ge g$$
$$\alpha \ge \frac{g}{\mu }$$