Question

A cart of mass M has a vlock of mass m in contact with it as shown in fig. The coefficient of friction between the block and the cart is $\mu$. What should be the minimum acceleration of the cart so that the block of mass m does not fall?

Answer 1

If the cart acceleration with $a$

Pseudo force on mass $F=ma$

Force of friction $=\mu N$

For horizontal equilibrium $F=N$

$f=\mu ma$

The block will not fall as long as

$f\ge mg$

$\mu ma\ge mg$

$a\ge \frac{g}{\mu }$