Question

A blog of mass m is placed on a cart of mass M as shown in the figure, The coefficient of friction between the block and the cart is $\mu$. What is the minimum acceleration of the cart so that block m does not slip on the cart?

Answer 1

Given, Mass of the block is $m$, MAss of the cart is $M$, $Coefficient=\mu$

If the cart $f$ accelerate with 'a' Then, the pseudo force on the mass $F=ma$

Force of friction is $\mu N$

For horizontal equilibrium $F=N=\mu ma$

The block will not fall as,

$f\ge mg\Rightarrow \mu ma\ge mg$

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