The minimum acceleration that must be imparte | vedclass

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(B) Let $m$ be the mass of block $A$ and $a$ be the acceleration of the cart.When the cart accelerates with $a$,a pseudo force $F_p = ma$ acts on the

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$g/\mu$

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(B) Let $m$ be the mass of block $A$ and $a$ be the acceleration of the cart.When the cart accelerates with $a$,a pseudo force $F_p = ma$ acts on the block $A$ in the direction opposite to the acceleration of the cart.This pseudo force acts as the normal force $N$ pressing the block against the vertical surface of the cart,so $N = ma$.The maximum static frictional force that can act on the block is $f_{max} = \mu N = \mu ma$.For the block $A$ not to fall,the upward frictional force must balance the downward gravitational force $mg$.Thus,$f \geq mg$,which implies $\mu ma \geq mg$.Solving for $a$,we get $a \geq g/\mu$.Therefore,the minimum acceleration required is $a_{\min} = g/\mu$.

The minimum acceleration that must be imparted to the cart in the figure so that the block $A$ will not fall (given $\mu$ is the coefficient of friction between the surfaces of the block and the cart) is given by

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