Question

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

• A. $\alpha>\frac{mg}{\mu}$
• B. $\alpha>\frac{g}{\mu m}$
• C. $\alpha\ge\frac{g}{\mu}$
• D. $\alpha$

Answer 1

Answer: (C)

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

Answer 2

Pseudo force or fictitious force, $F_{fic}=m\alpha$

Force of friction, $f=\mu N=\mu m \alpha$

The block of mass m will not fall as long as

$f\ge mg$

$\mu m \alpha\ge mg$

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