First slide

Friction on horizontal surface

Question

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

Moderate

A

$μg$
B

$\frac{g}{μ}$
C

$\frac{g}{\sqrt{μ}}$
D

$\frac{μ}{g}$

Solution

The friction force on the block will prevent the block from falling it.
From figure:
$N = ma and$
F = mg $\Rightarrow μN = mg \Rightarrow μma = mg \Rightarrow a = \frac{g}{μ}$

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