Block on a Cart

A block is placed against the vertical front of a cart. What acceleration must the cart have so that block A does not fall? The coefficient of static friction between the block and the cart is \(\mu_s\).

Discussion: 

A block is placed against the vertical front of a cart. Let the mass of the block be \(m\) and the common acceleration of the system be \(a\).

The force equation can be written as
$$ F=ma$$

Now,

$$f-mg=0$$ Since the coefficient of static friction is \(\mu_s\),

$$f=\mu_s$$

Therefore,$$ \mu_s ma=mg$$  $$\Rightarrow a=\frac{g}{\mu_s}$$

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