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