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,$$ \mu_s ma=mg$$ $$\Rightarrow a=\frac{g}{\mu_s}$$
Ashani Dasgupta, is pursuing Ph.D. in Geometric Group Theory at University of Wisconsin, Milwaukee. He is the founding faculty and admin at Cheenta. 
