A side of a simplified form of verticle latch B is as shown in figure The lower member A can pushed forward in its horizontal channel . The slide of the channels are smooth , but at the interfaces of A and of which are at `45^(@)` with the horizontal there exists a static coefficient of friction `mu = 0.4` what is the minimum valueforce `F` that must be applied horizontal to A to start motion of the latch B

Explanation

For equilibrium of block B
`sum F_(x) = 0` and `sum F_(y) = 0`
`mg + (mu N)/(sqrt(2)) = (N)/(sqrt(2))`
`N = (sqrt(2)mg)/(1 - mu)`

For equilibrium of block A
`sum F_(x) = F - (N)/(sqrt(2) - (mu)/(sqrt(2) = 0`
`F = (N)/(sqrt(2))[1 + mu] = mg. ((1 + mu))/((1 - mu))`
`= 6.0 xx 10 ((1 + 0.4))/((1 - 0.4)) =(6 xx 1.4)/(0.6) = 14 N`