In figure the coefficient of friciton between the floor and the block B is 0.1. The cofficient of friction between the block B and A is 0.2. The mass of A is m/2 and B is m. What is the maximum horizontal force F can be applied to the block B so that two blocks move together?

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`