The three flat blacks in the figure are positioned on the `37%@` incline and a force parallel to the inclined plane is applied to the middle blocks. The upper blocks is prevented from moving by a wire which attaches it to the fixed support. The masses of three blocks in kg and coefficient of static friction for each of the three pairs of contact surfaces is shoen in the figure. Determine the maximum value which force P may have before slipping take place anywhere.

Explanation

`f_(AB)=0.3xx30gcos37^@`
`f_(AB max)=72N`
`f_(BC)max=0.4xx80gcos37^@=256N`
`f(C max)=0.5xx120gcos37^@=480N`
when B block is pulled two cases are possible
(1) A & C remains stationary only B tends to move downward.
(2) B & C both moves together and there is just slipping and A & B contact and C and wedge contact Taking case (2) let B & C moves together and there is just slipping between A & B and between wedge and C
`impliesP+40gsin37^@+50gsin37&=^@-72-480=0`
`impliesP=12N`
cheking friction between B & C
`f_(BC)=40gsin37^@-480=0`
`f_(BC)=240`
which is with in limit socase is correct so max. Force for which there will be no slipping `P(max)=12N` The at this force both B & C tends to move together.