The three flat blacks in the figure are positioned on the `37 degree 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.

Answer

3

Explanation

The three …………
`f_(Abmax)=0.3xx30g cos 37^(@)`

`f_(Abmax) = 72N`
`f_(Bcmax) = 0.4xx80g cos37^(@)=256N`
`f_(Cmax) = 0.5xx120g cos37^(@) = 480N`
when block 'B' is pulled two cases are possible
(1) `A & C` , remains stationary only 'B' lends to move downwards.
(2) `B & C` both moves together and there is just slipping and `A & B` contact and `C` and wedge contant
Taking case (2) Let `B & C` mmoves together and there is just slipping between `A & B` and between wedge asnd `C`

`implies P+40g sin 37^(@)+50g sin 37^(@)-72-480=0`
`implies P=12N`
checking friction between `B & C`
`f_(BC)+40g sin 37^(@)-480=0`

`f_(BC) = 240`
which is within limit so case is correct. so max.force for which there will be no silipping `P_(max) = 12N` the at this force both `B & C` tends to move together.