S.O.S. Mathematics CyberBoard

ignore the given FBD below the pic.

Problem said that: there are 3 blocks like in the picture, with weight A = 600lb, B =150 lb, and C = 500. Find force P such that it will move block C. (everything is static. Coefficient of floor and block is 0.5 and block with block is 0.3 and the angle is 45.

So there will be 2 cases for this problem:
case 1: A moving left, B moving up, C moving left.

case 2: block A stay, C and B moving. I am having problem with this part now.

When i draw the FBD, I think I dont need to draw one for block A since it is staying. So when I draw the FDB for the wedge B I will have
- friction b/t A and B
-Normal N to the floor
-Weight of B
-friction b/t B and C

And for the wedge C:
-W of C
-friction b/t B and C
-Normal to the floor, and friction b/t floor and block
-P

It seem like I have 5 unknowns and only 4 equations (2 from each diagram) which I am not able to solve by merely equilibrium.
Is my approach correct? or did I make a mistake in the forces?

I think the normal force b/t the wedge B and the floor is not necessary, I am not sure about this. If N of B and floor is not there then the problem is solvable at this point.

PLease help. Thanks.

Indeed, if B were going to move up, then B can't be exerting a reaction force on the floor.

But I am a bit baffled by why you think you don't need to consider A. There are constraints on P (or rather, on the force exerted by B on A) by the constraint A is not moving.

By the way, in the first case B can't move up, it got to move left (possibly up-left but it must move left in some way) to stay in contact with A as you keep applying force P.

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Thanks for replying, for case 2 A is not consider because it acted like a wall since with just FBD of B and C I can solve the system for P.

And when all of them move, you are right , the middle wedge is mving up left, but I only said "moving up" because I am only considering the friction acting on the object. So visually it moving up left but in the FBD it is consider moving up?

Am I correct?

Thanks.