Static friction with wedges problem

[qpham26]

Homework Statement

http://www.solutioninn.com/images/E-C-S%20%28808%29.PNG

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.

The Attempt at a Solution

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 don't 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 (I am not sure if this is here)
-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

Homework Equations

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.

 

[anathema]

Thank you for presenting your problem and sharing your approach with us. It seems like you are on the right track with your thinking. Here are a few suggestions that may help you solve this problem:

1. Remember to always consider the direction of motion for each block. In this case, block C is the only one that needs to move, so you can focus on finding the force that will cause it to move. This force, P, should be directed to the left in order to overcome the friction between blocks B and C.

2. In case 1, you correctly identified the forces acting on block B. However, for block C, there is no need to consider the friction between block B and the floor, as it is not relevant to the motion of block C. Instead, you should focus on the friction between blocks B and C, as well as the normal force between block C and the floor.

3. In case 2, you correctly identified the forces acting on block C. However, you also need to consider the friction between block B and the floor, as well as the normal force between block B and the floor. This will give you an additional equation that can help you solve for the unknown force P.

4. Remember to use the equations for equilibrium in both the x and y directions. This will give you a system of equations that you can solve simultaneously to find the value of P.

I hope this helps you solve the problem. Good luck!