Minimum force required to keep two blocks from not falling

[nafisanazlee]

Homework Statement

Two blocks P and Q are of weight 20N and 100N, respectively. These are being pressed against a wall by a force F as shown. If the coefficient of static friction between the blocks is 0.1 and between block Q and the wall is 0.15, what will be the minimum force to keep the blocks in equilibrium?
I've tried to solve it in this way, but I'm not sure if my approach is correct or not. Can you please check?

Relevant Equations

Fsmax = μsN

 

[PeroK]

Looks right. You might want to add why block P does not slide.

 

[nafisanazlee]

Looks right. You might want to add why block P does not slide.

because the maximum friction force that can be provided between the two blocks becomes 0.1*800= 80N, and we only need 20N for support, so it's fine..?

 

[PeroK]

because the maximum friction force that can be provided between the two blocks becomes 0.1*800= 80N, and we only need 20N for support, so it's fine..?

Yes, it was fairly obvious from the numbers that the maximum force was needed for Q (as it is much heavier). But, it does no harm to show the calculation for P as well.

 

[nafisanazlee]

Yes, it was fairly obvious from the numbers that the maximum force was needed for Q (as it is much heavier). But, it does no harm to show the calculation for P as well.

Thank you so much for your time. Much appreciated.