How do I solve this physics problem of mechanics and Newton's laws?

[mayalevy2]

Homework Statement

Mass M and mass m connected by rope and pulley. The kinetic friction coefficient between mass M and table is 0.2 and the coefficient of static friction between them is 0.25.
M = 3kg, m = 1kg.
Force F is applied on mass M directed at a 30-degree angle above the table surface.

1. Will the system slide to the left if Force F is removed?
2. Calculate the minimum value of force F that will prevent the system from sliding.
3. Can the system slide to the right without F being applied?
4. Calculate the minimum value of Force F that will allow the system to swipe right.
5. What is the minimum value of Force F that will allow the system to keep the system moving at a constant speed?
6. Why are the answers to questions 4 and 5 not the same?

Relevant Equations

1. Yes
2. 3.37N
3. No
4. 17.7N
5. 16.6N

 

[scottdave]

Please show what you've attempted so far. You should set up a free body diagram on the large mass M, showing all forces in the static state. Remember that static friction is the amount just enough to keep from moving up to the maximum available.

So are you just asking why 4 and 5 are different situations? Think about the force necessary to overcome static friction and the force necessary to overcome kinetic friction.

 

[mayalevy2]

Hey, I actually got stuck on Question 2 already, and I'm not sure if I solved Question 1 correctly either. I would love to see if you can help me. Here's what I've done so far:
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