How to I find what needs to be the mass of an object in a friction problem?

[Mustachio]

Homework Statement

In the figure the coefficient of static friction between mass mA and the table is 0.50, whereas the coefficient of kinetic friction is 0.42.
(a) What minimum value of mA will keep the system from starting to move?
(b) What value of mA will keep the system moving at constant speed?

Homework Equations

So I know that

Fs <= uN
Fk = uN

But I don't know what to do when I lack the Newtons.

Can anyone give me a hint on where to start?

The Attempt at a Solution

 

[Doc Al]

If the system isn't moving, what must be the tension in the rope?

 

[Mustachio]

Would it be 0 because it'd be at equilibrium when not moving?

 

[NascentOxygen]

If someone asked you to support that hanging mass m_B by holding the upper end of the rope, what force would your arm have to exert? It would not be zero.

 

[Mustachio]

A force greater or equal to that of the force that is pulling down mb?

 

[NascentOxygen]

A force of how many Newtons?

 

[Mustachio]

Can I multiply 2 * 9.8(m/s^2) to get the mkg/s^2 = N unit?

 

[NascentOxygen]

Can I multiply 2 * 9.8(m/s^2) to get the mkg/s^2 = N unit?

Yes.

 

[Mustachio]

So I made 2 FBDs.

...... ^ N
......|
......|
mSn...mKn...|.... T
<---<--------|---------->
......|
......|
......| Ma(g)
...... vT
|
|
o
|
|
2g

And I derived 2 sets of equations.For the first FBD I got
X: T - mkN - msN = (Ma)a
Y: N - (Ma)g = 0

Second one I got

Y: T - 2g = 2a.

Do I have the problem set it up right?

 

[Doc Al]

For the first FBD I got
X: T - mkN - msN = (Ma)a

What do mkN and msN stand for? If those are supposed to be the friction forces, realize that only one acts at any given time; it's either static or kinetic friction.

Y: N - (Ma)g = 0

OK.

Second one I got

Y: T - 2g = 2a.

OK. (What's a?)

Do I have the problem set it up right?

To solve the problem, answer the question I asked before:
If the system isn't moving--or is moving at constant speed--what must be the tension in the rope?

 

[Mustachio]

I don't understand the question. :\

 

[Doc Al]

I don't understand the question. :\

What does your equation for M_B tell you? (What's the acceleration?)