What values of F make the tension zero?

[HyperSniper]

Homework Statement

In the system shown in the figure below, a horizontal force x acts on the 7.00 kg object (m1). The horizontal surface is frictionless.

I solved the first part.
(a) For what values of Fx does the 4.00 kg object (m2) accelerate upward?
F_x> 39.24 N
I am totally confused on the second part.
(b) For what values of Fx is the tension in the cord zero?
F_x$$\leq$$ ?

Homework Equations

$$\sum$$F=ma
(I don't think any other equations play a role.)

The Attempt at a Solution

I would think that for the tension to the zero, the F_x should be opposite value of the weight of m₂. So -39.24 N. However, that's not right. I am confused about what forces are acting on the objects.

 

[Delphi51]

The tension holds m2 back, preventing it from accelerating at g.
So when the tension is zero, m2 and m1 WILL accelerate at g.
Looks like Fx will have to be negative so it makes m1 keep up with m2.

 

[HyperSniper]

Okay, so if m1 is accelerating towards the end of the table at the same rate as g, then the tension will be zero? That makes sense...

So, m1*g=7*-9.81=-68.67.

EDIT:
Which is right, thanks for clearing that up for me.

 

[HallsofIvy]

Which is the same as saying that if F_x= 0, there is no force supporting the weights and they fall freely- so no tension on the string.

 

[HyperSniper]

Hm? If F_x=0, then the tension in the string is the same as the weight of m₂, is it not?

 

[Delphi51]

Super - wasn't so tough after all!