Is the Tension in the String Equal for Both Blocks?

[theunloved]

4.0 kg block A and 6.0kg block B are connected by a string of negligible mass. Force a Fa = 12N acts on block A; force B Fb = 24N acts on block B. What is the tension in the string.

I was able to draw FBD and lists all the forces acting on A and B, but what I don't understand is the tension T acting on A and B.
A:
Fa - Ta = m1 A

B:
Fb - Tb = m2 A

In my understanding, Ta and Tb shouldn't be equal, since we have Fa and Fb exerts on each object and they have different value. What if Ta > Tb, then the cord between A and B should come loose, therefore we'd not have tension at all. But if we don't have have Ta = Tb, then there's no way we can solve the problem...
So my question is: Is it really Ta = Tb and why ?

 

[1MileCrash]

The tension is equal, it's just one string after all. What directions are the forces acting? If they are opposite from one another, your equations are close, but one of the applied forces should be negative, with tension adding, while one of the applied forces should be positive, with tension subtracting.

Knowing mass, and knowing the acceleration of the system is equal, and knowing tension is equal, you can solve for tension. You're nearly there, correct your equations, solve both for A, then set them equal to one another, and solve for T. At least that's how I remember doing these.

 

[theunloved]

The tension is equal, it's just one string after all. What directions are the forces acting? If they are opposite from one another, your equations are close, but one of the applied forces should be negative, with tension adding, while one of the applied forces should be positive, with tension subtracting.

Knowing mass, and knowing the acceleration of the system is equal, and knowing tension is equal, you can solve for tension. You're nearly there, correct your equations, solve both for A, then set them equal to one another, and solve for T. At least that's how I remember doing these.

Oh, yeah,
Both Fa and Fb have the same direction, going from left to right.
So it should be
Tension in the string
4.0 kg block A and 6.0kg block B are connected by a string of negligible mass. Force a Fa = 12N acts on block A; force B Fb = 24N acts on block B. What is the tension in the string.

I was able to draw FBD and lists all the forces acting on A and B, but what I don't understand is the tension T acting on A and B.

A:
Fa + Ta = m1 A

B:
Fb - Tb = m2 A

I know that its from one string, the tensions should be equal, but, here, we have Fa and Fb. Don't we on the force acting on A and B ? they are different, and they are the forces that make A and B moving. So, if you have Fa > Fb, A will be moving faster than B, and since it's moving faster, it'll catch up with B in a certain time, if that's the case, shouldn't the tensions be different ?

 

[JHamm]

A single massless string can not have different tensions at different parts

 

[PhanthomJay]

Oh, yeah,
Both Fa and Fb have the same direction, going from left to right.
So it should be
Tension in the string
4.0 kg block A and 6.0kg block B are connected by a string of negligible mass. Force a Fa = 12N acts on block A; force B Fb = 24N acts on block B. What is the tension in the string.

I was able to draw FBD and lists all the forces acting on A and B, but what I don't understand is the tension T acting on A and B.

A:
Fa + Ta = m1 A

B:
Fb - Tb = m2 A

I know that its from one string, the tensions should be equal, but, here, we have Fa and Fb. Don't we on the force acting on A and B ? they are different, and they are the forces that make A and B moving. So, if you have Fa > Fb, A will be moving faster than B, and since it's moving faster, it'll catch up with B in a certain time, if that's the case, shouldn't the tensions be different ?

If Fa > Fb, solve for T. Strings cannot take negative tensions, they go slack. The blocks accelerate independently from each other. What would be the value of T for that case? As noted,the tension in a massless string must be the same throughout.