Determining Tension in a Frictionless System with Given Mass and Tension

[physixnot4me]

Hi! If anyone could pass on any hints as to how to go about figuring out this type of problem...thanks! I just need guidance as to how to determine F... attached is a diagram.

The horizontal surface on which the object slides is frictionless. If M=4.0kg, the tension in string 1 is 12N. Determine F in N.

a) 10 b) 20 c) 25 d) 40 e) none of the above

 

[Fermat]

All the blocks are interconnecrted so have the same acceleration. The force F accelerates all three blocks.
The tension, T1, accelerates the last two blocks with the same acceleration.

Use Newton's 2nd law.

 

[dainbramaged]

While we're on the topic of tension (which I never really learned last year in ap physics b), can anyone show me where to start on this problem? I'm really regretting taking ap physics c, but I got a 5 on the exam for b so I can't be that bad, right?

I've determined the net force is 45 N and that the acceleration must be 5 m/s², but that's about it :/