When finding the answer for part b, do we just need to find the difference in kinetic energy and the change in energy from friction and equate that total energy to work by F(AB)?

On Part B it asks for the work done by Fab. Since work is force x distance this would be the Fab(deltaS) term and not just Fab. Does this sound correct?

Is it possible to solve this problem by summing the force components in the x direction, and solving for Force (which = mass*acceleration) and then using acceleration to solve for v_2 using basic physics?

You could, I suppose. The point of the homework, however, is to help in learning the new material, in this case, the work energy equation.

The work-energy equation is already set up to do all the things that you list here that you would do, including the integration of acceleration to get a change in speed. It would be good to use that equation to help you learn the method so that you can solve problems complicated enough that your process will not be easy.

Let us know if you need help in getting started with this.

I'm gathering that a second equation must be used to properly solve for part A, as we need to solve for Va and Vb with one big equation. Can I get some direction with what equation to use? I’m thinking the Va-Vb=V(a/b) equation.

Do we assume the mass of the string is negligible?

Yes, please do.

When finding the answer for part b, do we just need to find the difference in kinetic energy and the change in energy from friction and equate that total energy to work by F(AB)?

You should be right. I found the F_ab work by finding the difference between change of Kinetic Energy of block B and the work done by friction.

On Part B it asks for the work done by Fab. Since work is force x distance this would be the Fab(deltaS) term and not just Fab. Does this sound correct?

You are correct. U = work ≠ force.

Is it possible to solve this problem by summing the force components in the x direction, and solving for Force (which = mass*acceleration) and then using acceleration to solve for v_2 using basic physics?

You could, I suppose. The point of the homework, however, is to help in learning the new material, in this case, the work energy equation.

The work-energy equation is already set up to do all the things that you list here that you would do, including the integration of acceleration to get a change in speed. It would be good to use that equation to help you learn the method so that you can solve problems complicated enough that your process will not be easy.

Let us know if you need help in getting started with this.

I'm gathering that a second equation must be used to properly solve for part A, as we need to solve for Va and Vb with one big equation. Can I get some direction with what equation to use? I’m thinking the Va-Vb=V(a/b) equation.

It is even simpler than that: vA = vB.

When drawing the free body diagram for part b is the external force acting on the blocks included in the force of the cable acting on b?

I believe that force is accounted for in the Fab force.