Accelerating pulley system questions

[Salamon]

Homework Statement

Two objects, masses 6.0 kg and 8.0 kg, are connected by a lightweight cord that passes over a massless, frictionless pulley as shown in the diagram. An upward force of 250.0 N acts on the axle of the pulley, causing the entire system to move upward (the pulley is still free to rotate). Determine the acceleration of each mass and the acceleration of the pulley.

Homework Equations

Fnet = ma
Fg = mg

The Attempt at a Solution

I tried to analyze this situation such that the pulley system is initially at rest. So I drew freebody diagrams for each of the two masses and got the equations.

6a = T -60 N
and 8a = 80 N - T

I got 14a = 20N and found that the acceleration is 10/7 m/s^2 and that tension = 68.5 N

I wasn't really sure where to go from here since I wasn't sure how to treat the 250 N force because it isn't acting directly on either mass or the rope.

I was hoping I could just divide 250 N by 14 kg to get a value for acceleration of the total system which is 17 m/s^2 and add this to the acceleration of each mass to get the resultant acceleration of each mass. I know this isn't correct though.

 

[mfb]

The pulley is massless, so all forces there have to cancel. You have 250N upwards, do you see any forces downwards? This will give the tension in the cord, and that is everything you need.