How Do You Determine the Acceleration and Tension in a String and Pulley System?

[phizics09]

Homework Statement

The masses of blocks A,B, and C are 4kg, 10kg and 2kg respectively. Knowing that P=0 and neglecting the masses of the pulleys and the effects of friction, determine a) the acceleration of each block and the tension in the chord.

Homework Equations

Fnet=ma

The Attempt at a Solution

I know that we have to draw FBD's for each block and then figure out the equations of each Fnet. But first, how do you know the direction that this system will move? Because for example, if you know that block A is moving down, we can assume down is positive and its equation will be
ma=mg-2T (because we denote down as positive)? Also, for block B, will the tension be 4T, since it's connected to four strings?
I am confused about how system works.

Thanks!

 

[Spinnor]

Just pick directions that you think the masses will accelerate and then write out you equations accordingly. If you picked the wrong direction the acceleration will have a minus sign in the end.

See,

 

[phizics09]

Oh, okay thanks for the diagram! What is y and V though?

 

[Spinnor]

y_2, y_4, and y_10 label the distances the masses move and V_2, V_4, and V_10 are the velocities of those masses. The directions chosen are my guess as to which way the masses will move.

Good luck!