Force and Motion Sliding/Hanging Blocks

[Shatzkinator]

Homework Statement

In Figure 5-52, three ballot boxes are connected by cords, one of which wraps over a pulley having negligible friction on its axle and negligible mass. The masses are mA = 30.0 kg, mB = 42.0 kg, and mC = 14.0 kg. When the assembly is released from rest, (a) what is the tension in the cord connecting B and C, and (b) how far does A move in the first 0.260 s (assuming it does not reach the pulley)?

... there is block a which is on the surface and block b and c are hanging over the edge pulling it down.

Homework Equations

fnet = ma
T = ma
Fgc - T = ma
Fgb - T = ma

The Attempt at a Solution

I'm not sure what I'm supposed to do, i thought of subtracting the equations, but i don't think that will work based on what I'm looking at and i don't think substitution of a variable t or a will work... help?

 

[Chi Meson]

To answer both questions, you need to determine the acceleration of the system. This requires finding the net force of the system. This can be done with a bit of a shortcut: treat all forces in one, not two dimensions. The downward force on the hanging mass is the "same direction" as the sideways forces toward the pulley. It's not exactly correct, but it works out if the pulley is massless and frictionless.

Note: when summing all forces, the tensions are interior, and therefore do not contribute to the net force on the system.

 

[Delphi51]

There is no mention of friction force - I guess you assume it is zero.
The force causing the whole chain of masses to accelerate is the force of gravity on the hanging masses. Use that to calculate the acceleration.

The tension in the cord is the force acting on mass A, causing it to accelerate at the rate you have already calculated.

 

[Shatzkinator]

I don't seem to be getting the correct answer... this is what i did for the system:

The only forces i see that contribute to the acceleration are Fgb and Fgc... they are 411.6 and 137.2 respectively. Fgb + Fgc = ma... solving this i get 9.8 m/s^2 obviously gravity. But when i do T = ma on block a to solve for tension using 9.8, i don't ge tthe correct answer??

edit: wait i didn't include the mass of block a for calculating the acceleration. Thats probably my mistake.

edit 2: Yes it was my mistake! =)
Thanks for the help!