How Do You Calculate the Tension Tx in a Multi-Mass System?

[iamtrojan3]

Homework Statement

Four blocks are on a horizontal surface. The blocks are connected by thin strings with tensions Tx, Ty, Tz. The masses of the blocks are A=22.0 kg, B=21.0 kg, C=17.0 kg, D=27.0 kg. Two forces, F1=83.0N and F2=50.0N act on the masses as shown. Assume that the friction between the masses and the surface is negligible and calculate the tension Tx.

See attached Pic.

Homework Equations

F = ma

The Attempt at a Solution

First, I calculated the acceleration of this system.
a=(F1-F2)/(mA+mB+mC+mD). a = .3793m/s^2

Then consider A and B as a whole.

So F1-Tx=(mA+mB)*a

Solve for Tx, which = 66.69N
The correct answer is 74.7N... i really don't know what I'm doing wrong, any help / hint would be greatly appreciated.
Thanks!

 

[cepheid]

Although I can't see your diagram, if I assume that the four blocks from left to right are:

A B C D

and that

Tx is the tension in the rope connecting A and B
Ty is the tension in the rope connecting B and C
Tz is the tension in the rope connecting C and D

and that

F1 pulls to the left and acts on the leftmost end
F2 pulls to the right and acts on the rightmost end

then I get the right answer. I don't think your approach of considering both A and B makes much sense (because then you have three different forces to consider, two of which are unknown). You want to consider a block for which the only two forces acting are one that you already know, and Tx. In this case, that is block A. Set up a free body diagram just for block A and try it again.

 

[iamtrojan3]

Yeah, your right. someone on my online class said to consider A and B as a whole but i guess that's wrong.
thanks again!