How to find the aceleración and the rope forcé Fs?

[neon495]

<< Note -- formatting fixed up by a Mentor >>

1. Homework Statement

Please see the attached image for the problem statement.

Homework Equations

The Attempt at a Solution

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I uses the formula
Fs = Fg1 +Fg2 + Ft1 + Ft2
I asumed the acceleration is equal to (F1+F2)/ m
(4,9+19,6)/3 = 4,9ms^-2

but I am not Sure if this is correct

 

[gneill]

I uses the formula
Fs = Fg1 +Fg2 + Ft1 + Ft2
I asumed the acceleration is equal to (F1+F2)/ m
(4,9+19,6)/3 = 4,9ms^-2

but I am not Sure if this is correct

No, it's not correct.

I don't see where you've defined any of the forces that you are summing. What are F1 and F2 in your acceleration expression (which does not look correct to me)? You should always define your variables clearly to avoid confusion of others trying to interpret your work.

Did you start by drawing Free Body Diagrams for both blocks? This is a must for these kinds of problems.

 

[haruspex]

not Sure if this is correct

As gneill posted, it is wrong.
To avoid confusing yourself, it is safer to create an unknown T for the tension then consider the forces and acceleration of each mass separately. When you have those equations you can combine them to eliminate T.