Calculating Tension in a Two-Block System

[sweet877]

F2 <------[ M ]---T---[ m ]----> F1
F2 = 20 N
M = 2.0 kg
m = 1.0 kg
F1 = 30 N
Find T, tension.
So F1-F2 = (M+m)a.
a=10/3 = 3.3 m/s^2
Fnet= Ma
T-F2 = Ma
T = Ma + F2 = 2.0(3.3) + 20 = 27 N
However, I don't think this is right because I got a different answer when I used the other block:
Fnet = ma
F1 - T2 = ma
T2 = F1 - ma = 30-1.0(9.8) = 20 N
Where did I go wrong? Thanks.

edit: Never mind. Figured out I used g instead of a.

 

[vaishakh]

First take both of them together as your system. So ne force on your system is 10N towards F1. The mass of your system is 3kg till where you are correct. Now see the diagram. Ma = ma + T. Look at the diagram to see whether this is corect. Now you just need to look at forces internal to the system and not external forces.

So, in short your mistake is you need not look for F1 abd F2 cause they are external force to the system and you have already solved the system. This will make your steps more conducive to yourself.

Otherwise use stepwise analysis.
F1 - T = ma
T - F2 = Ma

 

[sweet877]

Thanks for your help!