Most of the time when I was solving physics problems I assumed that the tensions between several objects cancel each other if we consider a system of the objects and strings. I thought that was because tension is an internal force. Is this a correct understanding?
I know that the work done by a string is always zero, but I'm not so sure about the internal force and cancellation.
If you look at the diagram above, the tension of the $m_1$ is in the positive $x$ direction, while that of the $m_2$ is in the negative $y$ direction. Since force is a vector quantity, even if you consider a system consisting of the $m_1$, $m_2$, and the string, the two tensions cannot cancel each other therefore not a internal force, right?
My intuition says that they can still cancel each other, but I can't understand why. Can anyone help me?