I need help understanding why in problems tension is modeled as T-mg = ma. I und

Question

I need help understanding why in problems tension is modeled as T-mg = ma. I understand there are different variations, but the main concept is what I need help with. For example: If i have 2 masses hanging off a pulley (m1=5kg & m2=10kg) then m1 has a downward force of 49N down. The formula given is T-m1g=ma. and i understand that t-m1a=g is the force, which is why it is set = to ma, BUT i cannot grasp the concept of how tension is found that way and why for m2 it is m2g-T2=m2a.. I need a good concrete explanation. Baby steps and spell it out for me to understand please!!

Explanation / Answer

I think,perhaps, your lecturer is a bit too swift on this, and has made some simplifications that can seem rather confusing.

We'll start with the following observation:
The rope is taut, and of the same length all the time (agreed to that one?).
Now, try to formulate, in your own words:
If we call object 1's acceleration a_1, object 2's acceleration a_2, what must be the relation between these two accelerations

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