Shown above is an ATWOOD's Machine. The question is: Given m1 = 6 KG and m2 = 4 KG, what is the acceleration of the system?
NOTE: We make an important assumption, which is that the pulley is massless.
Mass 1 (6 kg) is more massive than Mass 2 (4 kg), so the net force is gravity subtracted by tension.
Mass 2 loses the tug-of-war, because it's less massive. Mass 2 still has two forces, tension and gravity. Tension wins now, so the net force equals tension subtracted by gravity.
Now, we have two expressions for tension that we can set equal to each other to find the acceleration.
Now, which way is it going? This is very simple to check: just look where the mass is greater. Mass 1 is greater, so the system will accelerate to the left at 1.96 m/s^2.
The Pulley has Mass
For the problem above, we assumed the pulley has no mass. However, assume the pulley is extremely massive. That should surely slow down the acceleration, right? Let's figure out what the acceleration would be if the pulley had mass 12 kg.