Problem: A 8 kg block is connected to a 3 kg block as shown; both are on greased inclines . The pulley is very light and frictionless. The static and kinetic coefficients of friction are 0.135 and 0.075, respectively. Find the acceleration and the tension in the cord.

Solution: Incomplete free body diagrams have to be drawn in order to decide which way the bodies move (and even if they move). Until we know more about the motion, we cannot assign a direction to the frictional force. So a free body is drawn of the system without friction and without directions as shown below:

The net force tending to accelerate the objects (looking at the system as a whole along the line of the cord) is:

So the system tends to move to the left. Whether it moves depends on the frictional forces:

There's 14.29 N of force due to the weights available for acceleration, countered by 8.98 + 1.49 = 10.47 N of possible maximum static friction. So the bodies will move, and they move to the left. The net force is therefore 14.29 - 4.99 - 0.826 = 8.47 N. Equating this to ma for the entire system (since we've essentially done a free body of the whole thing),

Finally, we use a free body of one of the masses (I use the left one but it doesn't matter) to find the tension. Until now, the cord was not cut - we used a free body of the whole system - and we can't get the tension without cutting the cord and replacing it by the force that the cord represents.