The Pulley Machine

Two weights of varying masses are attached to the same string, separated by a frictionless disk. With this setup, you can examine tension forces, potential energy and kinetic energy.

The pulley problem illustrates a correlation between a shared tension force and acceleration, seen through $$F_{tension} = mg + ma$$ $$F_{tension} = Mg - Ma$$ $$\therefore a = \frac{g(m-M)}{m+M}$$