Atwood's machine is simply a pair of masses hung by a string which goes over a pair of pulleys.

Draw freebody diagrams of the two masses in the space below. Use arrows to label all the forces on each mass, and label each arrow.

      freebody-diagram of M1                    freebody diagram of M2

        Forces on mass M1:                      Forces on mass M2:


 force       X             Y               force       X           Y
------------------------------------      ----------------------------------
                   |                                        |
                   |                                        |
------------------------------------      ----------------------------------
                   |                                        |
                   |                                        |
------------------------------------      ----------------------------------
                   |                                        |
                   |                                        |
------------------------------------      ----------------------------------
total              |                        total           |               
                   |                                        |
------------------------------------      ----------------------------------

Write down the Newton's Second Law in the Y-direction for each mass. Use "a1" as the acceleration of mass M1 in the Y-direction, and "a2" as the acceleration of mass M2 in the Y-direction.


       total F     =      M1 * a1               total F     =   M2 * a2

You should have two equations, one for the motion of block M1, one for the motion of block M2. Suppose that I tell you the values for the masses, M1 and M2. How many unknown quantities are left in the two equations?