Free Body Diagrams

The technique of free body diagrams is a powerful tool for analyzing mechanics problems.
These notes give an outline of the method.
Please apply this method systematically.  Use plenty of scratch paper .
1) Draw an accurate sketch of the physical arrangement
2) List all quantitative information given, in terms of specific variables
    (e.g. Tension Force = T = 23 N)  
    If specific data are not specified, then state clearly which are the independent variables
    (you are trying to find the answer as a function of these variables)
3) State mathematically the problem objective
    (e.g. solve for the acceleration a of the smaller mass m).
4) Try to use your intuition to state the form of the answer for special limiting cases of the input variables.
5) For EACH separate object, draw a Free Body Diagram.

If two objects move together, you can either treat them as one object or draw two separate Free Body Diagrams, one for each.
a) Make an accurate sketch of the specific object.  Clearly indicate your coordinate axes including +direction
b) Draw vectors indicating each external force (no internal forces and not the net force or m a)
For each force draw either the head or the tail of the vector at the actual point of interaction of the force with the object.  Draw the force of gravity with its tail at the center of mass of the object.
c) Label each force vector with a unique symbol

6) Make a table listing each force by symbol, name, and the object which caused the force
7) for your force symbols, specify whether the variable will refer to:

The force vector
The magnitude (always positive)
A particular component of the force vector (can be positive or negative).

8)     List all Action - Reaction pairs.
9)    List all other constraints and relationships:  e.g.

W = Mg
Normal force cannot be negative
Kinetic Friction F_k = [mu] N,...

10)  Write down Newton's 2nd Law F_net = Ma for each free body diagram.
        Write out F_net = Ma for each component (x, y, z).
11)     Systematically eliminate unknowns.  You must have as many equations as unknowns.  Solve for each variable in terms of the other variables.  For each unknown, substitute your expression back into all of your equations.  Repeat until all unknowns are solved.  If you have more unknowns than equations, you need to look for more equations (contraints) -- not just new ways of writing the same equations.