SPARTALIAN'S FOOLPROOF RECIPE FOR FREE BODY DIAGRAMS

Perform each of the steps in sequence.  Do NOT omit any steps.  If you cannot proceed, mark the last step you were able to reach and seek competent help.

(1)        Identify the system and draw it.

(2)        Identify all the pieces of the universe that interact with the system and count 'em.

(3)        Draw one and only one arrow representing the force exerted by each of the items in (2).

(4)        Choose a convenient coordinate system and draw it (see 6 below).

(5)        Enclose your diagram in a box with dotted lines.

(6)        Declare the acceleration.  Draw an arrow outside the box indicating the direction of the acceleration.  If you have chosen the coordinate axes wisely, the acceleration will be along one of the principal axes (x or y).

(7)        Add all the forces vectorially to obtain the net force F_net, the left side in Newton's Second Law.  If you don't know the value of a component, give it a name and proceed pretending that you know what you are doing.  Check that the vector sum of the arrows inside the dotted line gives a vector roughly in the direction of the acceleration that you drew outside the dotted line.

(8)        Write down Newton's 2nd Law, F_net = ma, remembering that, in two dimensions, this means that there are "two equations in one", one equation for the x-direction and one for the y-direction.

(9)        Solve the equations for what the problem is asking you to find.  If you still have unknown quantities, you may have to draw a free body diagram for a second, third, etc. system.