Brief review of forces and work

Time for a look back at the material we've covered so far. In brief, we've discussed two different approaches to solving physics problems:

using forces, which includes 1-D kinematics
using energy, which includes work

when using forces ...

one must identify the forces acting on an object, in order to compute its acceleration, and thus its changes in velocity and acceleration. The typical approach is

draw a free-body diagram
choose a set of coordinate axes
determine the sum of all forces acting in both X and Y directions
compute the acceleration of the object in each direction
if the accelerations are constant, apply the 1-D kinematic equations

when using energy ...

figure out which forces are conservative, and which are not. Compare the initial total energy of all objects in the system to the final total energy. A typical approach is

draw a picture showing the "initial" and "final" states
list all the forces which act during the motion
compute the total energy of the system in the "initial" state
compute the total energy of the system in the "final" state
account for the loss of any energy due to friction or other non-conservative forces
apply the law of conservation of energy (in the form below, note that the work done by friction or other non-conservative forces is NEGATIVE)