Problem-Solving Strategy

NEWTON'S SECOND LAW

1. Sketch the physical situation. Identify one or more moving bodies to which you will apply Newton's second law.                              
2. Draw a free-body diagram for each chosen body. Be sure to include all the forces acting on the body, but be equally careful not to include any force exerted by the body on free-body diagram; Never include the quantity ma in your free-body diagram, it's not a force!  Label the magnitude of each force with an algebraic symbol and the numerical value if it's given. Usually, one of the forces will be the body's weight; it is usually best to label this as W = mg. If a numerical value of mass is given, you can compute the corresponding weight.     
3. Show your coordinate axes explicitly in the free-body diagram, and then determine components of forces with reference to these axes. If you know the direction of the acceleration, it is usually best to take that direction as one of the axes (i.e. on a hill).  When you represent a force in terms of its components, draw a wiggly line through the original force vector to remind you not to include it twice. When there are two or more bodies, you can use a separate axis system for each body; you don't have to use the same axis system for all the bodies. But in the equations for each body, the signs of the components must be consistent with the axes you have chosen for that body.
4. Write the equations for Newton's second law using a separate equation for each component.
5. If more than one body is involved, repeat Steps 2 through 4 for each body. There may be relationships among the motions of the bodies; for example, they may be connected by a rope. Express any such relationships in algebraic form as relations between the accelerations of the various bodies. Then solve the equations to find the required unknowns.
6. Check particular values or extreme cases of quantities, when possible, and compare the results with your intuitive expectations. Ask, "Does this result make sense?"