Problem-solving strategies:
net force, motion in a straight line

For this kind of problem, there are three equations of interest:

        Fnet = ma (Newton's second law)
        Fnet = sum of all force components
               along the axis of motion
        zero = sum of all force components
               perpendicular to the axis of motion
   

Most textbooks suggest that force components be given positive or negative values, depending upon which way they point on a cartesian x-y grid. It is generally less confusing to do this:

1. Choose the +x axis or +y axis to lie along the direction of motion. For motion along an inclined plane, place the x axis parallel to the incline and the y axis perpendicular.
2. Draw the free-body diagram, showing all of the forces acting. Visualize every force as having components perpendicular and parallel to the axis of motion.
3. Use trigonometry and given angles to resolve any forces that are not entirely along one axis into components along each axis. Treat all components as positive numbers.
4. Organize the second equation above as: sum of all components in the direction of acceleration, minus sum of all components opposite to the direction of acceleration, equals net force.
5. If there are no components that are in opposite directions, the net force is simply the sum of components on the axis of motion.
6. Organize the third equation above as: sum of all components above the axis of motion equals sum of all components below the axis of motion.

Common pitfalls include: reversing sine and cosine functions when calculating components, forgetting to include one or more forces when setting up the equations, confusing net force with individual force, setting normal force equal to weight on an inclined plane (N = mgcosq).

Click here to see a worked out example (a harder problem than those you will encounter in quizzes or tests).