Guide to Solving Work Problems

Here are some important things to do in solving work problems.

  1. The angle between a force on an object and the displacement of the object is needed to calculate the work done by the force.  In order not to lose sight of that fact and inadvertently ignore the angle, always draw a force-displacement vector diagram (F-d diagram for short) for each force that acts on the object.  In these diagrams, specify the angle between the force and the displacement. You can see how this is done in Example 7-3 on page 185 (p.179 in 2nd ed).  There is an F-d diagram for each of the forces N, mg, and Fair that act on the car.

  2. In calculating work, start with the definition of work given in equation 7-3 on page 182 (p. 176 of 2nd ed.)  Never start with W = Fd.

  3. Always subscript the work symbol, W, with the name or initial of the force that is doing the work. Examples: WN, WT, Wmg, Wnet.  The bare symbol W must never appear in your solutions.

  4. Work isn't a vector but it isn't a magnitude either.  Work can be positive or negative.  It's negative if the angle between force and displacement is obtuse.  A check to apply to any calculation of work is to examine whether the sign is correct.

  5. If calculating the work done by a force requires that you determine the force first, then a net force problem is required.  It's frequently the case that you need to draw a force diagram and solve net force equations in order to calculate work.