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G07-1. Solving Work Problems

Here are some important things to remember about solving work problems.
  1. Always start with the definition of work in this form: Wi = Fidcosθ, where the subscript i is replaced with a symbol to represent the specific force that is doing the work. Examples: WN, WT, Wmg, Wnet

The bare symbol W must never appear in your solutions. Never write the definition of work as Fd. This only applies to the special case of the force in the direction of the displacement. In many of the situations you'll encounter, the direction between the force and displacement will not be 0.

  1. Since θ must be known in order to use the definition above, 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 the example problem below.  There is an F-d diagram for each of the forces N, mg, and fk that act on the block.

See this example problem.

  1. 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.

  2. 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.

You may find identities such as the following useful.

sin(90° - θ) = cosθ               cos(90° - θ) = sinθ
sin(90° + θ) = cosθ              cos(90° + θ) = -sinθ
sin(180° - θ) = sinθ              cos(180° - θ) = -cosθ


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