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A 5-Newton friction force acts upon a 2-kg object to slow it down as it moves it across a horizontal surface over a distance of 4 meters. The free-body diagram is shown at the right. Which of the following forces are doing work upon the object - either positive or negative?
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Mathematically, work (W) is calculated from knowledge of the force (F) that acts upon an object, the displacement (d) that the force causes, and the angle (Θ) between the force and displacement vectors. The formula is
W = F • d • cosine(Θ)
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A force does work upon an object if the object moves and the force somehow directly contributes to or hinders its motion. If there is no motion, then one can be sure that there is no work. If there is a motion, then one must consider which of the listed forces (if any at all) are doing the work. Cause must be considered. The force under consideration must be causing the displacement (positive work) or hindering the displacement (negative work).
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The best approach to this question is to consider each force individually and to ask "Does this force cause the object to be displaced?" The answer would be "no" if the force makes a right angle to the displacement vector (or to the direction of motion). In such instances of forces at right angles to the displacement, there is no work being done by that particular force. For instance, a vertical force cannot cause a horizontal force. The angle Θ for such a force would be 90 degrees and the cosine Θ is 0. The work calculated for such a force would be 0 Joule. See Formula Frenzy section.
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