Work, Work, Work

One of the things that a teacher encounter in a classroom are the misconceptions developed and even reinforced over the years. As 4th year teacher, I need to let them change their vehemently held ideas. One of them is the concept of Work. Defined by a student when called to recall it from their elementary and early high school, they recite this mantra: Work is  Force times distance of W=Fd . FALSE of course for several reasons.

1. Work is a scalar quantity, so it cannot be a product of a vector (Force) and scalar (distance). The result of such multiplication is a vector quantity. 
2. The multiplication used is a dot multiplication not algebraic multiplication and so must be expressed as Work = F•d.
3. The other factor is NOT distance but displacement. The dot product of displacement (Vector) and force (Vector) is Work (Scalar).

The usual equation given in books is W = Fdcosθ. This equation is the magnitude version of the above mentioned vector equation. The θ is the angle between the Force F and the displacement d and the usual angle between the two is 0º and the value of cosine zero (cos0º) is 1. The entire equation then simplifies to W = Fd, which is the magnitude version.


Furthermore, it is not always TRUE that when force causes motion, work is done. When Force causes motion that is perpendicular to its action [Cosine(90º)= 0], no work is also done. But that is the only instance it can happen. 


To some teachers also include the fact that Work is also the product of torque and angular displacement. W = Γθ. Here when a force acts on a body pivoted at a certain point, it spins and does not translate or change its position.