Work

Work, in ​a more common usage, essentially defines anything where you do something productive to achieve a goal, whether it be a job or working out physically. Work in physics is very different and has to do more with the energy you transfer to an object. Work can be intuitively defined as the energy you apply to an object by applying a force on it over some displacement. Mathematically, work can be simplified to:

Now, the two parallel lines mean that work isn't just the product of force and distance: it's the dot product of force and distance which in this case means that its the component of force that's parallel to displacement times the displacement. To exemplify, if the force is perpendicular to the distance, no component of the force is parallel to the distance and so no work is done. Remember that this parallelism disregards direction: as long as some part of the net force is parallel to the displacement, whether it's pointing in the same direction or not, that force contributes to the total work done on an object.

To calculate this parallel component between force and distance, you will likely need to use sine or cosine ratios in order to solve for the work, depending on how the applied force vectors look relative to the displacement. One important thing to know is if the force is NOT constant with respect to the displacement, then you'll have to integrate in order to solve for work.


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