Secondary IV â€¢ 2yr.

Why do we sometimes calculate the work with the cosinus of the angle between the force and the displacement and sometimes without it? Is this in a special case or an exception?

Explanation from Alloprof

This Explanation was submitted by a member of the Alloprof team.

Thank you for your question !

The formula to calculate the work in physics is as follows:

W = || F || â€¢ || âˆ†x || â€¢ cos (Î¸)

Legend:

â€¢ W: work

â€¢ || F || : norm of the vector force applied

â€¢ || âˆ†x || : norm of the vector displacement

â€¢ Î¸: angle between the force and the direction of displacement

As you noted, one sometimes omits the cos (Î¸) in the calculations to find the work. In fact, when the force and displacement are parallel, that is, the angle between them is 0 Â° (Î¸ = 0 Â°), the cosine equals 1. Effectively cos (0 Â°) = 1. Since 1 is the neutral element of the multiplication, it does not change the result, whether or not it is present in a multiplication.

In short, to save time, some prefer not to write cos (Î¸) in the equation when Î¸ = 0 Â°.

However, it is also possible that you encounter another form of the work calculation:

W = F â€¢ âˆ†x

Legend:

â€¢ W: work

â€¢ F: applied force

â€¢ âˆ†x: displacement

It is normal that this equation does not contain cos ( Î¸), since it is the calculation of a dot product. The point â€¢ between F and âˆ†x represents this operation, and not simply a multiplication as in the first formula.

Feel free to ask us more questions if you have any!