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Secondary IV • 8mo.

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?


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Explanations (1)

  • Explanation from Alloprof

    Explanation from Alloprof

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

    Team Alloprof • 8mo.

    Thank you for your question !

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

    W = || F || • || ∆x || • cos (θ)


    • W: work

    • || F || : norm of the vector force applied

    • || ∆x || : norm of the vector displacement

    • θ: angle between the force and the direction of displacement

    As you noted, one sometimes omits the cos (θ) in the calculations to find the work. In fact, when the force and displacement are parallel, that is, the angle between them is 0 ° (θ = 0 °), the cosine equals 1. Effectively cos (0 °) = 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 (θ) in the equation when θ = 0 °.

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

    W = F • ∆x


    • W: work

    • F: applied force

    • ∆x: displacement

    It is normal that this equation does not contain cos ( θ), since it is the calculation of a dot product. The point • between F and ∆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!