Magnitud VS. Component of a vector

[almarpa]

Hello all.

Sometimes, when reading a physics book, I find it difficult to distinguish between the magnitud of a vector and the component of a vector. For example, take the weight force, with the positive z direction pointing upwards (that is, F= -mg k). Sometimes, people write F=mg referring to its magnitude, but in other cases, people use F= -mg referring to the z component (the only component of the force vector, in this case).

Of course, it is important to distinguish between both cases, because components have sign, but amplitudes are always positive. For example, it could be a seious problem when evaluating the work done by the weight. When performing the integral ∫ Fdz, F is the component, and must have sign (and dz as well, depending on the direction of the movement).But it is easy to think that F is a magnitude, and forget about the sign, so we would get a wrong result.

Can you please tell me what is the general rule to know when F represents the magnitude of a vector, and when F represents component of a vector?

Thank you so much.

 

[BvU]

Hi,

Basically $\vec F$ is always a vector. But, as you describe, sometimes the direction is so evident that we only need the magnitude. Sloppy, but it happens.