Wikipedia:Reference desk/Archives/Science/2018 October 16

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October 16

corrosion on zinc platted MS parts when coming in contact with corrugated sheets

WE are facing problem of corrosion on zinc platted parts when they comes in contact with corrugated sheets .I would like to understand what is the chemical reaction happen when zinc platted MS parts comes in contact with corrugated sheets — Preceding unsigned comment added by WP-Kalyanbelsare (talk • contribs) 09:57, 16 October 2018 (UTC)

• The answer to your question is somewhere in the article redox or in the "see also" below it. If you want more from us, you will have to provide more details ("corrugated" is not extremely precise from a chemical point of view; plus, are you sure the contact is the cause of zinc oxidation?). Tigraan^{Click here to contact me} 11:43, 16 October 2018 (UTC)
• See Galvanic anode. Zinc is a fairly active metal (which is to say, it has a lower reduction potential compared to other metals); for that reason it is often used as a protective coating on galvanized metal; when zinc comes into contact with other metals, it prevents the other metals from corroding by instead corroding itself. --Jayron32 12:31, 16 October 2018 (UTC)

Are vector components vectors too?

If we decompose the vector V (1, forming an angle of 45° above the x axis) into its x,y components (0.707,0.707): aren't these components vectors too? You could think of them as two vectors with origin in 0, and perpendicular directions. One aligned with the x-axis and directed in ascending order. The other the same, but for the y-axis If we treated these components as vectors and added them, we would get the original vector V.

This however conflicts with two sources that I checked: "the x component of the ball’s velocity. The x component is a scalar (a number, not a vector), " from [1] and "Caution components are not vectors " from Universal Physics by Young.

What could go wrong if we treated these components as vectors? How can I know they are not vectors? What's the difference between adding two vectors (that match the x and y directions respectively) and decomposing the resulting vectors? Are these not just the inverse operation?--Doroletho (talk) 16:04, 16 October 2018 (UTC)

It's a matter of perspective rather than absolute right or wrong. You can look at the x component as a vector whose origin is (0, 0) and whose direction is along the x axis, OR you can look at the x component as the point on the x-axis where the head of that vector reaches. The final vector is either a) the sum of the two axial vectors or b) the vector whose start point is the (0, 0) and whose end point is the scalar coordinates (x, y). You get the same result either way. this page explicitly makes the case that the components of a vector are also themselves vectors. --Jayron32 16:16, 16 October 2018 (UTC)

• It depends how you decompose them.

If you decompose a vector as "the sum of two vectors", then they're vectors.

However, if you decompose them as "x,y components", then you've decomposed them into two scalars, each implicitly coupled to an axis. You can then consider each as the product of that scalar and a unit vector in the direction of that axis, then sum them again to return the original vector. But if you talk about them as "X or Y values along an axis" (that named axis implying the direction vector), then the quantity is just a scalar. Andy Dingley (talk) 16:29, 16 October 2018 (UTC)

Mm, I'm afraid this risks getting a little philosophical, but I don't really think it's correct to call them scalars. Scalars are rank-0 tensors, which means they're supposed to transform tensorially under coordinate transformations. In the case of rank 0, that means they don't change when you change coordinate systems. But the "components" are irreducibly tied to the coordinate system; use a different set of coordinates, and you get different components.

There's another word for things like components; that is, real numbers associated with a vector or tensor field, but that depend on the coordinate system. I think they might be called "numerics" or something like that? --Trovatore (talk) 18:27, 16 October 2018 (UTC)

• Certainly there's a semantic point in here, but I think they're either scalars or vectors, nothing inbetween.

They start out as vectors. When we strip away their implicit connection to an axis, by stating that axis explicitly through some other means, such as saying, "x units along the x axis", then all we have left is that scalar. If you solve a quadratic equation by plotting its function on a graph, then the values you obtain as solutions are purely that, purely real number values (i.e. scalars). Andy Dingley (talk) 18:54, 16 October 2018 (UTC)

Well, my point is not that they're "in between" scalars and vectors, but that they are neither one. Scalars and vectors are supposed to be objective, in the sense that they don't depend on the coordinate system. Components are subjective; they depend on the angle at which you look at the vector. --Trovatore (talk) 19:12, 16 October 2018 (UTC)

And don't get me wrong — I see your point. You're right at some level. Can a vector x-component be 5? Sure. Is 5 a scalar? Sure. So by transitivity....

But the OP may need to know that, in a lot of contexts, "scalar", "vector", and "tensor" carry other implications than just how many numbers you need to describe the quantity. A tensor is supposed to be an invariant property of the system being observed. So for example invariant mass is a scalar, but relativistic mass is not (I think it's the time component of the 4-momentum). As I say, if you try to nail down exactly what this means, it gets a little philosophical. Still, just at the level of social convention, it's something a student may need to know. --Trovatore (talk) 20:34, 16 October 2018 (UTC)

5 Is a scalar. (5,0) Is a vector in 2 dimensions. A Cartesian declaration of a vector must give explicit components in each dimension of the space it occupies. (5, 6, 4) Is an arbitrary vector in 3 dimensions. DroneB (talk) 01:32, 17 October 2018 (UTC)

Umm. Nothing you said is wrong, exactly. But I think you haven't quite followed what I was saying. --Trovatore (talk) 06:21, 17 October 2018 (UTC)

Mathematicians and physicists use the term "scalar" in different ways. See scalar (mathematics) and scalar (physics). Gandalf61 (talk) 16:19, 22 October 2018 (UTC)

Not really per the second article you linked "The concept of a scalar in physics is essentially the same as in mathematics." The definitions look different because the two pages are using different vocabulary, but they basically mean the same thing. --Jayron32 16:29, 22 October 2018 (UTC)

I think there is a difference here, but I wouldn't call it math versus physics. It's more abstract (linear) algebra versus differential geometry. In the theory of abstract vector spaces, you define a vector space over some underlying field (or in some contexts it might even be just a ring), called the field of scalars. This field is frequently, but not always, either R or C, the real numbers or the complex numbers.

In the context of abstract vector spaces over, say, the reals, it makes sense to say that any real number is a scalar, because that's the field of scalars underlying what you're talking about. A "vector", on the other hand, is just any element of a vector space, which is just any structure that satisfies the vector axioms. What a vector "is", we really don't care. (I think that's the hardest thing for new students of linear algebra to grasp.)

But in a differential geometry context, there's a lot more infrastructure. You have some smooth manifold and its tangent bundle, which gives you your concrete vectors (or "vector fields"; this is a different use of the word "field"). All your scalars, vectors, and tensors are relative to that. Now "scalar" doesn't mean just "any real number" anymore, and it's not really correct to say that a component of a vector in some given coordinate system is a scalar, because it doesn't transform correctly. --Trovatore (talk) 00:48, 23 October 2018 (UTC)

My understanding is that if you say "V = (0.707, 0.707)", what you mean is V = 0.707 x + 0.707 y, with x and y being unit vectors of interest to you. (I should really look up how to give them funny hats, but I'm being lazy...) But why isn't this at the Math desk? Wnt (talk) 01:10, 18 October 2018 (UTC)