Carbon Steel as an Interstitial Alloy and How its Chemical Structure Contributes to Elasticity of Collisions

Background

Back when our high school physics class was learning about elastic and inelastic collisions with the conservation of momentum, I noticed that a disproportionate number of the practice problems we were assigned that had to do with elastic collisions involved steel. Obviously, when we think of steel we think of its “hardness.” It is used in a lot of heavy-duty construction, after all.

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An example of a physics problem with steel assigned via WebAssign.

It just so happened that at precisely this time, we were learning about alloys in chemistry, and I remembered specifically my teacher talking about steel being an alloy of iron and carbon. Thus, I had a little flicker of inspiration and decided to connect the two and make a little presentation for my physics class. An added bonus? A little bit of extra credit.

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A snippet of my chemistry notes regarding alloys

An Introduction to Alloys

Well, an alloy is simply a mixture of two elements. Metallic alloys are when both of the elements being mixed are metals, as the name implies. With regards to alloys, there are actually two distinct types (as you may have gotten a glimpse of looking at the excerpt from my chemistry notes).

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The substitutional solid solution (or alloy) is simple when some atoms in a metallic lattice structure are swapped with another. This is particularly useful in industry when slight alterations to the physical properties of a metal are of interest. In the case of brass, a very common substitutional allow, some zinc atoms take the place of copper atoms to add physical integrity. The copper, being very high on the activity series, gives the resulting compound a degree of chemical resistance

As an aside, it may be useful to think about what brass is used for! As an avid saxophonist, whenever I think of brass I think about the production of musical instruments. The saxophone is made out of brass, and so are the traditionally “brass” instruments like the trumpet, trombone, french horn, and tuba. Now why might brass be used for musical instruments? Sure, it looks nice and shiny, but given that it is a substitutional alloy of zinc and copper, there are far better reasons. The hardness of zinc is needed to help prevent dents and scratches, and the copper resists the tarnishing and corrosion that can happen due to the chemicals in our breath and spit!

Interstitial alloys are slightly different. Instead of having atoms being directly swapped out for others, new atoms are merely added within the “spaces” or “gaps” of the existing metallic lattice. As in the case of steel, some carbon atoms are inserted into the gaps between iron atoms. This adds a less flexible overall compound, or added rigidity. Not surprisingly, the larger the amount of carbon there is, the more hard but also more brittle.

Another interesting note that I’d like to share is the famous use of carbon steel (as it is called) in the production of ancient samurai swords. These swords are world-renowned for its ability to keep an edge as well as incredibly durability and effectiveness in battle. How this amazing balance between rigidity and malleability is achieved all depends on having the right carbon to iron ratio.

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Back to Collision Elasticity

So let’s recall what we remember (or have forgotten) about collision elasticity:

  1. Inelastic collisions do not conserve kinetic energy
  2. Elastic collisions do conserve kinetic energy

Or, stated equivalently:

  1. Inelastic collisions lose kinetic energy
  2. Elastic collisions do not lose kinetic energy

This distinction may or may not help you understand the next part of my thought process.

How Inelastic Collisions Lost Kinetic Energy

Since I’m trying to focus on the intuitive approach to real-world problems and phenomenon, forgive me if I’m doing “too much” by discussing what happens when an object falls from some elevated position to the ground. From an introductory physics class, we know that the object had some potential energy by nature of it’s elevated position (if we let the ground be the zero level) and that energy is conserved (except in the case of nuclear processes, but that’s beyond the scope of what’s going on here). Thus, when the object calls, it’s potential energy is converted to kinetic energy. But what happens when that object finally hits the ground?

It may seem like all of the energy just dissipated because the velocity suddenly became zero and thus kinetic energy becomes zero and because there is no potential energy, however, all of that energy really went into the thermal energy of vibrations in the molecules that make up the object and ground.

Similarly, when two objects collide inelastically, all of the kinetic energy that is “lost” is really just gained by the sporadic vibrations, or thermal energy, of the atoms/molecules that make up the different atoms. More vibrations after a collision mean more kinetic energy is converted into thermal energy.

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Increases vibrational, random motion of molecules in an object after collision.

Back to Steel

As we now know, steel is (due to the carbon imbedded within its chemical framework) is a very rigid compound. The iron atoms have little space to move around or vibrate.

By this logic, because it cannot physically library as much, it doesn’t have as much potential to convert kinetic energy into thermal energy! Finally, this leads us to the conclusion that steel is used in physics problems for elastic collisions because little energy is lost.

I know… a seemingly convoluted to approach such a simple thing, but it’s all about the process, is it not? 🙂

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