VIPs: Very Important "Pers" (of The Power of "Per" Part 2)

VIPs: Very Important "Pers" (of The Power of "Per" Part 2)

In the previous article, The Power of Per, I discussed how equations can be bypassed by concentrating on language, on units and on the tiny work “per”. Formal mathematical relationships between quantities are ultimately shorthand for language, and our lives are experienced through language it seems sensible that so should our physics. In this article I’m sticking with the “per” theme, and looking at what the units of constants might tell us about the physics.

I discussed the gravitational field strength in the previous blog and this is a useful pointer for how units can help dive into the underlying physics, in this article I have the spring constant in my sights.

I’ll start by going off at a tangent, I have never liked the spring constant! I’m not necessarily holding Hooke responsible for this but I always felt it was upside down. If I were in Hooke’s shoes I would have wanted a number that would have described how something stretches when I apply a unit of force to it, in other words the extension per unit force, which would be measured in m/N. After all the experimenter is in charge of the applied force and the extension is outcome of that force, seems reasonable to me. However rather than the relationship being set up as the extension being dependent upon the applied force, we see a relationship in which the force exerted by the spring (as it attempts to restore its original length) is proportional to the extension, F = ke (or F = kx if that makes you happier).

So historical grumble now behind me, let’s look at the spring constant “k” and see what the units tell us. The units are N/m, so if you want to use the approach of the previous blog we should translate this into something like “the restorative force exerted by the spring for every metre it is extended” or (if we’re not worried about the force being applied to the spring or the spring exerting the force) “the extending force needed for every metre the spring is stretched”. Already this helps with making sense of a statement such as k = 80 N/m; we could say that if we wanted to stretch the spring by 1m then we’d need a force of 80 N. This is useful in comparing the stiffness of springs, as then it becomes obvious that if k = 120 N/m that it is a stiffer spring, as this requires a much larger force to stretch it by 1m. Granted there is a problem, one that I’ll leave you to solve, and that is that just about every spring I’ve ever used in school is only a few cm long so stretching it by 1 m may require a little imagination!

We have various constants and quantities that can be unlocked by looking at their units. Here’s a list (probably not complete) of units of some quantities and constants found at GCSE. These are the VIPs, the Very Important Pers.

• Velocity – m/s
• Acceleration – m/s² or m/s/s
• Frequency - /s (or Hz)
• Current – C/s
• Power – J/s
• Potential Difference – J/C
• Pressure – N/m²
• Density – kg/m³
• Gravitational field strength – N/kg
• SHC – J/kg/°C
• Specific latent heat – J/kg
• Spring constant – N/m

Using language can not only reduce the barrier to learning physics encountered whenever we write an equation on the board, it could remove it, showing that we can understand first of all and then use symbols afterwards. We know that many students lack confidence in maths and that this can be an insurmountable barrier. This can help build confidence in their ability to tackle physics, improve their enjoyment of the subject and actually develop real physics thinking.