The meaning and purpose of constants in physics (1 Viewer)

[Delirium]

When you see a constant in an equation in physics, what does it mean and what is its purpose? This has always puzzled me... What about this whole deal with "using SI units", etc... What influence does a change of units have on constants in physics? I read in Wikipedia that certain units exist (planck units, I think), where if you use them, all constants in physics may be made to equal 1... why is that? How does that relate to my previous question of purpose and meaning?

 

[alcalder]

As far as I can determine (and can I say this is a really interesting question), constants are there to establish an equality between values.

We can definitely say that certain variables are proportional is some way, eg that the Energy of a photon is proportional to its frequency. However, to establish the equality we need that number ie the constant (which would be the gradient of the E v f curve, in this case).

Indeed, constants are reliant on units because we use particular units when calculating the constant. If we were to change the units (and say measure Force in kg wt and not Newtons - why you would do that, I don't know but I have seen it done in some 4U Maths books) then you are using a different scale and therefore would have a different gradient on the curve and a different constant.

The reason we have SI Units is so that there is a consistent use of units across the world - remember the Mars lander that stuffed up because someone used SI Units and someone else used US Imperial measurements.

I guess if we define Units in such a way, the constant can be made to be 1 eg
F=ma, has no constant of proportionality, neither does v=lambda.f

Hope that helps.

 

[Trebla]

When you measure dependent variables (i.e. something that relies on another thing) you may measure a direct relationship between two variables. In mathematics you have learnt that when you have a relationship between two variables you say one variable is in proportion to the other variable (e.g. force is proportional to mass). However, you do NOT say (as a generalisation) that they are equal, because obviously they aren't. Therefore to make them equal you must multiply one of variables by a certain number (i.e. a constant) to get an equality relationship.
For example, a formula you will encounter in Year 12 is E = hf....
E = energy
h = planck's constant
f = frequency
Where did this formula come from?
Well to keep it simple, we know that there is a relationship between energy and frequency. However, they are not equal. So we say they are in proportion to each other. Mathematically speaking, say we let E = constant x f. To find that constant we use mathematical linear functions after having a set a values for E and f and we can get Planck's constant.
A more familiar example you may have seen is the inverse square law.
If you are a mathematical type of person, you may treat the constants of some equations like gradients to get y = mx + b linear function. For example for E = hf, the E can be the y-axis, the f can be the x axis and the h is the gradient (which is a constant).

 

[Delirium]

Thank you everybody. This has helped get the proper picture in my mind. Hopefully I won't have any more issues with visualizing things like this.

 

[Forbidden.]

..... remember the Mars lander that stuffed up because someone used SI Units and someone else used US Imperial measurements ......

Where ?

I will be grateful if you direct me to an article, recount or any form of information regarding this incident.


And I hate it when formulas like E = Pt don't use SI units, makes it so confusing ...
I thought an appliance using 1000 Watts for 2 hours was using up 3,600 kWh because I assumed t whose SI unit for time is in seconds, but noooo .... It's 1000 x 2 so it's 2000 kWh ....

 

[alcalder]

Here you go, a link about the mix-up, although I note at the bottom of the Wikipedia page there is a link to another site which suggests that the metric mix-up may not have been the problem.

http://en.wikipedia.org/wiki/Mars_Climate_Orbiter

And another note about UNITS! This is why you should always put units (inclusing the units of the constant) into your working, to make sure you know that you are using the correct units. Thus, knowing that Power is being recorded in kWh, then you would be aware that time should be in hours and not seconds.

How to do this -

Do the working with the numbers on the left and then to the right have all the units. It kind of works, but you also need to keep in mind that certain units are made up of other units eg Hertz = s^-1 since v=lamba.f (ie ms^-1=m x Hz)

 

[Forbidden.]

Here you go, a link about the mix-up, although I note at the bottom of the Wikipedia page there is a link to another site which suggests that the metric mix-up may not have been the problem.

http://en.wikipedia.org/wiki/Mars_Climate_Orbiter

And another note about UNITS! This is why you should always put units (inclusing the units of the constant) into your working, to make sure you know that you are using the correct units. Thus, knowing that Power is being recorded in kWh, then you would be aware that time should be in hours and not seconds.

How to do this -

Do the working with the numbers on the left and then to the right have all the units. It kind of works, but you also need to keep in mind that certain units are made up of other units eg Hertz = s^-1 since v=lamba.f (ie ms^-1=m x Hz)

And that is why there are SI Units, which save me from more confusion I already have to deal with ... Now that I have become so dependant on them any formula that does not use SI units e.g E = Pt (and my teachers special "Klumpp Dilution Euqation*) "I will make unusual mistakes ...


* Klumpp Dilution Euqation (Chemistry)

Used to find the concentration or volume of an acid or base. Volume doesn't have to be in SI Units ...

m_av_a=m_bv_b


but the n = Mv has to be in SI Units, my teacher confuses me ....