
Title:
04ps15 Dimensional Analysis

Description:

In this question, you're going to use dimensional analysis, which is a tool we mentioned

briefly in the unit, to do some basic analysis of two fairly advanced physics equations.

Here we have E=mc², one of Einstein's famous equations which relates mass and energy.

Energy isn't something we've talked about in class yet but with dimensional analysis

you don't need to know what energy is to be able to quantify its units and the way

we did dimensional analysis was we realized we can write the unit of just

about any physical quantity in terms of mass, length, and time.

So mass rates some power, lengths to some power, and time to some power.

So using your knowledge that m is the unit of mass and c is the unit of velocity or speed

you should be able to figure out what the units of energy are even if you do not know what it is yet.

That would be step one, but I really want you to do and what I want you to solve for this problem

I want you tell me the units of this number ħ, an ħ is a number that shows up

in quantum mechanics, which is a fascinating field of physics all the time.

So even if you have no idea what some of these symbols mean, there's

actually still a lot you could learn about this equation.

Let's take a look at this term for example.

Well there is a lot going on in this term but a lot of it does not affect the actual units of what's happening.

So for example, I don't have to pay attention to this guy at all.

This is the Greek letter Ψ Zand it's dimensionless, so we can ignore it.

This d are just some instructions of some math to do so you

don't have to pay attention to those either.

The negative sign doesn't really matter and the 2 doesn't matter either.

So what we've left with is this. This is the relevant part to this equation unit wise.

Well, we have ħ²we'll for something with units of mass times x which is L².

We know that this whole term has units of energy then what are the units of ħ?

You know we can write this as mass to the something, L to the

something and T for the something.

I've called those somethings a, b, and c. Enter in your answers here.

One of the points of this problem is to show you that even with very complicated physics

there's some very simple analysis that we already have the tools to do.

Now if you're having trouble solving this one, don't worry, it's another tricky question

so as always go to the forums for help.