## ← 04ps-15 Dimensional Analysis

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Showing Revision 1 created 07/03/2012 by Amara Bot.

1. In this question, you're going to use dimensional analysis, which is a tool we mentioned
2. briefly in the unit, to do some basic analysis of two fairly advanced physics equations.
3. Here we have E=mc², one of Einstein's famous equations which relates mass and energy.
4. Energy isn't something we've talked about in class yet but with dimensional analysis
5. you don't need to know what energy is to be able to quantify its units and the way
6. we did dimensional analysis was we realized we can write the unit of just
7. about any physical quantity in terms of mass, length, and time.
8. So mass rates some power, lengths to some power, and time to some power.
9. So using your knowledge that m is the unit of mass and c is the unit of velocity or speed
10. you should be able to figure out what the units of energy are even if you do not know what it is yet.
11. That would be step one, but I really want you to do and what I want you to solve for this problem
12. I want you tell me the units of this number ħ, an ħ is a number that shows up
13. in quantum mechanics, which is a fascinating field of physics all the time.
14. So even if you have no idea what some of these symbols mean, there's
15. actually still a lot you could learn about this equation.
16. Let's take a look at this term for example.
17. 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.
18. So for example, I don't have to pay attention to this guy at all.
19. This is the Greek letter Ψ Zand it's dimensionless, so we can ignore it.
20. This d are just some instructions of some math to do so you
21. don't have to pay attention to those either.
22. The negative sign doesn't really matter and the 2 doesn't matter either.
23. So what we've left with is this. This is the relevant part to this equation unit wise.
24. Well, we have ħ²--we'll for something with units of mass times x which is L².
25. We know that this whole term has units of energy then what are the units of ħ?
26. You know we can write this as mass to the something, L to the
27. something and T for the something.
28. I've called those somethings a, b, and c. Enter in your answers here.
29. One of the points of this problem is to show you that even with very complicated physics
30. there's some very simple analysis that we already have the tools to do.
31. Now if you're having trouble solving this one, don't worry, it's another tricky question
32. so as always go to the forums for help.