Solve Physics Problems: Splitting Algebraic Equations | Step-by-Step Guide

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In summary, the person is having a problem understanding a physics problem and needs help from someone. They have isolated variables and are stuck but are grateful for the help that is offered.
  • #1
Physics Dad
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Hi,

I am having a real senior moment and can't quite get my head around a physics problem.

I need to split an equation into two parts, in turn creating a coefficient and my mind has gone totally blank!

I need to split the Maxwell-Boltzmann distribution formula from:

f(v) = 4π(m/2(pi)kbT)3/2v2e(-mv2/2kbT)

formula into the following:

f(v) = aT-3/2v2e(-mv2/2kbT)

where a is a coefficient to be determined.

I understand that I am isolating variables in order to create a coefficient (a) but every time I get going I lead myself down a merry path and end up with something different!

Any help would be gratefully received
 
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  • #2
well, the second part of the formula(after ##v^2##) is equal in both forms so we only have to consider ##4\pi(\frac{m}{2\pi K_bT})^{\frac{3}{2}} = aT^{\frac{-3}{2}}##
remember that ##\frac{1}{T^{x}} = T^{-x}## and there you are
 
  • #3
I am getting an answer but I don't have confidence in my reasoning behind it.

Basically, if 4π(m/(2kbT))3/2=aT-3/2

am I right in thinking that T-3/2 becomes 1/T3/2?

if so, after doing a bit of rearranging magic from here, I get the answer that a=4π(m/2kb)3/2

I just feel like I am getting algebra blindness!

Thanks in advance for your patience!
 
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  • #4
yep, i also want you to notice that it is really immediate to see ##4\pi(\frac{m}{2\pi K_bT})^{3/2} = 4\pi(\frac{m}{2\pi K_b})^{3/2}T^{-3/2} = aT^{-3/2}## so the ##T^{-3/2}## just get canceled out and there's no magic at all :P

so you basically missed a ##\pi##, probably just for distraction, but you're there:
##a = 4\pi(\frac{m}{2\pi K_b})^{3/2}##
now ##4\pi \frac{1}{(2\pi)^{3/2}}## can be further simplified, give it a try
 
  • #5
Thanks a lot, and yes, you're right, I missed the π from the denominator.

I know it is obvious to see the cancellation, but I wanted to make certain by expanding and then just cancelling down to be sure.

Your assistance has been really greatly appreciated. I am sure it won't be the last time I am asking but it is great to know that a facility like this exists.
 

1. What is the purpose of splitting algebraic equations in solving physics problems?

Splitting algebraic equations in solving physics problems allows us to isolate specific variables and solve for them individually. This makes the problem more manageable and easier to solve.

2. How do you determine which variable to isolate first when splitting an algebraic equation?

The variable that is causing the most confusion or is the most complicated to solve for should be isolated first. This will make the problem easier to understand and solve.

3. Can you provide an example of splitting an algebraic equation in a physics problem?

Sure, let's say we have the equation F = ma, and we need to solve for acceleration. We would first isolate the acceleration by dividing both sides by the mass, giving us a = F/m.

4. What are some common mistakes when splitting algebraic equations in solving physics problems?

One common mistake is forgetting to apply the same operation to both sides of the equation. Another mistake is not properly isolating the variable and ending up with an incorrect answer.

5. How can I check my work when splitting algebraic equations in solving physics problems?

You can check your work by plugging your solution back into the original equation and making sure it satisfies the given conditions. You can also use a calculator to double check your calculations.

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