Simplifying the Equation: A Step-by-Step Guide for Beginners

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In summary, the conversation discusses the process of simplifying the equation 2\pi \sqrt{ \frac {Ml^2+2Mr^2/5+m(l-r)^2/3} {(Ml+m(l-r)/2)g}} using given values for the variables M, m, l, and r. The speaker is unsure of which parts of the equation are important and asks for clarification. The simplification would result in ~Mlg in the denominator and for very small r, l2 would be used instead of (l-r)2. The values of r/l and m/M are also mentioned.
  • #1
LENIN
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I have to find out how to make this simplification
[tex]2\pi \sqrt{ \frac {Ml^2+2Mr^2/5+m(l-r)^2/3} {(Ml+m(l-r)/2)g}} \approx 2\pi \sqrt{\frac{l}{g}(1+\frac{2r}{5l}-\frac{1m}{6M})}[/tex].

This is for a project I have to do, but I have never done any such simplifications before. I don't know which parts of the equation are important and which aren't. If it helps this are the values of the variables:

[tex]M\approx10kg[/tex]
[tex]m\approx20g[/tex]
[tex]l=227cm[/tex]
[tex]r=6cm[/tex]
 
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  • #2
[tex](Ml+m(l-r)/2)g[/tex] would simplify to ~Mlg, in the denominator under the root.

(l-r)2 would simplify to l2 for very small r, otherwise l2-2rl since r2 would be small.

r/l = 6/227 = 0.026

m/M = 0.02/10 = 0.002 so M-m ~ M is a good approximation.
 
  • #3
Thank you.
 

1. How do I know which steps to take when simplifying an equation?

When simplifying an equation, start by looking for any like terms that can be combined. Then, use the order of operations (PEMDAS) to simplify any parentheses, exponents, multiplication, division, addition, and subtraction in that order.

2. What is the purpose of simplifying an equation?

Simplifying an equation can make it easier to solve or understand, as it reduces the number of terms and operations. It also allows for easier comparison between multiple equations.

3. Can I skip steps when simplifying an equation?

No, it is important to follow each step in order to accurately simplify the equation. Skipping steps could result in an incorrect solution.

4. What should I do if I get stuck while simplifying an equation?

If you get stuck while simplifying an equation, go back and review the previous steps to see if you missed any like terms or made a mistake. You can also try breaking the equation into smaller parts and simplifying them individually.

5. Is there a specific method or strategy for simplifying equations?

Yes, the most common method is to use the order of operations and combine like terms. However, there may be other strategies that work better for certain equations, so it is important to practice and find what works best for you.

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