Trouble with algebra at the end of an elasticity problem

In summary, algebra is crucial in solving elasticity problems and requires a strong foundation in mathematical concepts. To improve algebra skills, it is important to practice and seek help from a tutor or teacher. Common mistakes to avoid in algebra include misplacing negative signs and making calculation errors, and accuracy can be checked by plugging answers back into the original equation or seeking help from resources such as online calculators or tutors. Resources such as online tutorials, textbooks, and practice problems can also aid in improving algebra skills.
  • #1
K29
108
0
I have a spherical shell with inner radius [itex]a_{1}[/itex] and outer radius [itex]a_{2}[/itex]

I have worked out that the tension at [itex]r=a_{1}[/itex] is
[itex]\tau=\frac{2a_{1}^3+a_{2}^3}{2(a_{2}^{3}-a_{1}^{3})}P_{1}[/itex]

([itex]P_{1}[/itex] is pressure from the inside of the shell, causing the tension.

Now if the shell is not very thick. [itex]t=a_{2}-a_{1}[/itex] is small. [itex]\frac{t}{a_1}<<1[/itex]

and I should be able to show

[itex]\tau\approx\frac{a_{1}}{2t}P_{1}[/itex]

But I am not sure about the first step to take in getting there. Any ideas? Please help.
 
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  • #2
You can factor a difference of cubes.
 
  • #3
Thank you
 

1. Why do I struggle with algebra at the end of an elasticity problem?

Algebra is a fundamental tool in solving elasticity problems and requires a strong foundation in mathematical concepts. If you are struggling with algebra, it may be helpful to review basic algebraic principles and seek additional support from a tutor or teacher.

2. How can I improve my algebra skills for elasticity problems?

Practice is key to improving your algebra skills. Make sure to familiarize yourself with the formulas and equations used in elasticity problems and work through practice problems to strengthen your understanding. Additionally, seeking help from a tutor or teacher can also be beneficial.

3. What are some common mistakes to avoid in algebra at the end of an elasticity problem?

Some common mistakes in algebra at the end of an elasticity problem include misplacing negative signs, forgetting to distribute terms, and making calculation errors. It is important to take your time and double-check your work to avoid these mistakes.

4. How can I check my algebra work for accuracy in an elasticity problem?

You can check your algebra work by plugging your answers back into the original equation and seeing if it satisfies the conditions given in the problem. You can also use online calculators or ask a teacher or tutor to review your work for any errors.

5. Are there any resources available to help me with algebra at the end of an elasticity problem?

Yes, there are many resources available to help with algebra at the end of an elasticity problem. Online tutorials, textbooks, and practice problems can all be helpful in improving your algebra skills. Additionally, seeking help from a tutor or teacher can provide personalized support and guidance.

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