Step-by-Step Guide: Solving Equations with Multiple Variables"

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SUMMARY

This discussion focuses on solving a system of equations involving multiple variables, specifically three equations with three unknowns derived from Newton's second law. The equations presented are m1a1 = m1g - T, -m2a2 = m2g - 2T, and a1 = 2a2. Participants emphasize the necessity of having an equal number of equations and unknowns to achieve a unique solution, highlighting the importance of clarity in defining the problem context.

PREREQUISITES
  • Understanding of Newton's second law of motion
  • Knowledge of systems of linear equations
  • Familiarity with algebraic manipulation techniques
  • Basic problem-solving skills in physics
NEXT STEPS
  • Study methods for solving systems of linear equations, such as substitution and elimination
  • Learn about matrix representation and the use of determinants in solving equations
  • Explore the application of Newton's laws in various physics problems
  • Investigate the implications of having more unknowns than equations in mathematical modeling
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This discussion is beneficial for students in physics, educators teaching introductory mechanics, and anyone interested in mastering systems of equations in mathematical contexts.

electron5
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How to solve this equation step by step?

m1a1 = m1g - T
-m2a2 = m2g - 2T
a1 = 2a2

How to solve a1, a2 and T?
 
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Hi electron5. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

It looks like you have 3 equations in 5 unknowns, is that correct?

What would you consider as "the solution" to that? Usually, if you need to solve for 5 unknowns you'll need 5 equations to give that unique solution.

Better explain what you are trying to do, and where these came from.
 
Last edited by a moderator:
NascentOxygen said:
Hi electron5. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

It looks like you have 3 equations in 5 unknowns, is that correct?

What would you consider as "the solution" to that? Usually, if you need to solve for 5 unknowns you'll need 5 equations to give that unique solution.

Better explain what you are trying to do, and where these came from.

Since this is an introductory physics question I'd guess it is, from looking at it, one of the basic Newtons second law type questions, where m1 and m2 are known, so really it's three equations with three unknowns!

And to the OP, how do you usually solve systems of linear equations?
How would you solve the system;
x + 2y = 25
2 x +y = 20
 
Last edited by a moderator:

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