Tension Equation Question - Algebra Related

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SUMMARY

The discussion centers on the tension equation for an upward moving object, specifically T - mg = ma. The correct solution for tension (T) is T = m(g + a), which confirms that mass (m) appears on both sides of the equation. The participant clarifies that the apparent disappearance of one mass is resolved through proper algebraic manipulation, reinforcing the importance of factoring in algebra. The conclusion emphasizes the necessity of understanding algebraic principles to solve physics equations accurately.

PREREQUISITES
  • Understanding of basic algebraic manipulation
  • Familiarity with Newton's second law of motion
  • Knowledge of the concepts of mass (m), gravitational acceleration (g), and acceleration (a)
  • Ability to factor equations in algebra
NEXT STEPS
  • Study the principles of Newton's laws of motion
  • Practice algebraic factoring techniques
  • Explore tension in various physical contexts, such as pulleys and inclined planes
  • Learn about the implications of mass and acceleration in dynamic systems
USEFUL FOR

Students in physics and mathematics, educators teaching algebra and mechanics, and anyone seeking to improve their understanding of tension in physical systems.

crono_
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Just a quick question regarding the following equation for tension of an upward moving object.

T - mg = ma

According to my textbook (for this question at least), solving for T gives us...

T = m (g + a)

Looking back at the initial equation we have an m on both sides of the equal sign. But when bringing - mg to the other side and thus solving for T we then only have one m. Where did the second m go?

Thanks!
 
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T = m(a+g) = mg + ma. See. There are two ms .
 
That makes perfect sense! Thank you! :)

Forgive my ignorance, I've got a lot to brush up on with math and algebra, that is called factoring...right?
 

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