Simple question regarding vectors in examples of physics textbooks

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SUMMARY

The discussion centers on the differing representations of force summation in classical mechanics textbooks. Specifically, the user contrasts the equation for net force in introductory texts, which states F_{net}=T-mg, with a mechanics textbook that presents it as F_{net}=T+mg. The confusion arises from the treatment of gravitational force directionality and vector notation. Understanding the definition of tension (T) and net force (Fnet) as vectors, along with the positive direction convention, is essential for reconciling these differences.

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  • Classical mechanics principles
  • Vector notation in physics
  • Understanding of force diagrams
  • Knowledge of gravitational force representation
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  • Study vector representation in physics, focusing on force vectors
  • Review classical mechanics textbooks for different force summation approaches
  • Learn about the conventions of positive and negative directions in physics
  • Examine examples of force diagrams to clarify tension and gravitational force interactions
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Students of classical mechanics, physics educators, and anyone seeking to clarify the representation of forces in different physics textbooks.

ghostfolk
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I have noticed that in my classical mechanics course and in the textbook I read for it, the portion in examples that require to look at the sum of forces for the system is different than what I am accustomed to in introductory texts. For example, if we were dealing with a system with a ball of mass ##m## tied to a ceiling and were asked to find the forces, in an introductory textbook (as least the ones I read) would state the summation of forces as ##F_{net}=T-mg##. However, in the mechanics textbook it is written as ##F_{net}=T+mg##. I'm wondering why it seems that the downward aspect of the gravitational force is ignored. I figure that overall it doesn't make a difference, but I'm just curious for the author's reasoning as it leads me confused in both reading and comparing answers for exercises from the textbook.
 
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Try reading the textbook more carefully to understand how T and Fnet are defined the notion of what direction is positive is critical to understanding the equation.
 
Chances are that the text that type F=T+Mg, is using a notation where F, T and Mg are vectors.
fnet.jpg
 
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