Why is weight positive if gravity is negative?

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SUMMARY

The discussion addresses the concept of weight in physics, specifically why weight is considered positive despite gravity being a negative force. The equation W = mg is highlighted, where W represents weight, m is mass, and g is the acceleration due to gravity. The key conclusion is that weight is defined as a magnitude, which is always positive, while the direction of the weight vector is downward. The positive constant for g reinforces that weight is expressed as a positive value, focusing on magnitude rather than direction.

PREREQUISITES
  • Understanding of basic physics concepts, specifically Newton's laws of motion.
  • Familiarity with the equation W = mg, where W is weight, m is mass, and g is gravitational acceleration.
  • Knowledge of vector quantities and their representation in physics.
  • Comprehension of the distinction between magnitude and direction in physical quantities.
NEXT STEPS
  • Explore the implications of vector quantities in physics, focusing on direction and magnitude.
  • Study the concept of gravitational acceleration, specifically the value of g on Earth (approximately 9.81 m/s²).
  • Investigate how weight is affected by changes in mass and gravitational force in different environments.
  • Learn about the applications of weight in real-world scenarios, such as engineering and aerospace dynamics.
USEFUL FOR

Students studying physics, educators teaching fundamental concepts of mechanics, and anyone interested in understanding the relationship between mass, weight, and gravity.

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Homework Statement


Why is weight positive if gravity is negative?


Homework Equations


W = mg


The Attempt at a Solution


So say there is some weight of an object, and the object's mass is multiplied by the acceleration due to gravity pointing downwards, so the weight becomes negative when the positive mass is multiplied by a negative acceleration. Weight should then be negative, but why is weight always positive?
 
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W = mg just gives the magnitude of the weight, which is positive. The direction of the weight vector is downward. (Note that g is a positive constant.) Often when you talk about the weight of something you just mean the magnitude.
 

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