Meaning of area under a acceleration vs mass curve

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SUMMARY

The discussion centers on the relationship between acceleration, mass, and force in physics, specifically addressing the misconception that the area under the acceleration vs. mass curve represents force. Instead, the area under the curve is defined as the integral \(\int \frac{F}{m} dm\), which does not equate to force. Participants clarify that the area under a curve in a graph of a function \(f(x)\) vs. \(x\) is represented by the integral \(\int f(x) dx\), emphasizing the importance of understanding integral calculus in this context.

PREREQUISITES
  • Understanding of Newton's Second Law of Motion
  • Basic knowledge of integral calculus
  • Familiarity with graphing functions
  • Concept of force, mass, and acceleration relationships
NEXT STEPS
  • Study the principles of Newton's Second Law in detail
  • Learn about integral calculus and its applications in physics
  • Explore graphing techniques for functions and their integrals
  • Investigate the relationship between force, mass, and acceleration through experiments
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Physics students, educators, and anyone interested in understanding the mathematical relationships between force, mass, and acceleration in physical systems.

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If I graph acceleration vs mass for constant force but variable mass experiment, shouldn't the area under the curve be the force? How do i determine the constant force from the graph?
 
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The area under the curve is not the force. The area equals the integral \int {\frac{F}{m}dm}.

In general when you make a graph of a function f(x) vs x then the area under the curve is NOT xf(x) it is rather the integral \int f(x)dx
 
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