Understanding physical meaning

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Discussion Overview

The discussion centers around the physical meaning of the density formula and the frictional force formula, exploring how these concepts are defined and understood in both mathematical and empirical contexts. Participants examine the implications of these formulas in terms of their physical interpretations and the nature of the coefficients involved.

Discussion Character

  • Conceptual clarification
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant explains that the density formula conveys the relationship between mass and volume, defining density as mass per unit volume.
  • Another participant describes the frictional force formula "Ff = μN" as an empirical equation, emphasizing that the coefficient of friction μ is a constant of proportionality that depends on the materials in contact and whether the friction is static or kinetic.
  • A different participant points out that while density is defined mathematically, friction is defined physically as the parallel component of the force when bodies are in contact, highlighting the empirical nature of the coefficient μ.
  • A participant expresses confusion about the physical meaning of the frictional force formula, seeking clarity on how to interpret the coefficient of friction in relation to the forces involved.

Areas of Agreement / Disagreement

Participants generally agree on the definitions of density and friction but express differing views on the interpretation of the coefficient of friction and its empirical nature. The discussion remains unresolved regarding the deeper physical meaning of the frictional force formula.

Contextual Notes

Participants note that the coefficient of friction μ is determined experimentally and varies with the materials in contact, indicating a dependence on specific conditions that may not be universally applicable.

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I'm missing to understand the physical meaning of frictional force formula
For example, talking about density formula; it conveys the essence that if a container with volume"V" can hold "m" mass of substance then " d" will be the density.

Jumping on to frictional force formula "Ff = μN", how do I know the physical meaning of the coefficient of friction from the equation?
 
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F_{f}=\mu N
This is an empirical equation about the force of friction rather than one derived from first principles (e.g., summing up inter-molecular forces and such).

As such, the coefficient \mu really is just a constant of proportionality between the friction force F_{f} and the normal force N.

\mu is a function of what kind of materials are in contact with each other, and whether we are talking about static friction or kinetic friction. The values of \mu are found experimentally and tabulated rather than derived from more fundamental physics.
 
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Density is defined as “mass per unit volume”, so you see the definition of Density is purely mathematical, all it says is what will be the mass of a substance if we take a unit volume of that substance.

But when we come to friction it is defined as “the parallel component of the force when the bodies are in contact”, you can see that the friction is defined physically not mathematically. When experiments are done it was found that the parallel component of the force was proportional to the normal force acting on bodies in contact. The proportionality constant ##\mu## was also once again found empirically, and it was also found that it depends on nature of the materials in contact.
 
Seeker69 said:
Summary:: I'm missing to understand the physical meaning of frictional force formula

For example, talking about density formula; it conveys the essence that if a container with volume"V" can hold "m" mass of substance then " d" will be the density.

Jumping on to frictional force formula "Ff = μN", how do I know the physical meaning of the coefficient of friction from the equation?
It conveys the essence that if a contact compressed with force N resists sliding with force Ff then μ will be the coefficient of friction.
 

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