How to prove inertial force is potential force.

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Homework Help Overview

The discussion revolves around the concept of proving that inertial force is a potential force within the context of classical mechanics. Participants are exploring the definitions and implications of inertial forces and their relationship to potential energy.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to establish a relationship between inertial force and potential force using equations related to work and energy. Some participants question the definition of "inertial force" and its implications, while others express confusion about the nature of proving arbitrary forces as potential forces.

Discussion Status

The discussion is ongoing, with participants raising questions about the definitions and assumptions related to inertial forces. There is a lack of consensus, as some participants find the original poster's approach unclear, while others are seeking clarification on the fundamental concepts involved.

Contextual Notes

Participants are navigating the complexities of defining inertial forces and their potentiality, with some expressing skepticism about the feasibility of proving arbitrary forces as potential forces. The discussion may be constrained by the need for clearer definitions and the context of the homework assignment.

michaelexe
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Homework Statement



Prove inertial force is potential force.

Homework Equations



$$\mathbf{F}_i=-\nabla V_i$$

The Attempt at a Solution


$$\oint \mathbf{F}_i\cdot d\mathbf{r}=0$$
 
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What is "inertial force"?
 
$$\mathbf{F}=m\mathbf{a}$$
$$\mathbf{F}-m\mathbf{a}=0$$
$$\hbox{inertial force}\mathbf{F_i}=-m\mathbf{a}$$
$$\mathbf{F}+\mathbf{F_i}=0$$
 
inertial force

$$\mathbf{F}=m\mathbf{a}$$
$$\mathbf{F}-m\mathbf{a}=0$$
$$\hbox{inertial force}\mathbf{F_i}=-m\mathbf{a}$$
$$\mathbf{F}+\mathbf{F_i}=0$$
 
That is not making any sense. If ##F## is an arbitrary force, then ##F_i## is also an arbitrary force. Are you required to prove that an arbitrary force is potential? That won't work.
 

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