Displacement from velocity and time dependent force

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Homework Help Overview

The problem involves determining the displacement function x(t) from a force that is dependent on both velocity and position, specifically given by F(x) = Av²/x, with initial conditions x(0) = 0 and vx(0) = 0.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the setup of the problem using the equation mdv/dt = F and express difficulty in separating variables due to the velocity's dependence on position. One participant suggests using the chain rule to express dv/dt in terms of dv/dx and dx/dt. Another participant questions the validity of canceling terms in their derived equation.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to handle the relationship between velocity and position. Some guidance has been offered regarding the use of the chain rule, but there is no explicit consensus on how to proceed with the problem.

Contextual Notes

Participants are navigating the complexities of a force that varies with both velocity and position, which may lead to assumptions about the relationships between these variables. The initial conditions provided may also impose constraints on the discussion.

briteliner
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Homework Statement



The Force is F(x)=Av2/x. find x(t) if x(0)=0 and vx(0)=0

Homework Equations





The Attempt at a Solution


My issue is that i set this up as mdv/dt=F but when i try to separate the variables i don't know what to do about the v since it depends on x. any suggestions?
 
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briteliner said:
… My issue is that i set this up as mdv/dt=F but when i try to separate the variables i don't know what to do about the v since it depends on x. any suggestions?

Hi briteliner! :smile:

Standard trick …

dv/dt = dv/dx dx/dt (chain rule) = v dv/dx :wink:​
 
okay, so i do that.. and i get that (mv)dv/dx-kx(dv/dx)=0. can i cancel the dv/dx?
 
briteliner said:
… (mv)dv/dx-kx(dv/dx)=0 …

uhh? :redface: have you changed the question? :confused:
 

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