Newtonian Mechanics - single particle

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Homework Help Overview

The discussion revolves around a problem in Newtonian mechanics concerning the motion of a particle with a speed that varies with distance, described by the equation v(x)=ax^(-n). Participants are tasked with finding the force acting on the particle, determining its position as a function of time, and subsequently the force as a function of time.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the derivation of the force from the given speed function, with one participant providing a formula for F(x) and referencing a textbook for validation. Others question the interpretation of constants in the equations and the application of fundamental principles such as F=m(dv/dt).

Discussion Status

The discussion includes attempts to clarify the relationship between speed, force, and acceleration, with some participants expressing confusion over the use of constants in the equations. There is no explicit consensus on the correctness of the approaches, but multiple interpretations and validations are being explored.

Contextual Notes

Participants are navigating through the implications of the variable definitions and constants in the equations, with some noting the limitations in notation available for their expressions.

McHead36
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Homework Statement


The speed of a particle of mass [m] varies with the distance[x] as v(x)=ax^(-n). Assume v(x=0)=0 at t=0.
a)Find the force F(x) responsible
b)Determine x(t)
c)Determine F(t)

Homework Equations


The Attempt at a Solution


My solution to part a is F(x)=-ma^2nx^(-2n-1).

Homework Statement


Homework Equations


The Attempt at a Solution

 
Last edited:
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F=m(dv/dt), not what you did.
 
Thats how i got to my answer for part a. I started with that and solved it to get F(x)=-ma^2nx^(-2n-1). This answer was also in the back of my book. I am stuck on part b and c.
 
The a in your first formula is not the acceleration.
It is just an arbitrary constant.
 
I know this already too. I put in "a" because I don't have a way to put in alpha.
 

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