Reaction force on a semi-cubical parabola

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Homework Help Overview

The problem involves a particle moving along a semi-cubical parabolic curve described by the equation y² = 4ax³. The focus is on determining the reaction force acting on the particle at a specific point on the curve while it moves with a constant speed.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the formula for the reaction force and the need to identify the radius of curvature. Questions arise regarding how to calculate this radius and its significance in the context of the problem.

Discussion Status

Some participants have suggested that the radius of curvature is relevant to the problem, while others have pointed out the need for clarification on how to find it. There is an acknowledgment of existing resources that may assist in understanding the concept further.

Contextual Notes

There appears to be some confusion regarding the interpretation of the variable 'r' and its role in the calculation of the reaction force. The discussion reflects a mix of attempts to clarify definitions and explore the mathematical concepts involved.

zorro
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Homework Statement



A particle of mass m moves without friction along a semi-cubical parabolic curve given by y2=4ax3 with a constant speed v. The reaction force of the curve on the particle when it is at the point (x = 1, y = 2) is given approximately by

The Attempt at a Solution



F=mv2/r

How do I find out 'r' here?
 
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I suggest that the r value is the radius of curvature of the path on which the particle travels.
 
I did not ask 'what does r stand for?'! :rolleyes:
 
Have you investigated how to find the radius of curvature of a curve? There's a http://en.wikipedia.org/wiki/Radius_of_curvature_%28applications%29" that might shed some light.
 
Last edited by a moderator:
Oh I see!...so there is a 'ready made' formula for that. Thanks!
 

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