Optimizing Velocity for Motion on a Banked Track

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Homework Help Overview

The problem involves an object moving around a banked circular track, where the goal is to determine the ideal velocity for the object to maintain a stable position without sliding, considering both frictionless conditions and scenarios with a friction coefficient.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the importance of drawing a free-body diagram and applying Newton's laws in both horizontal and vertical directions. There is a focus on how to incorporate the incline of the track into the analysis.

Discussion Status

Some participants have provided guidance on the initial steps, such as creating a free-body diagram and considering the forces involved. However, there remains uncertainty about how to effectively account for the incline in the calculations.

Contextual Notes

The original poster expresses a lack of understanding regarding the initial approach to the problem, particularly in relation to the incline of the track compared to a flat surface.

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Homework Statement


An object travels around a circular track with a given radius that is banked/inclined (inward) at a given angle. Find the ideal velocity for the object to travel around the track (so that it does not slide up or down but stays in the middle) with no friction or with a given friction coefficient.


Homework Equations



I have no idea how to begin to solve this or where to begin.

The Attempt at a Solution

 
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Start by drawing a free-body diagram, identifying all forces, and writing Newton's law for both the x and the y directions.
 
I have done this, but I want to know how i would take the incline of the track into account. The problem would be simple enough if it was on a flat track.
 
You need to account for the incline to draw gravity and the normal force at the correct angle to each other. Just draw the incline, draw the car, and analyze away.
 

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