Quick sign question for uniform circular motion

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Homework Help Overview

The discussion revolves around a problem in uniform circular motion, specifically regarding the maximum speed a car can maintain while turning without sliding. The scenario involves a 1500kg car navigating a curve with a radius of 50m on a level road.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster questions the sign convention used in the equation for centripetal force, particularly why the force is considered positive despite its direction in the free body diagram. Other participants clarify that the relevant direction is centripetal, not left or right.

Discussion Status

Participants are exploring the concept of centripetal force and its representation in equations. Some guidance has been provided regarding the sign convention, indicating that as long as the force points toward the center, it is treated as positive. There is an ongoing examination of how to interpret forces in the context of circular motion.

Contextual Notes

There is a focus on understanding the implications of directionality in force diagrams and how it relates to the equations governing circular motion. The discussion does not resolve the original poster's confusion but provides insights into the reasoning behind the sign convention.

hachi_roku
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Homework Statement


what is the maximum speed with which a 1500kg car can make a left turn around a curve of radius 50m on a level road without sliding?




Homework Equations





The Attempt at a Solution


i already got the answer...but my question is:

f_s points left and the equation sigmaF_r =
f_s = mv^2/r

why isn't it negative if the force in the free body is pointing left? is it because the car is turning left?
 
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The F in F = mv^2/r is the force in the direction of the center of the turning circle. The friction force is in that direction, so it is positive. I don't think you want to confuse things by thinking about left and right when the essential direction is centripetal - toward the center.
 
the book says the radial component is simply the magnitude of the vector...so in doing probs with uniform circular motion, where a is pointing towards the center...it is positive regardless of where it points in the free body diagram?
 
Yes, positive as long as it points toward the center.
 
thank you
 

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