What Is the Minimum Coefficient of Friction Required to Navigate a Curve Safely?

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Homework Help Overview

The problem involves a car navigating a flat, unbanked curve on a highway with a specified radius and speed. The goal is to determine the minimum coefficient of friction required to prevent the car from sliding off the curve.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between centripetal force and frictional force, with some attempting to derive the necessary equations. Questions arise regarding the absence of mass in the problem and how to proceed without it.

Discussion Status

Some participants have offered guidance on equating centripetal force to frictional force, while others express uncertainty about the implications of missing mass. Multiple interpretations of the problem setup are being explored, and there is an ongoing exchange of ideas without a clear consensus.

Contextual Notes

Participants note the lack of mass information as a constraint in their calculations, which is affecting their ability to proceed with the problem-solving process.

reticpythons
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Homework Statement


A flat (unbanked) curve on a highway has a radius of 260 m. A car rounds the curve at a speed of 18.0 m/s . What is the minimum coefficient of friction that will prevent sliding?


Homework Equations



A= v2/R I got the acceleration but the problem does not give the mass for caluculating the normal force

The Attempt at a Solution


1.246 m/s is what I got for the acceleration after that I do not know what I should be doing.
 
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Hi reticpythons, welcome to PF.
The car rounds the curve due to the centripetal force provided by the frictional force.
write down the expression for both and equate them to get the required result.
 
the centripetal force is v2/R but I can not think of what i need to equate it to Fnet= Fn-fk=ma but I do not have mass or I might be totally spacing something I should know but I am looking through my notes and can not find or think of anything
 
reticpythons said:
the centripetal force is v2/R but I can not think of what i need to equate it to Fnet= Fn-fk=ma but I do not have mass or I might be totally spacing something I should know but I am looking through my notes and can not find or think of anything
Normal force is mg and frictional force is μ*mg.
Centripetal force is m*v^2/r. Frictional force provides centripetal force to the car to go round the curve without skidding.
Equate them to find μ.
 

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