Top speed of vehicle on a curved road

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Homework Help Overview

The problem involves determining the top speed of a vehicle navigating a curved road, given specific parameters such as the radius of the curve and the coefficient of static friction. The subject area pertains to mechanics, particularly the dynamics of circular motion and frictional forces.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the forces acting on the vehicle, including weight, centrifugal force, and friction. There is an emphasis on the relationship between these forces and the motion of the vehicle around the curve. Some participants express confusion about how to apply the equations related to these forces.

Discussion Status

The discussion is ongoing, with participants attempting to clarify the relationships between the forces involved. Some have offered insights into setting equations equal to each other to find the speed, while others are still grappling with the concepts and how to proceed.

Contextual Notes

Participants note the importance of drawing a diagram to visualize the forces, and there is mention of the need to consider the mass of the vehicle, which ultimately cancels out in the equations. There is no consensus yet on the best approach to solve the problem.

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Homework Statement



Fifteen clowns are late to a party. They jump into their sporty coupe and start driving. Eventually they come to a level curve, with a radius of 31.5 meters. What is the top speed at which they can drive successfully around the curve? The coefficient of static friction between the car's tires and the road is 0.800.

Homework Equations



Ac=V^2/r
Fc=mv^2/r


The Attempt at a Solution



I don't know...i'm kinda confused on this problem
 
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In mechanics the first step is always to draw a diagram of the forces.
You have the weight of the car (acting downwards) the centrifugal force acting outward parralel to the rowd and friction acting inward (opposing the outward slide)

Note, Friction force is = friction coef * downward force.
 
hmm i know F,friction= coef friction x normal force...but its still not helping me
 
You know the outward force F = m V^2 / r
You know the frictional force resisting this F = cf * weight = cf m g

Set these equal and solve for V, note that m cancels, you don't need to know it.
 

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