Friction problem with banked curve given static friction coefficient

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Homework Help Overview

The problem involves determining the maximum speed of a rubber-tired car navigating a banked curve, given specific parameters such as the radius of the curve, the angle of the bank, and the coefficient of static friction. The context is centered around concepts of forces acting on the car, including normal force, weight, and friction.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the forces acting on the car, including the normal force and friction. There is an exploration of the equations governing the motion, with attempts to derive the maximum velocity without slipping. Some participants question the assumptions made regarding acceleration and the setup of force equations.

Discussion Status

The discussion is ongoing, with participants providing insights into the problem setup and questioning the original poster's approach. There is a suggestion to analyze the vertical and horizontal components of forces separately, indicating a productive direction for further exploration.

Contextual Notes

Participants note the importance of correctly identifying the forces in both the vertical and horizontal directions, as well as the implications of the incline angle on the calculations. There is an acknowledgment of potential misunderstandings regarding the maximum velocity and the role of static friction.

zenith12
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Homework Statement



What is the maximum speed with which a 1200 rubber-tired car can take around a banked curve with radius of 80.0 meters an angle of 19.0 degrees? (static friction coefficient is 1.0)


Homework Equations


Fs=mu*F(normal)
F(netxdirection)/m=acceleration
acceleration=velocity2/radius


The Attempt at a Solution


I tried answering this problem several times and I failed at each; although I swear my first answer was correct (31.6 m/s). My professor's answer was 40.1 m/s and I have no idea how he got that.

Please help...
 
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Show how you solved it. What are your vertical and horizontal force equations?
 
Hey...sorry for being so short. I was in a hurry to just get the question asked. I spent all day on homework and no time to fully explain.

Here are my notes on this problem:

Known:
incline angle=19.0 degrees
Radius of turn=80.0 m
Mass of car=1200 kg
mu(s) tire on cement road=1.0

Forces:
Normal
Weight
Friction

Find:
Max velocity without slipping on cement

Steps:
1. Find Friction force by finding the Normal force for the y-axis by adding up the forces in the y direction. This was done by F=ma. Acceleration=zero, so solved for Normal.
2. Enter Normal in Friction equation (F=mu*N) to get Friction force.
3. Enter Friction force in F(netx)=ma for x-axis to solve for acceleration in the x direction which is also the radial/centripetal direction btw.
4. Use a=v^2/r to find the velocity.

Maybe this velocity is not the maximum? Am I missing something conceptual?
 
zenith12 said:
1. Find Friction force by finding the Normal force for the y-axis by adding up the forces in the y direction. This was done by F=ma. Acceleration=zero, so solved for Normal.
Careful! The acceleration is horizontal, so you cannot say that the acceleration is zero normal to the incline.

Instead, analyze vertical and horizontal force components. Set up two equations and solve them together.
 

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