What Angle Is the Road Banked for a 1000kg Car on a 25m Radius Track at 30m/s?

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Homework Help Overview

The discussion revolves around determining the angle at which a road is banked for a car of mass 1000kg traveling on a frictionless track with a radius of 25m at a speed of 30m/s. The problem is situated within the context of dynamics and circular motion.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the relationship between the normal force and the angle of banking, with one participant attempting to calculate the normal force to find the angle. Questions are raised about the components of forces acting on the car, particularly the component of weight directed towards the center of the circular path.

Discussion Status

There is an ongoing exploration of the forces involved, with participants suggesting the use of free body diagrams and trigonometric relationships to find the angle. Multiple interpretations of how to relate the forces to the angle of banking are being discussed.

Contextual Notes

Participants note the absence of certain information, such as the angle itself, which is central to the calculations. The discussion also highlights the need to consider the centripetal force in relation to the banking angle.

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Homework Statement


a 1000kg car negotiates a banked friction free track or radius 25m with speed 30m/s

to what angle to the horizontal is the road banked?


Homework Equations





The Attempt at a Solution


tried to calculate the normal force of the car, to find the angle between the weight vector and the normal force vector, which would be equal to the angle that the road is banked.
However, I could not find the angle fo the normal force
 
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If the angle of baking is θ, what is the component of the weight that points towards the center of the path?
 
mgsin theta, you don't know theta though..
 
superaznnerd said:
mgsin theta, you don't know theta though..

A free body diagram will allow you to use trigonometry to find theta.
 
superaznnerd said:
mgsin theta, you don't know theta though..

if that force provides the centripetal force, you can find θ.

Fc=mv2/r remember?
 

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