Centripetal Force - Banked Curve

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Homework Help Overview

The problem involves a 1000kg car navigating a frictionless banked curve with a radius of 80m and a banking angle of 20 degrees. The focus is on determining the specific speed required for the car to maintain a constant radius while considering the forces acting on it.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of perpendicular and parallel components of gravitational force on the incline, questioning why the perpendicular component is relevant in this context. There is also a mention of deriving equations based on the forces acting on the car.

Discussion Status

The discussion is active, with participants exploring the relationships between forces and motion on a banked curve. Some have provided diagrams and equations to clarify their reasoning, while questions about the definitions of parallel and perpendicular forces remain open.

Contextual Notes

Participants are navigating the complexities of force components in the context of banked curves, with an emphasis on understanding the physical implications of these components in relation to the car's motion.

Nicolaus
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Homework Statement


A 1000kg car travels around a frictionless banked curve having a radius of 80m. If the banking is 20 degrees to the horizontal, at which specific speed must the car travel to maintain a constant radius?


Homework Equations


Fc = mv^2/r
Fg(perp.) = mgcos(20)

The Attempt at a Solution


Would someone explain to me why we use the perp instead of the parallel angle on the incline? Is it because the car is traveling in the straight (toward the plane) direction along the banked curve?
 
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What do you mean by "parallel" and "perpendicular" angles?
 
I meant the force of gravity parallel and perp to the incline.
 
In the parallel and perpendicular coordinate axes, what is the reaction force and what is the acceleration?
 
Here's a diagram I made. N_x=m*v^2/r and N_y-G=0
we get two equations
N*sin20=mv^2/r and
N*cos20=mg
Then solve for v.
 

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Thank you.
 

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