Centripetal Force - Banked Curve

AI Thread Summary
To determine the speed at which a 1000kg car must travel on a frictionless banked curve with a radius of 80m and a banking angle of 20 degrees, the centripetal force equation Fc = mv^2/r is applied. The discussion clarifies the use of perpendicular and parallel components of gravitational force, emphasizing that the perpendicular component (Fg(perp.) = mgcos(20)) is relevant for maintaining the car's circular motion. Participants explore the significance of these components in deriving the necessary equations for speed, specifically N*sin(20) = mv^2/r and N*cos(20) = mg. The solution involves solving these equations to find the required speed. Understanding the distinction between parallel and perpendicular forces is crucial for correctly applying the physics of banked curves.
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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