Solve Banked Curve Problem: tan θ = ν^2/rg

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SUMMARY

The discussion centers on the mathematical proof for the relationship in a banked curve, specifically that tan θ = ν²/rg, where θ is the banking angle, ν is the velocity, r is the radius of the curve, and g is the acceleration due to gravity. Participants clarify that the normal force acts perpendicular to the road surface, while the centripetal force is directed horizontally towards the center of the curve. The relationship involves understanding the components of these forces in a right triangle formed by the normal force, gravitational force, and centripetal force. The banking angle of 45 degrees is also referenced, indicating a specific scenario for analysis.

PREREQUISITES
  • Understanding of basic physics concepts such as force, acceleration, and motion.
  • Familiarity with banked curves and their applications in physics.
  • Knowledge of trigonometric functions, particularly tangent, in relation to angles.
  • Ability to analyze force diagrams and resolve forces into components.
NEXT STEPS
  • Study the derivation of centripetal force in banked curves without friction.
  • Explore the role of normal force in circular motion and its components.
  • Learn about the effects of different banking angles on vehicle dynamics.
  • Investigate real-world applications of banked curves in road design and racing.
USEFUL FOR

Physics students, engineers, and anyone interested in understanding the dynamics of motion on banked curves, particularly in the context of vehicle handling and road design.

oreo
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A problem states " For a banked curve, ignoring friction, prove that tan θ = ν^2/rg". I tried to prove but I thought that as the normal force is at right angle to track then how could be the component of normal force provide the centripetal force as my book is saying. Please someone help. I would be greatful.
 
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I have solved it but still can't understand how is component of normal force providing centripetal force.
 
Think about the resultant of the normal force and centripetal force being equal to the gravitational force.
 
I want to confirm this that is centripetal force of curved bank directed towards its center which is perpendicular to normal force or is directed towards the axis of curved road. Please reply
 
Normal is perpendicular to road surface. Gravity is vertical. Centripetal is in horizontal plane. The road is banked at 45 degrees according to your post.
You caught me, didn't you. Normal would be hypotenuse of force triangle, centripetal would be one leg, and half of gravitational would be other. Best double-check me on that.
 

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