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On a circular curve, the rate of superelevation is e. While negotiating the curve a vehicle comes to a stop. It is seen that the stopped vehicle does not slide inwards (in the radial direction). The coefficient of side friction is f. Which of the following is true:
  • a)
    e ≤ f
  • b)
    f < e < 2 f
  • c)
    e ≥ 2f
  • d)
    none of the above
Correct answer is option 'A'. Can you explain this answer?
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Understanding Superelevation and Friction
When a vehicle negotiates a circular curve, the forces acting on it include gravitational force, centrifugal force, and the frictional force between the tires and the road surface. Superelevation (e) refers to the banking of the road, which helps counteract centrifugal force.
Key Factors
- Superelevation (e): The angle or rate at which the road is banked.
- Coefficient of Side Friction (f): The friction available to prevent the vehicle from sliding inward due to centrifugal force.
Vehicle at Rest on a Curve
When a vehicle comes to a stop on a circular curve without sliding inward, the following equilibrium conditions apply:
- The outward centrifugal force is countered by the inward frictional force and the component of gravitational force acting down the slope of the banked road.
Static Condition and Inequality
The condition for the vehicle to not slide inward can be expressed mathematically as:
- Centrifugal force ≤ Frictional force + Component of gravitational force
This leads to the relationship:
- \( e \leq f \)
Conclusions
- If the vehicle does not slide, the superelevation must be less than or equal to the frictional force:
- \( e \leq f \)
Thus, the correct option is a) e ≤ f. This ensures that the vehicle remains stable on the curve, demonstrating that the banking (superelevation) and friction work together to maintain the vehicle's position.
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On a circular curve, the rate of superelevation is e. While negotiating the curve a vehicle comes to a stop. It is seen that the stopped vehicle does not slide inwards (in the radial direction). The coefficient of side friction is f. Which of the following is true:a)e ≤ fb)f < e < 2 fc)e ≥ 2fd)none of the aboveCorrect answer is option 'A'. Can you explain this answer?
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