Vehicle turning on a circular path: Dependence of the banking/lean angle on mass. Context: A vehicle moves along a horizontal circular path of radius R at speed v (steady turn). Choose the correct statement regarding how the angle of inclination depends on vehicle mass.
Mechanical Engineering
Engineering Mechanics
Difficulty: Easy
Choose an option
Answer
Correct Answer: Independent of mass
Explanation
Given data
- Vehicle negotiates a curve of radius R at speed v.
Concept/Approach For a vehicle that leans (or a banked road), the required lean/bank angle θ satisfies tanθ = v2 / (gR) which does not include the vehicle mass m.
Step-by-step reasoning Centripetal requirement: Resultant of weight and normal provides v2/R. From force balance, tanθ = (centripetal acceleration)/g = v2/(gR). No mass term appears ⇒ θ is independent of mass.
Common pitfall Confusing tyre–road friction limits (which depend on normal reaction) with the geometric relation for the required angle, which is mass-independent.
Final Answer Independent of mass