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For an ideally banked curve with no friction, how does the ideal banking angle theta depend on the mass of the vehicle taking the curve?
AIt does not depend on the vehicle's mass at all
BIt is directly proportional to the vehicle's mass
CIt is inversely proportional to the vehicle's mass
DIt depends on mass only above highway speed
Answer & Solution
Correct answer: A. It does not depend on the vehicle's mass at all
1. The ideal banking equation is tan(theta) = v^2 / (r*g), which contains speed, radius, and gravity but no mass term.
2. The mass cancelled out earlier in the derivation when the horizontal and vertical force equations, each containing mass, were divided by each other.
3. Because mass does not appear in the final relationship, the ideal banking angle is the same for a heavy truck and a light car taking the same curve at the same speed.
4. Claiming a direct or inverse proportionality to mass, or a dependence that only appears above highway speed, contradicts the fact that mass cancels out of the derivation entirely.
_Source: OpenStax College Physics (CC BY 4.0), Ch 6 "Uniform Circular Motion and Gravitation", section 6.3 Centripetal Force_
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