The Tilting Train Pendulum · AI Generator #GEN-527D015C

Physics · mechanics

Problem

High-speed tilting trains use sophisticated systems to lean into curves, allowing them to maintain higher speeds while keeping passengers comfortable. A simplified model of this system can be understood by analyzing a pendulum hanging from the train's ceiling. Consider a pendulum of length L=1.2  mL = 1.2\;\text{m} hanging from the ceiling of a train car. When the train travels around a horizontal circular curve of radius R=800  mR = 800\;\text{m} at constant speed v=30  m/sv = 30\;\text{m/s}, the pendulum bob deflects from the vertical by an angle θ\theta. Find the angle θ\theta that the pendulum makes with the vertical when the train is moving at this constant speed around the curve. Take g=10  m/s2g = 10\;\text{m/s}^2.

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