PLEASE HELP me how to do this Physics problem: What is the speed of the train?

Question

A train traveling at a constant speed rounds a curve of radius 300 m. A chandelier suspended from the ceiling swings out to an angle of 16.5° throughout the turn. What is the speed of the train?

Answer 1

Draw vectors for the sideways (centrifugal) force and the downwards (gravitational) force acting on the chandelier. From that diagram you should notice that:

(centrifugal force) / (gravitational force) = Tan(16.5)

The formula for gravitational force is "mg"; and the formula for centrifugal force is "mv²/r". So:

(mv²/r) / (mg) = Tan(16.5)

or:

(v²/r) / (g) = Tan(16.5)

g is 9.8 m/s; and you are given "r". Solve for v.