A train traveling at a constant speed rounds a curve of radius 325 m. A chandelier suspended from the ceiling?

A train traveling at a constant speed rounds a curve of radius 325 m. A chandelier suspended from the ceiling swings out to an angle of 17.0° throughout the turn. What is the speed of the train?

$1.86

TOO FAST to safely negotiate the curve.

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(17)

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

(mv²/r) / (mg) = Tan(17)

or:

(v²/r) / (g) = Tan(17)

g is 9.8 m/s; and you are given "r". Solve for v.
V^2=tan(17)(9.8)(325)
V=31.20

by dhankmon Member since:
February 04, 2006
Total points:
338 (Level 2)
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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(17)

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

(mv²/r) / (mg) = Tan(17)

or:

(v²/r) / (g) = Tan(17)

g is 9.8 m/s; and you are given "r". Solve for v.
V^2=tan(17)(9.8)(325)
V=31.20