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Uniform Circular Motion problem?
Hi! How do you do this problem?
A train traveling at a constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to
an angle of 17.5º throughout the curve. What is the speed of the train?
1 Answer
- 5 years agoFavorite Answer
Consider the forces acting on the lamp of mass (m).
Vertically you have the weight force mg
Horizontally, you have the centripetal force mv²/r
Going round the curve, the angle of dangle of the lamp represents the angle of the resultant force of the reaction to these two forces: {The tension in the suspension}
(mv²/r) / (mg) = tan(17.5º)
{m cancels out}
v² / rg = tan(17.5º)
v² = rg * tan(17.5º)
v² = 235 * 9.81 * tan(17.5º) = 726.87
v = 27.0 m/s
