julz3216 said:Homework Statement
A train traveling at a constant speed rounds a curve of radius 218 m. A lamp suspended from the ceiling swings out to an angle of 16.6° throughout the curve. What is the speed of the train?
Homework Equations
mv^2/r
The Attempt at a Solution
I drew a diagram and attempted to calculate v by setting mv^2/r = -cos16.6 mg
I don't really know how to approach this?
julz3216 said:I tried and got 24.705 but that was wrong. Are there any other ways to approach the problem?
julz3216 said:Ok, I got it! Thank you so much.
When a train is rounding a curve, the centrifugal force generated by the train's movement pushes the train outward away from the curve. This force creates a lateral force, or sideways force, that must be countered by the train's wheels. This counterforce causes the train to slow down as it moves around the curve.
Trains stay on the tracks when rounding a curve due to the principle of coning. This means that the train's wheels are slightly tapered and angled inward, allowing them to roll smoothly along the curved track without slipping off.
Trains lean when rounding a curve because of the centripetal force exerted on the train. This force causes the train to tilt inwards towards the center of the curve, keeping it stable and preventing it from derailing.
The maximum safe speed for a train to round a curve is determined by a combination of factors such as the train's weight, length, and wheel size, as well as the curvature of the track and the train's speed. Engineers use mathematical calculations and real-world testing to determine the maximum safe speed for a train to round a curve.
While it is possible for a train to derail when rounding a curve, this is a rare occurrence and typically happens due to extreme circumstances such as high speeds, poor maintenance of the tracks, or unexpected obstacles on the tracks. Trains are designed with safety features and undergo regular inspections to minimize the risk of derailment when rounding curves.