The fast French train known as the TGV (Train a Grand Vitesse) has a scheduled a

Question

The fast French train known as the TGV (Train a Grand Vitesse) has a scheduled average speed of 216 kph. If the train goes around a curve at that speed and the magnitude of the acceleration experienced by the passengers is to be limited to 0.050g, where g is the acceleration due to gravity, what is the smallest radius of curvature for the track that can be tolerated? The figure below shows overhead views of four situations in which forces act on a block that lies on a frictionless floor. If the force magnitudes are chosen properly, in which situations is it possible that the block is stationary with respect to the floor, and moving at constant velocity with respect to the floor?

Explanation / Answer

3)Here we have centripetal acceleration a = v^2/r

where a = 0.050*9.8m/s^2 = 0.49m/s^2

So r = v^2/a = (216km/h*1000m/km*1h/3600s)^2/0.49m/s^2 = 7350m = 7.35km


b) again a = v^2/r so v = sqrt(r*a) = sqrt(1220m*0.49m/s^2) =
24.4m/s*(1km/1000m*3600s/1h) = 88.0km/h

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