Question

Assume for the following problem that it happens on the surface of another planet (Mass 6.39 x 10²³ kg, Radius 3390 km)

A train travelling at a constant speed rounds a curve of radius 250-m that is rated at a maximum safe speed of 20 m/s. A pendulum bob, suspended by a thread from the ceiling of the train car hangs vertically while the train is on a straight stretch of track but swings to the left at an angle of 17.5^o during the turn. Will the train safely negotiate the curve?

Answer 1

M = 6.39*10^23 kg

R = 3390 km

So, acceleration of gravity , g = GM/R^2

So, g = 6.67*10^-11*6.39*10^23/(3.39*10^6)^2 = 3.71 m/s