Radius of Curvature of a Train Turning North East

[harini_5]

A train is moving towards north at one place.
it turns towards north east.
here we observe that the radius of curvature of outer rail will be greater than that of inner rail
why?pls explain
velocity and radial acc. are the same and radius of curvature=v^2/a normal

 

[lstellyl]

I think you are focusing too much on the equations here...

if you consider a train going about a circular track, the inner and outer rail of the track will both be circular, but the outer rail will have a radius greater than the inner rail by the width of the train.

this is all this statement is saying.

in the equation for centripetal accelleration the radius is assuming a point particle, which a train is not.

the same equation is true for a non-point-mass where the radius is then for the center of mass.

 

[charng]

The reason for the difference in radius of curvature between the outer and inner rail is due to the direction and speed of the train. When the train is moving in a straight line towards the north, both the outer and inner rail have the same radius of curvature. However, when the train turns towards the northeast, the outer rail has to cover a longer distance compared to the inner rail, resulting in a larger radius of curvature for the outer rail. This is because the train is moving at a constant speed, but the direction is changing, causing the outer rail to travel a greater distance in the same amount of time. This also means that the velocity and radial acceleration are the same for both the outer and inner rail. The formula for radius of curvature is v^2/a, where v is the velocity and a is the radial acceleration. Since both v and a are the same for both rails, the only variable that affects the radius of curvature is the distance traveled, resulting in a larger radius for the outer rail.