Question

Problem 5

Magnetic levitation trains can go as fast as 500 km/h so when they go around a curve, if they do not bank, you would feel like you were being pushed against the wall of the car or the wall of the car was pushing you around a curve. Designers try to make the radius of curvature of the track large enough so that this centripetal acceleration is less than 0.5g.

Usually they bank the train (tip it at an angle towards the centre of the curve) so that all you experience is a net increase in force into your seat.

Given this information determine the radius of curvature of the track and the banking angle so that the force you experience going around the curve is directly down into your seat. If you have a mass of 80kg what would your apparent weight be as you go around the corner?

If you happened to be sitting on a set of bathroom scales as you went around the corner what value would they read?

Do you think you would find it uncomfortable going around the corners in one of these trains?

Answer 1

As the train is travelling around the corner centripetal accleration of the train is .

speed of the train is

consider mass m on the train, forces on the mass are vertically downwards, and Normal reaction due to seat .

Vertically net force is zero.

horizontally acceleration towards the center of the circle is

Hence

Radius of curvature of train's path =

Banking angle

Apparent weight is

Reading of bathroom scales

No, It is not so difficult to experience the above acceleration.