a) the picture for this part is shown beside. The body moves along the Meridian i.e. straight towards the north pole. There are two inertial forces acting on the body i) centrifugal force and ii) the Coriolis force. The centrifugal force acts outwards from the surface of the earth and thus does not put any pressure on the rails. The Coriolis force on the other hand acts along the surface of the earth and thus can cause pressure on the rails. The Coriolis force is given by
. Here
is the angular velocity of the earth (you can determine the direction of rotation based on "sun rises in the east"). The component of velocity of the train in the plane perpendicular to the earth's angular velocity is
as shown in the figure. The Coriolis force thus acts to the right rail as shown in the figure and has a magnitude of
.
b) If the total inertial force has to be zero, then the Coriolis force must act in the opposite direction of the centrifugal force and completely cancel it out. Now centrifugal force acts outwards from the Earth's surface as shown in the second figure and so the Coriolis force
Fco must act inwards as shown in the figure. For the Coriolis force to act in that direction, the velocity vector must be oriented perfectly along the latitude and in the opposite direction of the Earth's rotation as shown in the figure. Its magnitude will then be
. So in order for the two to exactly cancel out we have,
a) the picture for this part is shown beside. The body moves along the Meridian i.e. straight towards the north pole. There are two inertial forces acting on the body i) centrifugal force and ii) the Coriolis force. The centrifugal force acts outwards from the surface of the earth and thus does not put any pressure on the rails. The Coriolis force on the other hand acts along the surface of the earth and thus can cause pressure on the rails. The Coriolis force is given by 
. Here 
is the angular velocity of the earth (you can determine the direction of rotation based on "sun rises in the east"). The component of velocity of the train in the plane perpendicular to the earth's angular velocity is 
as shown in the figure. The Coriolis force thus acts to the right rail as shown in the figure and has a magnitude of 
.
b) If the total inertial force has to be zero, then the Coriolis force must act in the opposite direction of the centrifugal force and completely cancel it out. Now centrifugal force acts outwards from the Earth's surface as shown in the second figure and so the Coriolis force Fco must act inwards as shown in the figure. For the Coriolis force to act in that direction, the velocity vector must be oriented perfectly along the latitude and in the opposite direction of the Earth's rotation as shown in the figure. Its magnitude will then be 
. So in order for the two to exactly cancel out we have,
1 comment:
Desde España: Muchísimas gracias por su excelente aportación, usted enseña a "pensar" la física y nos hace amarla.
Otra vez: Gracias
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