A train A runs from east to west and another train B of the same mass runs from west to east at the same speed along the equator. A presses the track with a force ${\mathrm{F}}_1$ and B presses the track with a force ${\mathrm{F}}_2$.

Earth rotate about its axis from west to east.

For Train A: ${\mathrm{v}}_{\mathrm{A}} = \mathrm{v} - \mathrm{\omega r}$

For Train B : ${\mathrm{v}}_{\mathrm{B}} = \mathrm{v} + \mathrm{\omega r}$

For Train A

$\mathrm{mg} - {\mathrm{N}}_{\mathrm{A}} = \frac{\mathrm{m}{(\mathrm{v}-\mathrm{\omega r})}^2}{\mathrm{r}}$

${\mathrm{N}}_{\mathrm{A}} = \mathrm{mg}-\frac{\mathrm{m}{(\mathrm{v}-\mathrm{\omega r})}^2}{\mathrm{r}}$

Similarly for Train B :  ${\mathrm{N}}_{\mathrm{B}} = \mathrm{mg}-\frac{\mathrm{m}{(\mathrm{v}+\mathrm{\omega r})}^2}{\mathrm{r}}$

Clearly ${\mathrm{N}}_{\mathrm{B}} <\hspace{0.17em}{\mathrm{N}}_{\mathrm{A}} \mathrm{and} {\mathrm{F}}_1 > {\mathrm{F}}_2$