First slide

Vertical circular motion

Question

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 $F_{1}$ and B presses the track with a force $F_{2}$ .

Moderate

A

$F_{1} > F_{2}$
B

$F_{1} < F_{2}$
C

$F_{1} = F_{2}$
D

The information is insufficient to find the relation between $F_{1} and F_{2}$

Solution

$N_{B} = mg - \frac{m {(v + ωr)}^{2}}{r}$
Earth rotate about its axis from west to east.
For Train A: $v_{A} = v - ωr$
For Train B : $v_{B} = v + ωr$
For Train A
$mg - N_{A} = \frac{m {(v - ωr)}^{2}}{r}$
$N_{A} = mg - \frac{m {(v - ωr)}^{2}}{r}$
Similarly for Train B : $N_{B} = mg - \frac{m {(v + ωr)}^{2}}{r}$
Clearly $N_{B} < N_{A} and F_{1} > F_{2}$

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