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## Homework Statement

Depending on the college or university, this may be a 2nd or 3rd year question. For me, it is a junior-level course.

A train is heading due south through Edmonton at a speed of 300 m/s relative to the surface. Edmonton has a latitude of 53.5 degrees; the Earth has a radius of 6400 km. If the train has a mass of 1Gg (not sure, maybe a typo), what are:

(a) the centrifugal force (magnitude and direction) of the train?

(b) the coriolis force (mag. and dir.) of the train?

(c) if there is a coriolis force on the train, how come it continues due south?

## Homework Equations

I use star (*) to show the perspective of the non-inertial, Earthly reference frame.

[itex]\mathbf{F_{\mathrm{cf}}}=-m\boldsymbol{\omega}\times(\boldsymbol{\omega}\times\mathrm{\mathbf{r}^{*}})[/itex]

[itex]\mathbf{F_{\mathrm{co}}}=-2m\boldsymbol{\omega}\times\mathrm{\mathbf{v}^{*}}[/itex]

## The Attempt at a Solution

For parts (a) and (b), I'm having a hard time determining my position and velocity vectors. I know to find the omega vector in terms of the non-inertial basis vectors given latitude and angular speed, but I don't really know what my position vector is since up until now, I've only done problems where something is rotating on a turntable and moving, but now i have to take into account that the Earth is curved.

Once I've found a position vector r*(t), I can find velocity vector v*(t) = r'*(t). Then it's a matter of plugging it in and crossing the vectors.

The problem is I'm not sure what r*(t) is. Would r*(t) = 300t i*? And then v*(t) = 300 i*? Remember i* is the basis position vector in the non-inertial frame (which is the Earth basically), i* is tangential to the surface of the Earth, and i* points "south". Are my guesses right (not likely), or is it much more complicated than this (quite likely)?

For part (c), doesn't it just move south because the tracks create a third fictitious "m a" force that restrict its motion in one direction? An "m a" force is a fictitious force that is the result of acceleration of the non-inertial frame, so if I had a book on a car dashboard and stomped on the gas, the book experiences a fictitious "m a" force that pushes it off the dash (in my view).

My biggest questions stem from parts (a) and (b).

## Homework Statement

## Homework Equations

## The Attempt at a Solution

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