Exploring the Effects of Coriolis and Centrifugal Forces on Railway Motion

[Like Tony Stark]

Homework Statement

Suppose there is a train of mass $m$ which moves with constant velocity $v$. It moves on a horizontal railway which is (two options)
A) in the North Pole
B) in the Equator from South to North

What horizontal force would exert the railway on the train, and what horizontal force would exert the wheels on the railway?

Relevant Equations

Coriolis and centrifugal force

I think that there could be friction, but I try to think on forces related to the motion along the Earth, which rotates. Like when you're on a car that turns to the left and you feel pushed to the right. Do the wheels do the same to railway? Would there be Coriolis force? Because that's just centrifugal force

 

[scottdave]

Yes there is friction, but from the context it sounds like they are looking for forces due to motion of the earth.

When talking about friction be careful when thinking about friction between the wheel and the track. For example think about the extreme case where there is no friction with the track.

When thinking about Coreolis type force, remember what a force is. You can think about Mass x Acceleration, or think about Change in Momentum with respect to time. So as the Earth moves from West to East at a certain horizontal velocity, say 1 mile South of the equator, the train will have the same Eastward component since it is locked in with the track due to the rims. Now as it arrives at the Equator, how has the Eastward component of velocity (and momentum) changed?

You need to clarify what they mean by "in the North Pole" what direction is it moving? But there is a video that I will find which may help you.

 

[scottdave]

Here are a couple of videos you may find interesting. This one is from Veritasium showing water swirling down a drain. If you want to skip to about 4 minute mark you can get the explanation.


Here is one not much on Coreolis, but just about spinning forces.

https://www.physicsforums.com/media...ick-and-derive-centripetal-acceleration.6617/

 

[Like Tony Stark]

Yes there is friction, but from the context it sounds like they are looking for forces due to motion of the earth.

When talking about friction be careful when thinking about friction between the wheel and the track. For example think about the extreme case where there is no friction with the track.

When thinking about Coreolis type force, remember what a force is. You can think about Mass x Acceleration, or think about Change in Momentum with respect to time. So as the Earth moves from West to East at a certain horizontal velocity, say 1 mile South of the equator, the train will have the same Eastward component since it is locked in with the track due to the rims. Now as it arrives at the Equator, how has the Eastward component of velocity (and momentum) changed?

You need to clarify what they mean by "in the North Pole" what direction is it moving? But there is a video that I will find which may help you.

Let me see if I've understood... the train moves with its velocity but it suffers Coriolis force, which pushes it agains the ground (because the angular velocity is in $z$ and the velocity in $x$, so the cross producto would be in $y$). Then, it would have centrifugal force which will also push it to the ground (the cross product between $\omega$ and $\vec r$ is to the right, and the cross product between $\omega$ and the last one points inside)

I'll wait for the video!

 

[scottdave]

I think they want to know the "force" that the train feels in a horizontal direction (in relation to the track and the ground). Like this:

The train is moving at a certain speed toward
the east when south of the equator.
As it arrives at the equator, is it's
Easterly speed faster or slower
than before?

Then ask that question again after it has crossed the equator.

You may want to ask your instructor for clarification.

 

[haruspex]

Let me see if I've understood... the train moves with its velocity but it suffers Coriolis force, which pushes it agains the ground (because the angular velocity is in $z$ and the velocity in $x$, so the cross producto would be in $y$). Then, it would have centrifugal force which will also push it to the ground (the cross product between $\omega$ and $\vec r$ is to the right, and the cross product between $\omega$ and the last one points inside)

I'll wait for the video!

Take a look at https://en.m.wikipedia.org/wiki/Coriolis_force#Formula. The explanation distinguishes Euler, Coriolis and centrifugal forces.

There is no Euler force since the rotation is constant.

The angular velocity vector is along the axis of the Earth, not in the z direction. So what direction is the Coriolis force in?
Personally, I find it simpler to think in terms of whether the eastward velocity of the Earth's surface is greater where the object is coming from or where it is going to.

For centrifugal, note the question only asks about horizontal forces.

Btw, the question says the train's velocity is constant, but I think you should assume it stays on the ground.