Coriolis Force Across the Equator

[DarkMatter5]

Homework Statement

A fast sprinter with a mass of 80 kg runs across the equator. What is the value of the Coriolis force he experiences?

Homework Equations

F=ma
a=2ωV_radial
ω=7.27 x10^-5 rads^-1
Earth rotates from west to east.

The Attempt at a Solution

I pick a direction of travel - South to North. I know if you approach the equator from the poles the force makes a mass move in opposite directions. But, because he is still traveling north after crossing the equator then the Coriolis force doesn't seem to cancel out as he is approaching the equator from the south pole and then approaching the north pole from the equator. I know that there is no Coriolis force at the equator itself but I am not sure how much force he would feel when crossing the equator. All help is appreciated.

 

[haruspex]

know that there is no Coriolis force at the equator itself but I am not sure how much force he would feel when crossing the equator.

I don't get the distinction. Coriolis force arises when making North-South movements. In what sense could there be a Coriolis force "at" the equator other than in the sense of crossing it?

 

[DarkMatter5]

I meant that when crossing it at the instant that you touch the equator you experience no Coriolis force. I would like to know the total force felt when crossing the equator.

 

[FactChecker]

I think the question has been set up to allow an easy answer without doing any calculations. But you should be able to justify your answer.

 

[haruspex]

I meant that when crossing it at the instant that you touch the equator you experience no Coriolis force. I would like to know the total force felt when crossing the equator.

Let me give you an analogy. Throw a stone straight up. At its highest point it has zero velocity. You are effectively saying, yes, I know it has no velocity at its highest point, but what velocity does it have as it goes through its highest point?

 

[DarkMatter5]

Exactly! That is why I don't know how to answer the question. The question makes no sense.

 

[haruspex]

Exactly! That is why I don't know how to answer the question. The question makes no sense.

No, it makes sense. You need to understand that there is no distinction between the force at the equator and the force while crossing the equator. If you stand still, or move in an East-West direction, there is no Coriolis force anyway. In order to decide whether there is a Coriolis force "at" some point you must consider moving along a North-South line (or at least, partially in that direction) through the point.

If you want to consider a path of some length across the equator, there will be a very small Coriolis force one way on the approach, declining to zero at the equator itself, then gradually increasing, but now in the opposite direction.

 

[DarkMatter5]

So is the question asking about a path of some length or about the first thing you said about the force being zero? If it's asking about a path of some length, how should I answer?

 

[FactChecker]

So is the question asking about a path of some length or about the first thing you said about the force being zero? If it's asking about a path of some length, how should I answer?

The question specified a sprinter to make the path length very short. You should be able to say something about the Coriolis force so near the equator. If the runner is going South, there will be a tiny increase of radius till he crosses the Equator and a tiny decrease after that. You should be able to describe how tiny the radius is and how that tiny change causes a Coriolis force on each side.

 

[haruspex]

So is the question asking about a path of some length or about the first thing you said about the force being zero? If it's asking about a path of some length, how should I answer?

I believe you should take the question as referring to the instant that he crosses the equator.

 

[DarkMatter5]

I see. Thank you for your help.