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Homework Help: The coriolis effect

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data

    On its way to Paris the Eurostar train is travelling due South at 300 km/h
    at a point with latitude 49°. Assume the Earth is a perfect sphere of radius,
    RE, that rotates around its axis (North/South pole) once every 23 hrs 56
    (a) Calculate the magnitude of the acceleration of the train due to the
    Coriolis force. Note that latitude is defined as the angle [itex]\phi[/itex] with respect
    to the North-South pole axis where [itex]\phi[/itex] = 0 at the equator and [itex]\phi[/itex] = 90° at the North pole.
    (b) What direction is this acceleration in?

    2. Relevant equations

    Acceleration due to coriolis effect:

    [itex]\vec{a}[/itex]co = 2[itex]\vec{v}[/itex]×[itex]\vec{ω}[/itex]

    where aco is the accerlation due to coriolis effect, [itex]\vec{v}[/itex] is the velocity of the object in question and [itex]\vec{ω}[/itex] the angular frequency at that latitude.

    3. The attempt at a solution

    I know this question has something to do with 2 seperate reference frames, one inertial and one not, however for some reason I seemed to have ignored that completely and just attempted it this way:

    First of all I calculated the angular frequency at 49 degrees latitude this way:

    angular frequency at equator: [itex]\omega = 2\pi/\tau[/itex]
    angular frequency at 49° latitude = [itex]\omega = (2\pi/\tau) cos(49°)[/itex]
    [itex]\tau = 23+14/15[/itex] hours

    Then I moved on to converting the velocity of the train into spherical co-ordinates. I did this via ratios rather than standard conversions because well, I don't really know it just seemed easier, it's probably where I've gone wrong, I've drawn a diagram on my sheet of paper but hopefully it'll make sense without it.

    Ok so the train is travelling due south on the surface of the earth, with a velocity of 300 km/h, over a total distance of half the circumference of the earth (as the train is starting from a lower latitude it isn't actually covering this distance but hopefully that is irrelevant), what i'm looking for is [itex]\partial\phi/\partial t[/itex] and I calculated that:

    [itex]\partial v/ \partial t / 0.5 Ce= (\partial \phi / \partial t) / \pi[/itex]

    Where Ce = circumference of earth.

    I then solved for [itex]\partial\phi/\partial t[/itex] and got this equal to 0.047 rad / hour in the [itex][itex]\widehat{\phi}[/itex] direction.

    I then did the cross product of my angular frequency of the Earth at this point and the angular velocity multiplied by 2 and my result came out in the [itex]\widehat{r}[/itex] direction, and was negative so it is going into the planet. I know the drift should be to the left so I'm real confused.

    I'm pretty sure I've approached it all wrong so I'd appreciate any help. Thanks.
    Last edited: Dec 4, 2011
  2. jcsd
  3. Dec 6, 2011 #2


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  4. Dec 8, 2011 #3


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    I can not follow your work. The Coriolis force acts in a rotating frame of reference. Choose a coordinate system on the surface of the Earth, which moves together with the rotating Earth. Wikipedia explains it quite nicely: The axis of the local system of coordinates point to East, North, and Up with unit vectors [itex]\hat{e}[/itex], [itex]\hat{n}[/itex] and [itex]\hat{u}[/itex].The vector of angular velocity of the Earth is the same everywhere, but its components in a local frame depend on latitude: [itex]\vec{Ω}[/itex]=cosφ[itex]\hat{n}[/itex]+sinφ[itex]\hat{u}[/itex]. The velocity of the train going to South is [itex]\vec{v}[/itex]=-v[itex]\hat{n}[/itex].

    Calculate the vector product [itex]\vec{v}[/itex]x[itex]\vec{Ω}[/itex]. What are its non-zero components?. What is the direction of the product?

  5. Dec 8, 2011 #4
    Yeah I was approaching this all wrong, I looked at the method on wikipedia a few days ago and it worked out fine, thanks for the input.
  6. Dec 8, 2011 #5


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    Hi Chowie,

    Next time send a post, please, if you solved the problem. I thought you gave up all hope and left Physicsforums forever, not getting a proper help.

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