- #1
Pushoam
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Homework Statement
Because of the Coriolis force, falling objects on the Earth are deflected
horizontally. For instance, a mass dropped from a tower lands to the
east of a plumb line from the release point. In this example we shall
calculate the deflection of a mass m dropped from a tower of height h
at the Equator.
I have attached the example for your convenience, But I want to solve it on my own with your help.
Homework Equations
3. The Attempt at a SolutionDoes it matter whether I consider any point on the Earth or equator?
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The physical force acting on the system is the gravitational force : ## \vec F_{ph} = m \vec g ##
Assuming that h is small in comparison with the radius of the earth.
Wrt. the Earth frame( which is non - inertial ),
## \vec F_{n-in} = \vec F _{ph} + \vec F_{pseudo} ##
## \vec a_{n-in} = \vec g -\omega ^2 r \hat r - \omega v_{n-in} \hat n##
where I don't know the direction of Coriolis force i.e. ##\hat n## as I don't know the direction of ## \vec v_{in}##.
##\hat r ## is the direction from the center of the Earth towards the system
Now, what to do further?
Qualitatively, what I understand is , if the Earth is not rotating, then the path of the mass will be straight as observed from the Earth's frame. Let's mark the point on the Earth where the mass falls by B in this case.
In case of the rotating Earth, before the ball reaches to the Earth's surface, the point marked by B will have moved ahead and so it will fall on another point of the Earth's surface.To a person on the earth, it will appear as a deflection in the motion of mass.