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jasker
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Homework Statement
Two trains are traveling east and west on the equator at 50km/h. What is the difference in weight of an apple (mass = 200g) in each train? In which train is it lighter?
Homework Equations
x denotes vector (cross) product, bold denotes a vector quantity. Subscripts rot and in denote the rotating and inertial frames of reference respectively. Ω is the angular velocity of rotating earth. r is the position vector to a point on the equator (magnitude here equal to Re, the radius of earth)
The apparent force due to motion on a rotating Earth is:
Frot = marot
= main - m[2Ω x vrot + Ω x (Ω x r)]
= F + Ffict
The fictitious force Ffict consists of two terms, the Coriolis force and the Centrifugal force:
Coriolis force F = -2mΩ x vrot = -2mΩvrot
Centrifugal force F = -mΩ x (Ω x r) = -mΩ^2 * Re
The Attempt at a Solution
On the train traveling east, the Coriolis force points toward the axis of rotation of the earth, increasing the weight of the apple:
Frot = mg + 2mΩvrot - (mΩ^2 * Re)
On the train traveling west, the Coriolis force points outward from the axis of rotation of the earth, decreasing the weight of the apple:
Frot = mg - 2mΩvrot - (mΩ^2 * Re)
At this point, I am stuck. Is what I have correct so far? How do I calculate the weight of the apple given the two equations above? Do I just plug in these values?
m = 0.2kg
Ω = 2π rad / 86400 sec = 7.27*10^-5 rad/s
Re = 6378.14 km @ equator
vrot = 50 km / h = 13.89 m/s
Thank you!