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 Homework Statement:

Occasionally one hears the rumor that railroad tracks wear out on one side. The reason for this is the Coriolis force. Check this claim using an ICE with mass m = 400 t, which is traveling north at v = 300 km / h at the 50th degree of latitude (northern latitude).
a) Calculate the normal force and the Coriolis force. Which splint is more worn out?
b) What radius would a curve have to have if the centrifugal force should correspond to the Coriolis force with the same mass and speed?
 Relevant Equations:
 Equations for Coriolis force and Centrifugal Force
Hello!
So for a) I have done the following
m = 400t = 400000 kg
v = 300 km/h = 83,3 m/s
##\alpha## = 50 (degrees)
Now this is the formula for the Coriollis effect
$$ F = 2 \cdot m (v × \omega) $$
So in a book I found in the library regarding physics I've found a similar example that used this formula. (In the example the weight was given the velocity as well as the angle through "50 degrees of the lattitude" phrase. But there was no explanation nor steps to how this formula came to be. Which means either it is something really easy that expects the reader to see it, or it is commonly used when dealing with corriolis effect in the northern lattitude? Can anyone please clarify this it would be much appreciated.
$$ F = 2 \cdot m \cdot v \cdot \omega \cdot sin(\alpha) $$
Now I've calculated the corriolis effect using the second formula and I've gotten
##F = 3712,23 N##
For the normal force I'm not sure by what is exactly meant by normal force I assumed that it is this,lead by the examples and problems I've solved in the lectures prior.
$$ F = m \cdot g $$
F = 3924000 N
So according to my calculations the normal force is much greater than the corriolis force. Now under a we are sussposed to give this answer
"The rails are used more in direction (choose East West South North) by a factor of (choose 1/10 1/100 1/1000 1/10000) weight.
Now this is the part I'm uncertain. How can I determine in which direction the rail is used more. I'd go as far as saying if the coriollis force was greater than the normal force I'd say the rails are used more in the direction north because the ICE is moving north.If I'm not mistaken the normal force should be at an 90 degree angle,in regards to the point or object that the force is acting to.But in which direction does the normal force opperate, in regards to north west south? Also would anyone be able to confirm if my calculations are right.
Thank you in advance!
So for a) I have done the following
m = 400t = 400000 kg
v = 300 km/h = 83,3 m/s
##\alpha## = 50 (degrees)
Now this is the formula for the Coriollis effect
$$ F = 2 \cdot m (v × \omega) $$
So in a book I found in the library regarding physics I've found a similar example that used this formula. (In the example the weight was given the velocity as well as the angle through "50 degrees of the lattitude" phrase. But there was no explanation nor steps to how this formula came to be. Which means either it is something really easy that expects the reader to see it, or it is commonly used when dealing with corriolis effect in the northern lattitude? Can anyone please clarify this it would be much appreciated.
$$ F = 2 \cdot m \cdot v \cdot \omega \cdot sin(\alpha) $$
Now I've calculated the corriolis effect using the second formula and I've gotten
##F = 3712,23 N##
For the normal force I'm not sure by what is exactly meant by normal force I assumed that it is this,lead by the examples and problems I've solved in the lectures prior.
$$ F = m \cdot g $$
F = 3924000 N
So according to my calculations the normal force is much greater than the corriolis force. Now under a we are sussposed to give this answer
"The rails are used more in direction (choose East West South North) by a factor of (choose 1/10 1/100 1/1000 1/10000) weight.
Now this is the part I'm uncertain. How can I determine in which direction the rail is used more. I'd go as far as saying if the coriollis force was greater than the normal force I'd say the rails are used more in the direction north because the ICE is moving north.If I'm not mistaken the normal force should be at an 90 degree angle,in regards to the point or object that the force is acting to.But in which direction does the normal force opperate, in regards to north west south? Also would anyone be able to confirm if my calculations are right.
Thank you in advance!