Classical Mechanics: Coriolis Effect Problem

[Eyedbump]

Homework Statement

A bird of mass 2 kg is flying at 10 m/s in latitude of 60° N, heading due East. Find the horizontal and vertical components of the Coriolis force acting on it.

Homework Equations

The Coriolis Force, F = 2mw∧v. Where ∧ shows the cross product between angular frequency vector, w, and change in the position vector, v.

Θ will be the co-latitude -- that is, 90°- 60° = 30°.

The Attempt at a Solution

I started by deciding that my coordinates would be oriented so that x points East, y points North, and z points straight up (away from the earth). Thus, I believe, w = {wcosΘ, 0, 0} since the bird flies only East.

So taking the Cross product with v = {x' , y' , z'} (where ' indicates the change in position), I receive the following vector {0 , -z'cosΘ , y'cosθ}. Now, I've shown the product vector without the coefficients, because my confusion arises at the presence of the y' and z's. Exactly what am I to do about them?

It's one of those problems where I can't tell if I'm missing something terribly basic, or having been working under a more general misapprehension. I'd very much appreciate any help!

p.s. This is my first post in the forum, and so I'm sure I've broken a plethora of the rules/etiquettes for which you must forgive me.

p.p.s. This is not a homework problem, just a kind of review (which makes the fact that I'm struggling with it so much more embarrassing), so don't feel ashamed at helping me cheat!

 

[ehild]

Welcome to PF!

Homework Statement

A bird of mass 2 kg is flying at 10 m/s in latitude of 60° N, heading due East. Find the horizontal and vertical components of the Coriolis force acting on it.

Homework Equations

The Coriolis Force, F = 2mw∧v. Where ∧ shows the cross product between angular frequency vector, w, and change in the position vector, v.

You miss a minus sign. The Coriolis force is F = -2mw∧v.

Θ will be the co-latitude -- that is, 90°- 60° = 30°.

The Attempt at a Solution

I started by deciding that my coordinates would be oriented so that x points East, y points North, and z points straight up (away from the earth). Thus, I believe, w = {wcosΘ, 0, 0} since the bird flies only East.

The angular velocity is a vector parallel to the axis of rotation of Earth and pointing upward. In your coordinate system it has both y and z components, and zero x component.

So taking the Cross product with v = {x' , y' , z'} (where ' indicates the change in position), I receive the following vector {0 , -z'cosΘ , y'cosθ}. Now, I've shown the product vector without the coefficients, because my confusion arises at the presence of the y' and z's. Exactly what am I to do about them?

The velocity vector is (10, 0,0) as it has only East (x) component.

 

[Eyedbump]

Welcome to PF!You miss a minus sign. The Coriolis force is F = -2mw∧v.
The angular velocity is a vector parallel to the axis of rotation of Earth and pointing upward. In your coordinate system it has both y and z components, and zero x component.
The velocity vector is (10, 0,0) as it has only East (x) component.

Oh my god. Thank you so much!

 

[ehild]

You are welcome. :)