How Does the Coriolis Force Affect a Northbound Plane's Flight Path?

[karnten07]

Homework Statement

A plane with a fully laden mass of 500 tonnes is flying due north at a steady speed of 1000kmh^-1 and is located at a latitude of 51 degrees north at a specific time.

What force in an east-west direction is required to keep the plane on course along a fixed line of longitude.

Homework Equations

The Attempt at a Solution

So due to the inertial effect of the Coriolis force, the plane requires a force acting east to keep it on a fixed line of longitude because the coriolis force is acting west on the plane.

The magnitude of the coriolis force is given by this equation:

mx'' = -2mw(z'cos(theta) - y'sin(theta))

where x is the east direction , z is vertically up, y is north, theta is the latitude

So in this case, because there is no velocity in the z direction, it becomes:

mx'' = -2mw(-y'sin(theta))

Is this right?

 

[karnten07]

Hi guys, i think I've got this right, but I am not entirely sure, i get a force of 16000 N.

 

[ogb p]

Yes, your understanding of the Coriolis force on a plane is correct. Due to the Earth's rotation, an object moving in a straight line on its surface will appear to curve to the right in the northern hemisphere and to the left in the southern hemisphere. This is known as the Coriolis effect. In the case of a plane flying north at a constant speed, the Coriolis force will act to the west, causing the plane to veer off course to the west if not corrected for. Therefore, a force acting to the east is required to counteract the Coriolis force and keep the plane on a fixed line of longitude. Your equation correctly represents the magnitude of the Coriolis force in this scenario.