How Much Does a Plumb Bob Deviate at 40 Degrees North Latitude?

[tubworld]

I have this problem here.
Let's say: A plumb bob does not hang exactly along a line directed to the center of the Earth's rotation. How much does the plumb bob deviate from a radial line at 40 degrees north latitude if we assume that the Earth is spherical?

 

[Astronuc]

One needs to establish the force component due to the angular acceleration of the plumb bob's mass at the point on the Earth at 40° latitude.

F = m\omega^2r, where r is the distance from the Earth's axis to the plumb bob.

 

[tubworld]

? Huh?

 

[Doc Al]

In the rotating frame of the Earth there are three forces on the bob: the tension in the string (a passive force), gravity (which acts towards the center of the earth), and a centrifugal force that Astronuc described (which acts outward from the Earth's axis). If you add up the gravitational force and the centrifugal force, that resultant will tell you how the string must be aligned to support the bob.