Determining Effective Force of Gravity

[ffanxii4ever]

How do you find the effective force of Gravity when at a particular latitude?

I keep trying to figure it out, but I can't seem to wrap my head around it. I understand that some small portion of the force of gravity goes towards your centripetal acceleration at certain latitudes, but I can't seem get the idea, since you seem to have three unknowns, but only two equations.

For example (45 degree latitude):

You are not moving in the y-direction, so the y-component of your weight must be equal to the y-component of your normal force; http://ffanxii4ever.googlepages.com/hp1.bmp/hp1-medium;init:.jpg
and then the net force in the centripetal acceleration is:
http://ffanxii4ever.googlepages.com/hp2.bmp/hp2-medium;init:.jpg

But you only have these two equations, but you have three variables, the normal force, the acceleration of gravity (and as a result the force of gravity) and the angle that the normal force is at (it is offset from the force of gravity).

Does anyone have any idea as to what I am missing, that is making me incapable of understanding this? Thanks.

 

[Doc Al]

There are only two forces acting on the object: The weight, W = mg, which acts toward the center of the Earth, and the normal force, N. You also know the acceleration, a = ω²r = ω²Rcosθ, which acts toward the axis of rotation. (R is the radius of the Earth.)

You have all you need to solve for the normal force (which gives you the effective weight of the object). Think vectorially:
$$\vec{W} + \vec{N} = m\vec{a}$$

Looking at just the radial components, you have:
$$-mg + N_r = -m\omega^2R\cos^2\theta$$

Or:
$$N_r = mg -m\omega^2R\cos^2\theta$$

 

[charng]

I can understand your confusion and frustration with trying to determine the effective force of gravity at a particular latitude. It is a complex concept and can be difficult to grasp at first. However, there are several key factors that need to be taken into consideration in order to accurately calculate the effective force of gravity at a specific latitude.

Firstly, it is important to understand that the force of gravity is not constant across the Earth's surface. It varies depending on the distance from the center of the Earth and the mass of the Earth. This means that the effective force of gravity will be different at different latitudes.

Secondly, as you mentioned, the Earth's rotation also plays a role in determining the effective force of gravity. This is because objects at the equator are moving faster than objects at higher latitudes, resulting in a centrifugal force that can slightly reduce the force of gravity.

To accurately calculate the effective force of gravity at a specific latitude, you would need to consider the following factors:

1. The distance from the center of the Earth at that latitude
2. The mass of the Earth
3. The rotation of the Earth at that latitude
4. The angle at which the normal force is acting (which is dependent on the incline of the surface at that latitude)

Once you have all of these factors, you can use the equations you mentioned in your post to calculate the net force at that latitude. It is important to note that this calculation will give you an approximation of the effective force of gravity, as there are other factors such as the Earth's shape and density variations that can also affect the force of gravity.

In summary, determining the effective force of gravity at a particular latitude is a complex process that takes into account various factors. it is important to carefully consider all of these factors and use accurate measurements and equations to calculate the net force at a specific latitude.