# Finding the apparent acceleration due to gravity versus latitude

• pandafish
In summary, the conversation involves solving a force balance equation for apparent gravity, which is defined as the net force per unit mass. There is some discussion about the equations used and the direction of the force balance, as well as finding an expression for g. Ultimately, it is clarified that the apparent force is made up of the normal force and the component of the centrifugal force tangential to Earth's surface.
pandafish
Homework Statement
A mass at rest on the surface of the earth at latitude λ , experiences a reaction from the earth that consists of a normal component S per unit mass and a tangential frictional component F per unit mass, directed towards a point vertically above the north pole. The earth is assumed to be a uniform sphere of radius R and mass M rotating with an angular velocity ω about its axis. How is the magnitude and direction of the apparent ’acceleration due to gravity’ g , acting on the mass at latitude , related to these forces?

Show that:

$$g^2 = [\frac{GM}{R^2}-R\omega^2cos^2\lambda]^2 + [\frac{1}{2}\omega^2Rsin2\lambda]^2$$
Relevant Equations
$$g=-\frac{GMm}{R^2}$$
I began by drawing a diagram and resolving the forces. Since the question asked for 'apparent gravity' I tried to find the normal force.

I started with the equations:

## How does altitude influence the apparent acceleration due to gravity?

Altitude influences the apparent acceleration due to gravity because gravity decreases with the square of the distance from the center of the Earth. As altitude increases, the distance from the Earth's center increases, leading to a reduction in gravitational acceleration.

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