Frictionless body on Earth's Surface

AI Thread Summary
A frictionless body placed on Earth's surface would theoretically move due to the Earth's rotation, with its velocity dependent on latitude, reaching approximately 1040 mph at the equator. The body would experience centripetal and Coriolis forces, while gravitational and normal forces would cancel each other out. The discussion highlights the challenges in identifying equations that encompass these forces, especially considering Earth's non-spherical shape. Examples of near-frictionless objects include fluids and mag-lev trains, which could be influenced by rotational forces if stationary. Overall, the interaction of these forces determines the body's path and acceleration on Earth's surface.
DBirk
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Homework Statement


Will a frictionless body placed on the Earth move, and if so, describe it's path and acceleration.

Homework Equations


I was given no equations, but I believe that coriolis and centripetal forces would act on the body.

The Attempt at a Solution


I assume that we have to assume an initial velocity of 0 relative to the earth. However, from an external reference frame, the body would appear to be moving as a point on the earth. At the equator this would be approx 1040 mph. However, at latitude angle φ this would decrease as you move towards a pole to cosφ.
The coriolis acceleration, centripetal acceleration, gravity and a force normal to the Earth's surface would act on the body. I assume that gravity and the force normal to the Surface would cancel each other out, but I am not certain. I am having trouble identifying an equation that would capture all of these forces on the body.
 
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You need to allow for the actual shape of tne Earth, i.e. not as a sphere.
Or just consider an object that exists on the Earth's surface and does behave pretty much as frictionless. Can you think of anything?
 
I can only think of fluids as such, water and atmosphere. Those have different behaviors though.
One man-made object that approaches frictionless would be a mag-lev train.
Similar question, would a mag-lev be (slowly) induced into movement by coriolis or other rotational Earth force if it was left stationary?
 
DBirk said:
I can only think of fluids as such, water and atmosphere. Those have different behaviors though.
One man-made object that approaches frictionless would be a mag-lev train.
Similar question, would a mag-lev be (slowly) induced into movement by coriolis or other rotational Earth force if it was left stationary?
I was thinking of a boat.
 
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