Direction of (Inertial) centrifugal force here?

[AHashemi]

Homework Statement

an object is sliding on an elliptical hill shown in picture. what is the direction of (inertial) centrifugal force at each moment?

Homework Equations

F=mv^2/r

The Attempt at a Solution

I think it should be towards the center of ellipse and value of r in the formula varies by time.
Not sure.

 

[gneill]

Perhaps you should consider what the "r" is in the centripetal or centrifugal force equation. Can you estimate the center of curvature of a local bit of the ellipse at various locations? How is the direction of the radius of curvature related to the tangent of the curve?

 

[AHashemi]

Perhaps you should consider what the "r" is in the centripetal or centrifugal force equation. Can you estimate the center of curvature of a local bit of the ellipse at various locations? How is the direction of the radius of curvature related to the tangent of the curve?

r is distance from center of rotation. in circular motions r is constant but here it changes by time.
is center of a small curve center of a larger circle which that curve is departed from?

 

[gneill]

r is distance from center of rotation. in circular motions r is constant but here it changes by time.
is center of a small curve center of a larger circle which that curve is departed from?

I'm not sure that I understand your intended meaning for that last statement. But it is true that for the ellipse the radius of curvature changes at every point, in both length and the direction to its "center". If you can estimate the line along which the radius of curvature lies at several places on the sketch then you will have found the direction of the centrifugal force vector for those locations.

 

[jcruise322]

I am pretty new, but wouldn't it be, by definition, orthogonal and pointing outwards?

 

[AHashemi]

I am pretty new, but wouldn't it be, by definition, orthogonal and pointing outwards?

Yes.
Centripetal force and centrifugal inertial force have opposite directions. When I said it should be towards center of ellipse I was talking about centripetal force.