Homework Help: Direction of (Inertial) centrifugal force here?

1. Dec 1, 2015

AHashemi

1. The problem statement, all variables and given/known data
an object is sliding on an elliptical hill shown in picture. what is the direction of (inertial) centrifugal force at each moment?

2. Relevant equations
F=mv^2/r

3. 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.

Last edited: Dec 1, 2015
2. Dec 1, 2015

Staff: Mentor

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?

3. Dec 1, 2015

AHashemi

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?

4. Dec 1, 2015

Staff: Mentor

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.

5. Dec 1, 2015

jcruise322

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

6. Dec 2, 2015

AHashemi

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.