Direction of (Inertial) centrifugal force here?

In summary, the direction of the (inertial) centrifugal force at each moment for an object sliding on an elliptical hill is orthogonal and pointing outwards from the center of the ellipse. The value of r in the formula for centrifugal force varies by time and the center of curvature for the ellipse changes at every point. The direction of the centrifugal force vector can be found by estimating the line along which the radius of curvature lies at different locations on the ellipse.
  • #1
AHashemi
25
0

Homework Statement


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

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.
 
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  • #2
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
gneill said:
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?
 
  • #4
AHashemi said:
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.
 
  • #5
I am pretty new, but wouldn't it be, by definition, orthogonal and pointing outwards?
 
  • #6
jcruise322 said:
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.
 

1. What is the direction of the (inertial) centrifugal force?

The direction of the (inertial) centrifugal force is always perpendicular to the direction of motion and points away from the axis of rotation.

2. How is the direction of the (inertial) centrifugal force related to the direction of motion?

The direction of the (inertial) centrifugal force is always perpendicular to the direction of motion. This means that if an object is moving in a circular path, the centrifugal force will be directed away from the center of the circle.

3. Does the direction of the (inertial) centrifugal force change with the speed of rotation?

Yes, the direction of the (inertial) centrifugal force changes with the speed of rotation. As the speed increases, the force also increases and the direction becomes more outward.

4. How does the direction of the (inertial) centrifugal force affect the motion of an object?

The direction of the (inertial) centrifugal force is responsible for changing the direction of an object's motion and keeping it moving in a circular path. It also creates a counteracting force to the centripetal force, which keeps the object from flying off in a straight line.

5. Can the direction of the (inertial) centrifugal force be manipulated?

Yes, the direction of the (inertial) centrifugal force can be manipulated by changing the speed or direction of the object's motion. It can also be altered by changing the axis of rotation or the mass of the object.

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