A marble rolls around the inside of a frictionless cone. Draw a free-body diagra

Question

A marble rolls around the inside of a frictionless cone. Draw a free-body diagram (FBD) of the marble when it is on the left side of the cone.
If the weight is given by the vector E, find the normal force (from vectors A-X) and the direction of the acceleration (from vectors Q-X) when the marble is on the left side of the cone. E.g., if the normal force is A and the acceleration is in direction Q, enter AQ.

A marble rolls around the inside of a frictionless cone. Draw a free-body diagram (FBD) of the marble when it is on the left side of the cone. If the weight is given by the vector E, find the normal force (from vectors A-X) and the direction of the acceleration (from vectors Q-X) when the marble is on the left side of the cone. E.g., if the normal force is A and the acceleration is in direction Q, enter AQ.

Explanation / Answer

The normal force must be at least as large as M and opposes not only M (vertical), but the (horizontal) centripetal force as well. How big the latter is depends on the speed of the marble and the radius of its "orbit". The configuration of the cone suggests to me that the vertical and horizontal forces should be about equal, so I'd say "P". However, the answer could be "H". "X" has the proper direction, but is too small.

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