Imagine a vertical cone that is at an angle $θ$ with the ground.
In one of the cone's sides we place an object of mass $m$ giving it a initial velocity of $v_0$. Is it possible that our object, under only the effect of the normal force exerted to it by the cone and its weight, performs circular motion? If it is can this motion be uniform?
I feel that this is impossible because the normal force would always be less than the weight of the body and therefore there would always be a force dragging the object towards the center of the cone. However I have seen in textbooks that given an initial velocity large enough the object can perform circular motion. How is this possible?
Best Answer
Decompose the gravity force in two directions: one perpendicular to the cone surface and another tangential to it. The component perpendicular to the cone surface will be counterbalanced by the normal force. The component tangential to the surface will be just enough to keep the object moving in a circle at the velocity your textbook talks about.
If the velocity of the object were higher than this one, the object would slide up the cone. If it were smaller, it would fall to the center of the cone.