A small metal sphere of mass m is released from rest at point A and slides without A friction down a smooth track as shown to the right.  At point B it enters at the bottom of a part of the track that is a vertical circle of radius R.  Point D is at the top of the circular portion of the track, and point C is halfway from B to D.  The ball slides completely around the circular portion of the track, just barely keeping contact with the track at point D.  Answer the following in terms of m, R and g. A)  What is the speed of the ball at point D if it is just barely in contact with the track? B)  Find the speed of the ball at point B. C)  Find the speed of the ball at point C. D)  Find the height above B at which the ball was released from rest. E)  Find the normal force of the track on the ball at point B. F)  Find the normal force of the track on the ball at point C.

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.