As shown in the figure below, a small mass is released from rest at point A along the horizontal diameter on the inside of a frictionless, hemispherical bowl. The mass has a mass m = 265 g and the bowl has a radius R = 30.5 cm. 2R/3 (a) Calculate the gravitational potential energy of the mass-Earth system (in J) when the mass is at point A relative to point B. (b) Calculate the kinetic energy of the mass (in J) at point B. (c) Calculate its speed (in m/s) at point B. m/s (d) Calculate its kinetic energy (in J) when the mass is at point C. (e) Calculate the potential energy (in J) when the mass is 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.