A small cube of mass m slides back and forth in a frictionless hemispherical bowl of radius R. The position of the cube is defined by the angle it is moved around the edge of the bowl starting from the bottom of the bowl. Suppose the cube is raised to an angle θ and released. What is the cube’s speed at the bottom of the bowl? Your solution must include labelled diagrams (initial and final) of the problem.
Your solution must address the following questions:
i. What is your definition for the system for this problem?
ii. Is any external work done on the system?
iii. What is the main principle or concept used to solve this problem?
iv. Discuss how this problem could be solved by using Newton’s laws, what problems are encountered?