A small cube of mass m slides back and forth in a frictionless, hemispherical bowl of radius R. Suppose the cube is released at angle .
What is the cube's speed at the bottom of the bowl?
a. Begin by drawing a before-and-after pictorial representation. Let the cube's initial position and speed be . Use a similar notation for the final position and speed.
b. At the initial position, are either zero? If so, which?
c. At the final position, are either zero? If so, which?
d. Does thermal energy need to be considered in the situation? Why or why not?
e. Write the conservation of energy equation in terms of position and speed variables, omitting any terms that are zero.
f. You're given not the initial position but the initial angle. Do the geometry and trigonometry to find y_1 in terms of R and theta. Use your result of part f in the energy conservation equation, and then finish solving the problem.
