A small rock with mass 0.28 kg is released from rest at point A, which is at the top edge of a large, hemispherical bowl with radius R=0.46 m. Assume that the size of the rock is small compared to R, so that the rock can be treated as a particle, and assume that the rock slides rather than rolls. If the surface of the bowl is frictionless, (a) what is the speed of the rock as it reaches point B? (b) What is the work done by gravity on the rock as it moves from point A to point B?

Along wire of diameter 1 mm is submerged in an oil bath of temperature ∞ 31°c. the wire has an electrical resistance per unit length of 0.01 ω/m. if a current of 103 a flows through the wire and the convection coefficient is 500 w/m2·k, what is the steady-state temperature of the wire? from the time the current is applied, how long does it take for the wire to reach a temperature that is within 1°c of the steady-state value? the properties of the wire are 8000 kg/m3, 500 j/kg·k, and 20 w/m·k.