A bead slides down a vertical, helical track of radius 6.5 cm and height 32.9 cm with a constant speed of 2.4 cm/s. The helix is wound clockwise with 4 turns per cm down the axis. Take the origin to be at the bottom of the helix in the center of the spiral and the initial position of the bead to be in the x-z plane.

(a) What is the initial position of the bead? F(0) =6.5 cm V 32.9 cm 0 cm
(b) What is the position of the bead after the bead has fallen half the way to the bottom? 16.45 cm
(c) What is the vertical component of the bead's velocity? [Remember that it's falling.]
(d) How log did it take for the bead to travel half way down the helix?
(e) What is the velocity of the bead after it has fallen half the distance to the ground? dr/dt =
(f) What is the acceleration of the bead after it has fallen half the distance to the ground? d2F/dt2=
(g) What is the magnitude of the acceleration of the bead?

The inside surface of a cylindrical-shaped cave of inner diameter 1.0 m is continuously covered with a very thin layer of water. the cave is very long and it is open on both ends. the water on the cave surface is at a constant temperature of 15.5 °c. the cave is constantly exposed to wind such that 15.5 °c air flows through the cave at 4.5 m/s. the kinematic viscosity of the air is 14.66 x 10-6 m2/s and the molecular diffusion coefficient of water vapor in the air is 0.239 x 10-4 m2/s. because the cave diameter is so large, the flow of wind down the length of the cave, in the x direction, can be treated like it is external flow and the cave surface can be approximated as flat where appropriate. calculate the x value, in a) the transition to turbulent flow occurs at rex meters, where the air flow transitions from laminar to turbulent along the inside surface of the cave b) calculate the x value, in meters, where the bulk steady state concentration of water vapor in the air flowing in the cave is 10% of the saturation concentration. assume the air at the surface of the water layer is 100% saturated with water vapor. assume the wind entering the cave contained no moisture before it entered the cave. take into account the transition from laminar to turbulent flow when solving part b