Speed and net work of bead down a frictionless track?

Question

Speed and net work of bead down a frictionless track?
A bead of mass m = 5.10 kg is released from point A and slides on the frictionless track shown in Figure P5.30. The height of A is ha = 5.90 m.

Figure P5.30: http://i165.photobucket.com/albums/u78/RLB31384/p5-30alt.gif
(a) Determine the bead's speed at points B and C. point B m/s
point C m/s
(b) Determine the net work done by the force of gravity in moving the bead from A to C.

Answer 1

Initial potential energy PE0 = m*g*ha
Initial kinetic energy KE0 = 0
At each point x in [B, C] with height hx,
PEx = m*g*hx
KEx = KE0 + PE0 - PEx
Vx = sqrt(2 * KEx / m) (answer a)
Work done in moving from A to C:
W = PE0 - PEC (as defined above) (answer b)