Physics question with green bead sliding! please help!?

Question

A 0.390 kg green bead slides on a curved frictionless wire, starting from rest at point A in Figure P6.52. At point B the bead collides elastically with a 0.600 kg blue ball at rest. Find the maximum height the blue ball rises as it moves up the wire. In m please! the figure is on this page: http://www.webassign.net/sercp/p6-52.gif

Answer 1

Since the wire is frictionless, all that matters from your diagram is that point A is 1.5 m higher than point B.

Set the zero for potential energy at point B. Then the initial energy of the system is

E = ( .390 kg ) ( 9.8 m/s^2 ) ( 1.5 )

Just before the green bead strikes the blue bead, the energy is entirely kinetic:

E = 1/2 ( .390 kg ) ( v^2 )

Set the two energies equal and solve for v.

Now we have a conservation-of-momentum problem. The initial momentum is

( .390 kg ) ( v )

and the final momentum is

( .390 kg ) ( vg ) + ( .600 kg ) ( vb )

where vg and vb are the final velocities of the green and blue beads. And now you are stuck with one equation and two unknowns. However, the problem asks for the MAXIMUM height that the blue bead can obtain, and that will happen with a PERFECTLY elastic collision. That means we also know that

1/2 ( .390 kg ) v^2 = 1/2 ( .390 kg ) vg^2 + 1/2 ( .600 ) vb^2

Now you have two equations and two unknowns; solve for vb. Then determine the height at which all of the blue bead's initial kinetic energy is converted into potential energy:

1/2 ( .600 kg ) vb^2 = ( .600 ) ( 9.8 m/s^2 ) h

and solve for h, the maximum height reached by the blue bead.