Particle on a parabolic wire. a particle of mass m slides down parabolic wire under the action a of gravity. the equation for the wire is y x2. (a) determine the equations of motion for this system using lagrange multipliers |(b) determine the equation of motion for this system using the con- straint equation to eliminate y from the problem

Two conductors, a and b, are each in the shape of a tetrahedron. but of different sizes. they are charged in the following manner: 1. tetrahedron a is charged from an electrostatic generator to charge q. 2. tetrahedron a is briefly touched to tetrahedron b. 3. steps 1 and 2 are repeated until the charge on tetrahedron b reaches a maximum value. if the charge on tetrahedron b was q/4 after the first time it touched tetrahedron a. what is the final charge qbmax on tetrahedron b?