jquery red rover

Trying to get to the end of my jquery experiment and have a few basic questions. I'm thinking that I don't need a heavyweight like backbone.js - at this point, my interest is primarily to manage group memberships and being able to drag and drop between them.

This is working...
### view
    <div class="block" id="member_management">
      <ul id="unassigned_users">
        <h4>Unassigned People</h4>
        <% for p in @unassigned -%><li id="moveable-<%= p %>" class="ui-widget-content"><%= p %></li><% end -%>
      <ul id="droppable2" class="ui-widget-header" align="left">
        <h4><%= @group %> Members</h4>
        <% for m in Group.find('admins_all').memberlist %><li><%= m %></li><% end %>

### js
$(function() {
$( "[id^=moveable]" ).draggable();
  $( "#droppable2" ).droppable({
    drop: function( event, ui ) {
      $( this )
      .addClass( "ui-state-highlight" )
     $( "<li></li>" ).text( ui.draggable.text() ).appendTo( this );

and it definitely adds the the dragged 'user' to a new LI in the target but of course, what I want to actually do is send this to my controller, update the records and refresh the view. So my questions...

1 - how do I send this value to :controller => 'people', :action => 'update_memberships', :id => whatever (Is it ui.draggable.text() ? )

2 - Is there a way to update just the <div> or must I do as I did with Rails 1.26 and render :partial => 'some_partial' for on screen updates?

3 - I've been reading all sorts of jquery stuff (books, web pages, etc.) which got me this far but I'm uncertain how to properly send data back to rails controllers... is there a particular web page that explains this to me?