Sidebar from static home page showing up on blog page- don't want that.

please start by creating a child theme of Twenty Eleven to work with ( http://codex.wordpress.org/Child_Themes ) if you haven’t done so already.

the blog page will be using the index.php template of the theme;

edit this index.php and see if you can remove the code with get_sidebar();

this will probably need some further adjustments in functions.php;

please post a link to your site so someone can have a look at it.