I don't think you can drag items directly from the sidebar to the dock. Moving it to the dock would be a two step process.
1. Open Finder. Select Macintosh HD from the sidebar. The Applications folder should appear along with all the others on the HD. Select the Applications folder from here and drag it to the right side of the dock.
2. If desired, you can delete the Applications shortcut from the sidebar by simply dragging it off the sidebar and then releasing the mouse over the desktop.
You don't drag from the sidebar as the sidebar is simply a link to the Applications folder much like an icon in the Dock is. Open a Finder window, navigate to your root directory (unless you changed the name, go to "Macintosh HD") and drag the Applications folder from there.
And if you move anything from the Sidebar or the Dock, it goes poof! and disappears. It's easy to put it back, just find the real thing and drag it to either spot.
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