When a drawer is screwed to a shelf and then rolled out, it acts like a lever on the shelf…pushing down on the front of the shelf pulling up on the back of the shelf. If you have 40 lbs in the drawer, roughly 40 lbs is pushing down on the front of your shelf…and 40 lbs is pulling up on the back of your shelf. If you attach the drawer to a floating shelf, the drawer and the shelf, being one, will tip towards you…likely emptying the contents of the drawer onto your lap!
To prevent a floating shelf from tipping, the shelf must be secured by attaching a couple ‘L’ brackets or a strip of wood on top of the shelf at the back, and ensuring they are screwed into the back of the cabinet.