Story related.
To clean the entrance hall you need to retrieve a broom from the display case in the staff room. To open the display case to get the broom you need to exhaust conversation with the troll, The troll with share that he hates when someone sticks a penny in the doorway to jam it closed ... so, do just that: put a coin in the front door, call it to the troll's attention, and when the troll is addressing the door, cast the flap open spell on the troll's keying.
After collecting the keys and opening the display case and getting the broom, use it. You'll tire and will then need to case an Automation spell on the broom. After this, retrieve a law book from the library and hand it to Headmaster Bloch to show it's illegal for you to have to reach high places ... getting you out of cleaning the cobwebs.