According to Grok: Based on your description, the silent movie you're referring to is likely "The Floorwalker," a 1916 film written, directed, and starring Charlie Chaplin. In this short comedy, Chaplin plays his famous Tramp character. The scene you’ve described aligns with a sequence in the film where Chaplin’s character is in a department store. There’s a moment involving an escalator (which could be the "thing being propelled by rope from the ceiling" you mentioned, though it’s not exactly a rope), and a series of comedic misunderstandings unfold.
In "The Floorwalker," Chaplin’s Tramp gets into various antics, including knocking into people and objects, and there’s a general slapstick tone that matches your recollection. While the janitor-specific details (like kicking him or the bucket of water) might be slightly off or blended with another Chaplin short, the barbershop mention could be a confusion with a different film, like "The Barber Shop" (1933, a later sound short). However, "The Floorwalker" features a confrontation and physical comedy in a public space that fits your memory best. The hat-knocking and escalating chaos are classic Chaplin gags.
If this doesn’t sound quite right, it could also be a mix-up with another of his early works like "The Rink" (1916) or "Behind the Screen" (1916), which involve similar slapstick setups. But "The Floorwalker" seems the closest match.