Question: Is one allowed to brush a carpeted floor on Shabbos?
Answer: There is a machlokes in the Gemara (Shabbos 95a) as to whether sweeping a dirt floor on Shabbos is assur mideoraisa or miderabanan. While Rambam (Shabbos 21:3) and the Shulchan Aruch (OC 327:2) allow one to sweep a tiled or stoned floor, the Rema writes that the custom is not to.
Nonetheless, the Aruch Hashulchan (OC 337:5) and Mishna Berura (337:9; Biur Halacha) explain that the Rema (and other rishonim) forbade sweeping such floors as one may come to sweep dirt floors. As we don’t have dirt floors in our houses nowadays, one may sweep tiled floors.
The Rema (OC 337:2) writes that one mustn’t use a hard brush on Shabbos if doing so means that some of its bristles will break (See Mishna Berura 337:14).
The Shearim Metzuyanim Behalacha (80:68) and R’ Yisroel Dovid Harfenes (Nishmas Shabbos 6:297) write that one may use a carpet sweeper (Ewbank) on Shabbos, providing that they don’t press down too hard.
R’ Yitzchak Yaakov Weiss (Minchas Yitzchak 3:50; 5:39:1), R’ Moshe Stern (Baer Moshe 1:32:15) and R’ Mordechai Yaakov Breisch (Chelkas Yaakov 4:6), however, forbid using them. Among other reasons, by brushing the carpet, one is cleaning the pile, which is a prohibition of melaben, whitening.
R’ Ribiat (The 39 Melochos, p710), however, notes that not all of these reasons apply to a regular brush. Thus, R’ Yehoshua Neuwirth (Shemiras Shabbos Kehilchasa 23:4) writes that one may sweep a carpet with a soft brush, though one must be careful not to brush vigorously.
In conclusion, one may sweep a carpet softly with a brush, providing one knows that the bristles won’t break.