The Rama (Rav Moshe Isserles of Cracow, 1530-1572), in discussing the laws of Shabbat (end of Orah Haim 337; listen to audio recording for precise citation), forbids the use of a brush with bristles made from small pieces of wood. These brushes were used to clean garments or tables, or as brooms to sweep floors. The Rama explains that when one uses this brush, it is inevitable that several bristles will break, and it should therefore not be used on Shabbat.
The Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) comments that although breaking these bristles falls under the category of "Mekalkel" – a destructive, rather than constructive, act – and should therefore be allowed, nevertheless, one should avoid breaking them on Shabbat. However, in his Be’ur Halacha, the Mishna Berura brings the lenient ruling of the Birkeh Yosef (by the Hida, Rav Haim Yosef David Azulai, 1724-1806), citing Mahari Castro (Egypt, 1525-1610). The Hida noted that using this brush should be entirely permissible, since breaking the bristles serves no constructive purpose, and the bristles are not being removed from their life source (as in the case of removing vegetation from the ground or fruit from a tree). And even if this in principle is forbidden Mi’de’rabbanan (by force of Rabbinic enactment), nevertheless, according to the majority of the Halachic authorities, it is permissible to perform an action that will have an unwanted and unintended result that is forbidden Mi’de’rabbanan. Even if this result is inevitable ("Pesik Resheh"), nevertheless, as long as one does not intend for this result, and has no interest in this result ("Lo Niha Leh"), the act is permitted. Therefore, the use of this brush should be allowed. This is, indeed, the ruling of Hacham Ovadia Yosef in his Yabia Omer (vol. 4, Orah Haim 30:18), as well as in Yehaveh Da’at (2:46) and Hazon Ovadia – Shabbat (vol. 4, p. 48).
Summary: One may use on Shabbat a brush or broom made with small wooden bristles, even though some bristles will inevitably break as a result.
