Once again a subject that came up that my knowledge was lacking on. The chart below spells it out so yeah being a light hafted weapon I'd say for a bow you'd defiantly break it with your attack. The other data for doing this and such is in the below link.
http://www.d20pfsrd.com/equipment---final/damaging-objectsTable: Common Armor, Weapon, and Shield Hardness and Hit Points
Weapon or Shield Hardness1 Hit Points2, 3
Light blade 10 2
One-handed blade 10 5
Two-handed blade 10 10
Light metal-hafted weapon 10 10
One-handed metal-hafted weapon 10 20
Light hafted weapon 5 2
One-handed hafted weapon 5 5
Two-handed hafted weapon 5 10
Projectile weapon 5 5
Armor special4 armor bonus × 5
Buckler 10 5
Light wooden shield 5 7
Heavy wooden shield 5 15
Light steel shield 10 10
Heavy steel shield 10 20
Tower shield 5 20
1 Add +2 for each +1 enhancement bonus of magic items.
2 The hp value given is for Medium armor, weapons, and shields. Divide by 2 for each size category of the item smaller than Medium, or multiply it by 2 for each size category larger than Medium.
3 Add 10 hp for each +1 enhancement bonus of magic items.
4 Varies by material; see Table: Substance Hardness and Hit Points.
