Thoughts of Insanity [and science].

“All composite bows are made with a particular strength rating (that is, each requires a minimum Strength modifier to use with proficiency). If your Strength bonus is less than the strength rating of the composite bow, you can’t effectively use it, so you take a -2 penalty on attacks with it. The default composite longbow requires a Strength modifier of +0 or higher to use with proficiency. A composite longbow can be made with a high strength rating to take advantage of an above-average Strength score; this feature allows you to add your Strength bonus to damage, up to the maximum bonus indicated for the bow. Each point of Strength bonus granted by the bow adds 100 gp to its cost.”

Of course, as a ranged weapon, aiming is a different story than being able to pull back a bowstring. Thus, your Dexterity modifier is added to your base attack bonus for attack rolls, while your Strength modifier (limited by the rating of the composite bow) is added to damage. Both are required for effective use of such a weapon.