# Physics of a Bow and Arrow

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• Published : January 16, 2012

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The longbow has been used over the years, first as a weapon to hunt, later as a war weapon, and now its used as a sport, but its physics had always been the same over the years, regardless of its use. This physics involves two components: bow mechanics and arrow flightBow mechanics: when an archer pulls back the string, he does work on the bow, and is converted to potential energy. Upon release of the arrow, this potential energy is converted into kinetic energy, most of which is transferred to the arrow and gives it its initial velocity.

The force that the archer applies to the bow to bend it is actually the weight that he feels on his fingers as he pulls back the string. The archer feels a greater weight on his fingers as he pulls the string farther away from its resting position.

The limb of the bow acts like a complicated spring. As the string is pulled back, the shape of the limb changes as does the spring force it exerts. This spring force is labeled S in the adjacent diagram. Thus, the tension, T, in the string is S*cos(B)The area under a straight-line curve, F*d/2, is the amount of energy stored in the bow.

There are several types of straight bows; the most common ones are the longbow and the short bow. The main difference, and the reason on which the longbow was used more and is more effective is that because of the size of it, the longbow can store more energy and by consequence, have a larger range than the short bow, but it does need more force to operate it.

The range of the arrow depends on the following: Its initial velocity and angle of departure, the amount of air resistance and wind effects, and the weight of the arrow. The potential energy stored on the bow is converted to kinetic energy as the archer lets go off the string, and this energy gives the arrow its initial velocity.

When the arrow leaves the bow, both it (the arrow) and the bow move. Thus, the total kinetic energy is the sum of the kinetic energies of both the...