PURPOSE: To determine the velocity with which an arrow is shot by a bow using a ballistic pendulum.

DESCRIPTION: The arrow is shot into a box which acts as a ballistic pendulum. Ballistic pendulum equations can be used to determine the velocity of the arrow. Photographs below show details of the measurement of the horizontal displacement of the target box.

Alternatively, weights can be hung onto the bow, and a graph constructed showing the displacement of the bow as a function of weight. Because it is nearly linear, this curve can be integrated very easily to obtain the energy stored in the bow when it is fully extended. This stored potential energy in the bow can be compared quite accurately with the kinetic energy of the arrow determined from its velocity. Photographs below show the measurement of the force vs. displacement curve; the displacement is 0 for 0 weight, 15 cm for 6 kg, and 38 cm for 12 kg, as seen, which is reasonably linear.

SUGGESTIONS: CAUTION!! AIM CAREFULLY.

REFERENCES: (PIRA 1M40.43) See equations and sample data in Demonstration Reference File.

EQUIPMENT: Bow and arrow, ballistic pendulum assembly, stand with meter stick, 16 kilograms of weights, transparency grid for graph.

SETUP TIME: 10 min.