The ballistic pendulum used to be a common tool for the determination of the muzzle veloci...

The ballistic pendulum used to be a common tool for the determination of the muzzle velocity of bullets as a measure of the performance of firearms and ammunition (nowadays, the ballistic pendulum has been replaced by the ballistic chronograph, an electronic device). The ballistic pendulum is a simple pendulum that allows one to record the maximum swing angle of the pendulum arm caused by the firing of a bullet into the pendulum bob.

Figure P5.43

Suppose we want to build a ballistic pendulum to test rifles using standard NATO 7.62 mm ammunition, i.e., ammunition for which a (single) cartridge weighs roughly 147 gr (1 lb = 7000 gr) and the muzzle speed is typically 2750 ft/s. If the pendulum’s length is taken to be 5 ft, and if we are to fire from a short distance so that there is a negligible decrease in speed before the bullet reaches the pendulum, what is the minimum weight we need to give to the pendulum bob to avoid having the pendulum swing to an angle greater than 90°?