Question

Hollywood often portrays bows as extremely lethal. In reality, however, they were replaced by firearms on the battlefields of Europe after the 100 years’ war (1337-1453). While all early projectile weapons were very inaccurate (sights are a recent invention), the most striking difference between the bow and the musket lies in the kinetic energy carried by the projectile. A well trained archer using the famous English Longbow could fire an arrow of about 100 grams (0.1 kg) with an initial energy of approximately 100 J.

A: Compare this to a black-powder musket and a modern rifle. Flintlock muskets typically fired a 30 gram projectile with an initial velocity of 200-300 m/s, whereas a modern US M4 carbine fires a 4 gram bullet at 910 m/s.

B: What would the recoil momentum be for all three weapons?

C: If we assume that the longbow stores energy like a spring, what would the spring constant k be? For simplicity, assume that the displacement is equal to the length of the arrow, which was about 30 inches (0.76 m).

Answer 1