Why does a cannonball shot from a cannon with a long barrel travel faster than the same cannonball shot from a cannon with a shorter barrel?
The cannonball shot from a cannon with a long barrel travels faster than the same cannonball shot from a cannon with a shorter barrel due to several factors.
One of the key factors is the length of time the accelerating force acts on the cannonball. In a longer barrel, the expanding gases generated by the combustion of gunpowder have a longer distance to push the cannonball forward, resulting in a greater acceleration over a longer period. This allows the cannonball to gain more speed before leaving the barrel.
Additionally, the longer barrel provides a greater amount of time for the expanding gases to exert pressure on the base of the cannonball, leading to a more efficient transfer of energy. This results in a stronger initial push, allowing the cannonball to achieve higher velocities.
Furthermore, a longer barrel allows for better control and stabilization of the cannonball's trajectory. The extended length provides a longer distance for the expanding gases to act as a sort of "guiding force" on the cannonball, reducing wobbling and increasing accuracy.
To summarize, the longer barrel of a cannon provides a longer acceleration period, improved energy transfer, and enhanced trajectory control, which collectively contribute to the increased speed of the cannonball compared to one shot from a shorter barrel.