When a cannon with a longer barrel is fired, the force of expanding gases acts on the cannonball for a longer distance. What effect does this have on the velocity of the emerging cannonball? (Do you see why long-range cannons have such long barrels?)
The length of the barrel of a cannon does indeed affect the velocity of the emerging cannonball. By having a longer barrel, the force of expanding gases from the ignited gunpowder acts on the cannonball for a longer duration.
This is due to a principle known as the impulse-momentum theorem in physics. According to this theorem, the change in momentum of an object is equal to the impulse applied to it. The impulse experienced by the cannonball is directly related to the force and the time over which the force acts.
In the case of a longer barrel, the expanding gases have a longer distance to act on the cannonball. As a result, the force is applied for a longer duration, producing a larger impulse. By applying a larger impulse to the cannonball, its momentum increases, ultimately resulting in a higher velocity.
Therefore, the longer barrel allows the cannonball to achieve a higher velocity when fired. This is why long-range cannons have such long barrels - they allow for greater acceleration of the cannonball, resulting in longer-range shots.