Physics conversion of momentum

Question

QUESTION: a cannon is sitting loaded with a cannonball making the total momentum of the system before firing 0 kg*m/s. in order to conserve momentum after firing what has to happen to the cannon and the cannonball in order to maintain a total momentum of 0 kg*m/s. Use details about the direction and the relative sizes of the cannon and cannons ball's velocities and masses in your response.

Answer 1

First of all I would like to correct your typos mistake. We are talking about the law of conservation of linear momentum, not conversion!

Before the cannon fired, it was not moving, so its total linear momentum together with the linear momentum of the cannonball is zero. Hence, according to the law of conservation of linear momentum after the cannon fires, it still must be zero. Linear momentum is a vector quantity, it means it has magnitude and direction. If the cannon fired so, that the cannonball moves to the right (choosing right direction as positive), its momentum is positive. Because total linear momentum of the system is not changing ( still is 0), the cannon's momentum will be negative. As a result, it will be moving to the left or in opposite direction to the direction of the cannonball.

P.S. Sizes do not play any role. As for masses, of course we assume, that the mass of the cannon ball is much smaller then the mass of the cannon itself. As a result the muzzle velocity of the cannonball is much greater then that of the cannon.