Let’s do a quick thought experiment. Let’s say you’re tossing a cannonball in your hand, and the mage shrinks it just as it leaves your hand (maximum momentum). If momentum is conserved, the cannonball would have to dramatically increase speed to conserve momentum.
shrunken size would be about a marble, with a mass of ~2.7g
Initial momentum of the cannonball would be 83.6 kg·m/s. If momentum is conserved, the marble would travel 30963 m/s, or Mach 90. That’s unreasonable.
So for this to make any sense, conservation of momentum shouldn’t be preserved. In other words, mass would be added with the current velocity, so it would increase momentum as it unshrinks.
Bullets typically weigh between 20 and 40 grams. In addition, we can calculate kinetic energy as KE = m * v^2, which means the velocity changes exponentially relative to the mass (I think I incorrectly assumed a linear relationship before).
So in your thought experiment, the 19kg to, say, 19g transformation would change the velocity by a factor of 1000^0.5, or about 32. 32 * 4.4m/s = 140.8 m/s, which is totally reasonable (slower if the bullet is heavier, not sure about the density of a cannonball).
Why assume a conservation of momentum?
Let’s do a quick thought experiment. Let’s say you’re tossing a cannonball in your hand, and the mage shrinks it just as it leaves your hand (maximum momentum). If momentum is conserved, the cannonball would have to dramatically increase speed to conserve momentum.
Example data/assumptions:
Initial momentum of the cannonball would be 83.6 kg·m/s. If momentum is conserved, the marble would travel 30963 m/s, or Mach 90. That’s unreasonable.
So for this to make any sense, conservation of momentum shouldn’t be preserved. In other words, mass would be added with the current velocity, so it would increase momentum as it unshrinks.
Bullets typically weigh between 20 and 40 grams. In addition, we can calculate kinetic energy as
KE = m * v^2, which means the velocity changes exponentially relative to the mass (I think I incorrectly assumed a linear relationship before).So in your thought experiment, the 19kg to, say, 19g transformation would change the velocity by a factor of 1000^0.5, or about 32. 32 * 4.4m/s = 140.8 m/s, which is totally reasonable (slower if the bullet is heavier, not sure about the density of a cannonball).