As another poster mentioned, this is likely the reason this isn’t already done in the fantasy setting. Either the mass is the same (in which case your flintlock isn’t going to launch it terribly far) or the mass changes and it would reduce momentum.
That being said, it’s still a useful way to transport cannonballs, and could still be quite useful. Just not quite a “free” Catapult spell on demand.
If the mass increases after the ball is already moving, then velocity should be conserved and momentum would increase with the mass. That breaks all kinds of physics rules, but this is DnD in a magical universe, there are worse violations going on.
Sorry, I should say that the momentum is conserved, but it would affect the velocity (that is, the overall kinetic energy is the same, which means velocity has to drop by an equal factor to conserve energy). It would be similar to if the extra mass were to be suddenly tethered to the bullet, which would understandably slow it down.
That being said, it’s D&D and people can rule however they want.
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).
Would the momentum stay if the mass increases?
Lol the ball just falls out the end like a defective Acme gun
As another poster mentioned, this is likely the reason this isn’t already done in the fantasy setting. Either the mass is the same (in which case your flintlock isn’t going to launch it terribly far) or the mass changes and it would reduce momentum.
That being said, it’s still a useful way to transport cannonballs, and could still be quite useful. Just not quite a “free” Catapult spell on demand.
If the mass increases after the ball is already moving, then velocity should be conserved and momentum would increase with the mass. That breaks all kinds of physics rules, but this is DnD in a magical universe, there are worse violations going on.
Sorry, I should say that the momentum is conserved, but it would affect the velocity (that is, the overall kinetic energy is the same, which means velocity has to drop by an equal factor to conserve energy). It would be similar to if the extra mass were to be suddenly tethered to the bullet, which would understandably slow it down.
That being said, it’s D&D and people can rule however they want.
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).
Momentum could still be conserved if the velocity is unchanged, but it would mean there’s now a lot of kickback once it gets big…
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