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[EDIT: Losing my cool, gonna let past events slide.]

I've got one object colliding into another. Weapon and Target. Weapon is assumed to be a rigidbody, and the area of the weapon's surface and the target match perfectly. Target has some elasticity.

My variables are therefor currently as follows:
Weapon - Mass and Velocity
Target - Mass, Elasticity, and the Depth of the target's volume (applying yet more stress to the strain over time)

How exactly does the target's stress from the collision's strain affect the velocity of the weapon?
SmallTownGuy's avatar

Beloved Elder

Maybe it would help if you explained why the answers those other physicists gave were unsatisfactory? We'd hate to simply repeat what they've already said.
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Shadowy Rogue

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SmallTownGuy
Maybe it would help if you explained why the answers those other physicists gave were unsatisfactory? We'd hate to simply repeat what they've already said.


"We do physics here, not video games."
SmallTownGuy's avatar

Beloved Elder

Then perhaps you should rephrase it as a golf club hitting a compressible golf ball?

The short answer is that the golf club slows down, the golf ball speeds up, and the total momentum is conserved. Whether kinetic energy is also conserved depends on whether the ball's compression is lossy.

The longer answer is that the forward pressure on the ball compresses the ball in proportion to its Young's modulus. The ball's center of mass accelerates in proportion to that pressure / its mass. Just integrate over the few milliseconds of the impact, and you'll get the ball's motion. I can't tell you more detail without knowing how lossy the ball's compression is.
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Shadowy Rogue

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SmallTownGuy
Then perhaps you should rephrase it as a golf club hitting a compressible golf ball?

The short answer is that the golf club slows down, the golf ball speeds up, and the total momentum is conserved. Whether kinetic energy is also conserved depends on whether the ball's compression is lossy.

The longer answer is that the forward pressure on the ball compresses the ball in proportion to its Young's modulus. The ball's center of mass accelerates in proportion to that pressure / its mass. Just integrate over the few milliseconds of the impact, and you'll get the ball's motion. I can't tell you more detail without knowing how lossy the ball's compression is.


Young's Modulus is something I've been looking at, and it's the main variable between targets.

The other site tossed f=ma at me, but I don't see that working. It might be approximately correct for something where the whole of the target is being accelerated at a rate with negligible variance.

But imagine a sword striking a rubber replica of the Great Wall of China. The only part of the wall that's going to make a great deal of difference is what's in the immediate striking area. Common sense tells me that the sword is going to get a nice chop into it regardless of the wall's mass a mile away.

As a sword travels, it begins to apply strain to the target in a very concentrated area, and intuition tells me that it will continue traveling and applying strain, while the stress of the immediate area tries to decelerate it. The rubber would quickly reach the fracture point of its stress/strain relationship, splitting to the sword's motion.
The point where the rubber stops the sword is where the stress has finally decelerated the sword enough, leaving it stuck somewhere inside the rubber.

Contrast this with the real Great Wall of China, where a sword might scratch it but make very little progress, due to a much higher modulus of elasticity.

Perhaps f=ma might apply somehow, but I'm not sure I envision much of a difference between a mile-long wall and a 1000-mile-long wall. As I see it, the sword would make a pretty similar strike either way. This is why I think it's more from the immediate stress than the mass itself.
SmallTownGuy's avatar

Beloved Elder

Well, you said the area of the weapon's surface and the target match perfectly. That would hardly describe a sword hitting the Great Wall.

We also have to assume other details are within reasonable limits. A golf club hitting a golf ball would have different results than a golf club hitting an egg.
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SmallTownGuy
Well, you said the area of the weapon's surface and the target match perfectly. That would hardly describe a sword hitting the Great Wall.

We also have to assume other details are within reasonable limits. A golf club hitting a golf ball would have different results than a golf club hitting an egg.


Ah, right. Isolating the Area variable was to figure out exactly how stress itself works; for sharp weapons like a sword stress would work the same way, but the strain is much higher in that particular spot. So the mechanic doesn't change, just the intensity at any given spot.

As far as targets I'm assuming pretty regular makeup; solid rubber, golf ball, big stones, etc.
Continuum mechanics isn't my area, but you want to get to know the stress wiki page and probably look up a few stress-strain curves.
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Tuah
[EDIT: Losing my cool, gonna let past events slide.]

I've got one object colliding into another. Weapon and Target. Weapon is assumed to be a rigidbody, and the area of the weapon's surface and the target match perfectly. Target has some elasticity.

My variables are therefor currently as follows:
Weapon - Mass and Velocity
Target - Mass, Elasticity, and the Depth of the target's volume (applying yet more stress to the strain over time)

How exactly does the target's stress from the collision's strain affect the velocity of the weapon?


Now, for some reason I can't exactly figure out all the information you given us. But from the limited physics I know, It seems like the momentum from the weapon firing, would affect the velocity.

You have three masses, the weapon, the bullet, and the target, all are at a stand-still. You fire the weapon, it recoils, the bullet moves forward, the target is hit. I don't think the target directly affect the weapon.


EDIT: ******** me I assumed it was a gun, I understand now, one second.
shinigami ryukie's avatar

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shinigami ryukie
Tuah
[EDIT: Losing my cool, gonna let past events slide.]

I've got one object colliding into another. Weapon and Target. Weapon is assumed to be a rigidbody, and the area of the weapon's surface and the target match perfectly. Target has some elasticity.

My variables are therefor currently as follows:
Weapon - Mass and Velocity
Target - Mass, Elasticity, and the Depth of the target's volume (applying yet more stress to the strain over time)

How exactly does the target's stress from the collision's strain affect the velocity of the weapon?


Now, for some reason I can't exactly figure out all the information you given us. But from the limited physics I know, It seems like the momentum from the weapon firing, would affect the velocity.

You have three masses, the weapon, the bullet, and the target, all are at a stand-still. You fire the weapon, it recoils, the bullet moves forward, the target is hit. I don't think the target directly affect the weapon.


EDIT: ******** me I assumed it was a gun, I understand now, one second.


Weapon: M1, V1
Target: M2, V2

Every action has an equal and opposite reaction, and there's a change in momentum.
[(M1)(V1)+(M2)(V2)]i = [(M1)(V1)+(M2)(V2)]f
[(M1)(V1)]i = [(M1)(V1)+(M2)(V2)]f
If it's elastic it has to have the same total KE before and after. So either the target absorbs the majority of the energy, or the weapon bounces back with move force than before.

Bare in mind I'm talking half out my rear end here, and assume you're a nuclear physicist in a lab and know all of this,
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Shadowy Rogue

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shinigami ryukie
shinigami ryukie
Tuah
[EDIT: Losing my cool, gonna let past events slide.]

I've got one object colliding into another. Weapon and Target. Weapon is assumed to be a rigidbody, and the area of the weapon's surface and the target match perfectly. Target has some elasticity.

My variables are therefor currently as follows:
Weapon - Mass and Velocity
Target - Mass, Elasticity, and the Depth of the target's volume (applying yet more stress to the strain over time)

How exactly does the target's stress from the collision's strain affect the velocity of the weapon?


Now, for some reason I can't exactly figure out all the information you given us. But from the limited physics I know, It seems like the momentum from the weapon firing, would affect the velocity.

You have three masses, the weapon, the bullet, and the target, all are at a stand-still. You fire the weapon, it recoils, the bullet moves forward, the target is hit. I don't think the target directly affect the weapon.


EDIT: ******** me I assumed it was a gun, I understand now, one second.


Weapon: M1, V1
Target: M2, V2

Every action has an equal and opposite reaction, and there's a change in momentum.
[(M1)(V1)+(M2)(V2)]i = [(M1)(V1)+(M2)(V2)]f
[(M1)(V1)]i = [(M1)(V1)+(M2)(V2)]f
If it's elastic it has to have the same total KE before and after. So either the target absorbs the majority of the energy, or the weapon bounces back with move force than before.

Bare in mind I'm talking half out my rear end here, and assume you're a nuclear physicist in a lab and know all of this,


I drawed a diagram!
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I'm actually kind of a noob to actual physics. I've got some good common sense on the subject since I've worked with physics engine approximations, but no real schooling on the subject. I only know enough to ask this question.

Essentially I'm trying to figure out how much of the object gets deformed to the point of plastic deformation/fracture, which will be entirely based on how far the weapon accelerates the target's surface before it's slowed to a halt. Propping the target against a wall illustrates what principles I'm trying to understand a little better.


Addendum: Hm... Stress is in units of Pressure which is Force per unit of Area. This is useful perspective to move forth from.

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