Three lions try to take on a croc, but croc skin is like sheetmetal

F=MA describes the force that the croc's muscles apply to accelerate its tail, not the force felt by the leg.

Yes, I wanted to keep things simple because once we start trying to work with impulse and collisions, it gets messy because there are a ton of variables we don't know-- how much kinetic energy is lost, the time over which the collision occurs, etc.

We can presuppose that the croc has some constant amount of muscle power (F_croc) that doesn't change.

Why? The whole point is that the croc generates so much force that it can swing its tail with enough force to propel a 1000 lb creature out of the water.

Yes, if magically its tail weighed a lot less and it was swinging it with the same force, it would be moving a lot faster and impart the same change in momentum in an impact, but that's not really the question we're asking.

The hydraulic press example is invalid, because the press only applies significant force to things that are trapped against something. That's why speed isn't important for the hydraulic press, but it is important in the case of striking a bone.

And your leg is partially trapped as it is connected to your foot which experiences friction against the ground, unless we're also assuming this collision happens in a frictionless vacuum?

To understand why the mass of the tail is effectively a constant, you have to note that Δt is itself a function of mass. If F_croc is constant, then A_tail is inversely proportional to mass, as I mentioned above.

I'm not following. Again, WHY are we holding supposing the force is constant when we are trying to compare force scalars?

Also Δt is NOT a function of mass, it's a function of the elasticity of the collision, aka how much kinetic energy is lost in the form of heat/ friction. A perfectly elastic collision assumes lim Δt -> 0. A foam ball that crumples? Much higher Δt, much lower impulse felt, and much more of the kinetic energy lost to heat and friction. A harder/ less compressible object? Lower Δt and higher impulse.

Again, a heavy object moving slowly can impart just as much momentum change (impulse) as a light object moving quickly.

Another quick note about your original comments that "water is highly resistive" and "[a]t no point is the tail actually moving very fast"-- the tail would be moving much faster without water resistance.

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