I’m pretty sure I could do a discreet analysis if I had the stress-strain curve.
:smack:you’re right, nevermind. I guess a better thing to do for a ballpark upper boundary would be to assume constant deceleration for the sponge, and use the kinematic equation[d=t*(vi+vf)/2], where: vi=19.44m/s, vf=0m/s, d=1m and solve for time (0.1s)
Just think the problem through as if you were falling from the sky into either water or land.
Google on “blasting mat”.
No wait! You cannot just make the sponge any size you want. The OP clearly says the sponge is the same mass as the car. Assume the weight of the sponge itself negligible, making it then a block of water of appropriate dimensions to weight whatever it is we are saying the car weighs.
I think the friction of the sponge with the floor will be an issue. Can the car move this sponge from where it is?
It’s been a delightfully long time since I studied physics and I don’t miss it one bit, but can’t you treat the sponge like a spring? As the material compresses, the resistance to squishing is going to increase much like a spring would (ignoring the complexity of the exiting water).
I don’t think this is analogous, as the water will be more confined when it’s in the sponge, which will severely attenuate the wave propagation.
All the blasting mats I’ve seen (and the ones I just googled) came up as woven cable and rubber products. Googling blasting mat foam and “blasting mat” foam doesn’t seem to give any relevant hits.
ETA:
Yep! The slope of the stress-strain curve is k, where F = k * x, where x is the amount of deformation. the stress-strain curve plots force versus deformation, or F/x.
That’s why I suggested a 1 x 1 x 2 sponge. It would be about 2000 kg, ignoring the sponge’s mass (which, at this size, might not really be negligible).
Solfy and Santo: could this be modeled as a car hitting, simultaneously, a spring and a large block of water?
It could be done just by modeling it as a spring; that would take into account the water as well. The trick is to find the k value of the spring, or the slope of the stress-strain curve. I’m not sure where to find that information, as all my references are for structural materials.
But the water is forced out as the sponge compresses. A regular spring doesn’t lose mass as it compresses.
The stress-strain diagram should account for this. Once the system becomes non linear, the problem becomes much more complicated. It wouldn’t be that much more difficult, though, instead of having F = k * x, we might have something like F = a x[sup]2[/sup] - bx (there won’t be a c term, because there is no force at no deformation).
Also remember, the power exerted on the car will be the same regardless of the amount of time it takes to slow it down. The power is the area under the curve of the time versus force diagram. This will be equal to 1/2 m * v[sup]2[/sup], the kinetic energy of the car.
I don’t think this is right, either: A quadratic spring would still be elastic, where this pretty clearly isn’t. The force exerted by the sponge isn’t going to just depend on how much it’s compressed, but also on its history. I suspect without proof that in practice, the force is going to quickly asymptote to some nearly-constant value, which would be the optimum for a safe-stopping system.
Using the calculations **Santo Rugger ** proposes, it’s not necessary to know the mass loss in the sponge. The mass loss from water is part of what determines the k value for the springy sponge, but that k value is made all the more difficult to predict because of the water loss. It’s not likely to behave in a simple, predictable manner.
I just wanted to pop in and say that the idea of a car ramming into a ginormous damp sponge is just really funny to me. And I’m trying desperately to not post a GQ pertaining to an airplane nosing into a brick wall vs. an infinitely large damp sponge on a treadmill.
I’m not a physics guy, so ignore me when it comes to calculations.
That said, I’d like to contribue some “common sense” (I hope) observations.
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The key to me would be elasticity. You’re not hitting a rigid surface, you’re hitting a surface that gives to some unknown degree. The size and weight of the sponge is irrelevant-- the elasticity is what is key (there may be a better technical term than that, forgive me).
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Jump ten feet into a tank filled with one hundred tons of water vs. ten feet onto one hundred tons of concrete. Weight is irrelevant to the calculation, no?
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Fire a rifle at a steel wall-- the bullet stops but is deformed. Fire a bullet into water-- the bullet is slowed but unlikely to be deformed to the same extent. Water, by having give, allows an object otherwise thought as very powerful (a bullet) to be slowed quickly.
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We already use sponges to stop car crashes-- in addition to the aforementioned crumple zones and water barrels (which are there to protect drivers & passengers from impacting solid walls), there’s also the lowly airbag. It’s just an air-filled sponge.
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I may be completely wrong here, but a sponge soaked with water may actually have more give than a sponge without water, as the water can be ejected in an opposite direction of the impact force to counteract the impact.
To borrow a very random example, I’m thinking of the principles behind countershot anti-tank weapons like the Armbrust.
When the giant water-soaked sponge is hit, how much of the impact’s energy is applied to water that would then escape the sponge vs. how much is applied to the structure of the sponge itself?
Just a few thoughts to chew over.
If the sponge is 1 meter tall, isn’t a large part of the sponge going to slide under the car? If we’re talking significant speed, this car is going to flip over from hitting the sponge!
No. Or, rather, you can’t accurately model the sponge as solely a spring. At a minimum, the sponge has a distributed mass, and that mass has been defined to be equal to the mass of the car. Some portion of the kinetic energy of the car must go into accelerating the mass of the sponge.
As a simplified analogy, consider two cases: one where the car collides with a giant massless spring attached to a wall on the far end, the other where the car collides with a giant massless spring attached to a wall on the far end and a block of steel on the near end. Will the dynamics be different? Yes they will, because the block of steel has to be accelerated.
In the same way, the distributed mass of the sponge must be accelerated. Now, if this were the only complicating factor, you could write a 1D partial differential equation to describe the compression of the sponge, which looks like the wave equation for elastic motion in a longitudinal rod:
E([symbol]d[/symbol][sup]2[/sup]u)/([symbol]d[/symbol]x[sup]2[/sup]) = [symbol]r/symbol/([symbol]d[/symbol]t[sup]2[/sup])
However, the real system is more complicated, because it includes both friction, non- 1D deformation, and the effect of water spraying out of the sponge. This last changes the mass of the sponge and, more importantly, the apparent stiffness – the amount of water leaving depends, I think, on velocity (try it for yourself by wetting a sponge and punching it).
So, all that leads to, approximately, a second-order 1D partial differential equation, with a velocity term, with unknown stiffness (that may be a function of deformation distance) and velocity coefficients, a mass coefficient that’s dependent on velocity, and an additional friction term that’s probably non-constant. Whew. Sounds like a PhD dissertation to me.
I believe you intended to say energy is constant. Power is not.
I can offer some personal experience here.
Years ago I was driving on a lonely stretch of poorly lit Interstate when suddenly out of the darkness a huge oblong object (at least three feet high and probably six feet long) loomed up on the road directly in front of me. I had no time to get out of the way and struck it head-on.
From the way it bounced harmlessly off the car and out of my way, I deduced that it was an enormous chunk of sponge-like packing material that had evidently fallen off another vehicle. Logically if it had been wet and weighed as much as my car, I might not be here now.
If you jump off a bridge and hit water as opposed to concrete, it won’t help. The impact is likely to kill you either way. Hit another car at high speed or an equal weight of wet sponge, and you will be severely damaged or killed in either instance.
No facts, all anecdote.
Many, many people have jumped of bridges into water an survived: http://www.straightdope.com/columns/read/2587/could-you-jump-off-a-bridge-or-a-tall-building-and-survive-the-fall