Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Curious Cat on 26/09/2021 16:40:17
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Because mv and ½mv2 are quantities called momentum and energy.
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But why does speed really kill?
Because the transfer of large amounts of momentum and energy to the human body tends to disrupt its vital functions.
If I have a head-on with another car doing 50 each, I would expect to walk away, unscathed, in my big car,
Prepare to be disappointed. Briefly.
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But why does speed really kill?
It doesn't kill at all. It's unequally distributed acceleration which tends to disassemble an object. Absent the acceleration, one has no problem.
So I might die by being accelerated by a bridge abutment moving at 60 km/hr, but the guys in the ISS are moving at 26000 km/hr (approx) and are not hurt at all by it.
Why is it that if a car doing 100K crashes into a stationary car, it's a gonner,
and yet if I have a head-on with another car doing 50 each,
I would expect to walk away, unscathed, in my big car,
That's the same accident. Maybe the airbags didn't go off in the parked car because it isn't armed when the engine is off. I'm assuming the same two cars colliding. You're equally protected in both situations.
A car doing 100 has twice the KE of 2 cars doing 50 each, combined.
But KE is utterly abstract, and is frame dependent. In a different frame, both cars might have massive KE. It isn't a function of KE.
I had an accident on the highway 10 years ago with both vehicles moving at well over 100 km/hr and it resulted in a minor dent in my car and no visible damage to the other larger one. The fairly large KE we both had (him more than me) had nothing to do with it. It's the acceleration imparted to my vehicle that caused the damage, and there was very little of that.
The abutment on the other hand is a problem. Hitting that at a delta-V of 100km/hr will likely cause serious injury because the acceleration is far higher than when hitting the parked car.
My mother, in her 80's, hit (broadsided) a much larger nearly stationary vehicle at at least that speed and came away with massive bruises but nothing broken except what little remained of the car. Try that with a car made in the 70's and see what happens.
Take care. Drive careful, hey?
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...Yes of course I've heard of "It's not the speed that/which kills, U. It's the sudden deceleration/stopping".
Come on, guys. Get Ur head/s out of Ur physics books. Get real.
It’s nothing to do with physics books, just common sense.
Two people of same weight jump from same floor of a burning building.
They both have same terminal velocity, momentum and KE.
One hits the deck, the other into a fireman’s blanket (or whatever they are called).
Who survives?
Change of momentum f=ma. A human body can only withstand a certain amount of g force.
Obviously, you need enough speed to get the deceleration, which is where I suspect the confusion comes from, add in crumple zones etc.
Dunces, with cars, know this, instinctively!
I wonder why they are dunces? ???
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Why does double the velocity double the momentum and quadruple the KE?
It comes down to Integration.
When you see E = ½mv2, the association of the ½ and the v2 suggests that there is integration going on here
I'll leave it to others to describe what is being integrated (and why).
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Why does double the velocity double the momentum and quadruple the KE?
This is a fantastic question and very difficult to give an example of why it is so. I will try an example if we have two circles and one is twice the diameter of the other one we get 4x the surface area. Now with a projectile, if we double the velocity the impact force is increased by a factor of 4x the diameter of the projectile has not changed but the speed and the kinetic energy has the impact force is measured by the force applied over the diameter of the front the mass of the projectile that is made up of particles that are all doubling the velocity and each particle must contend with the particles behind them each particle is loaded up by the mass of particles behind them the first particle is x2 second particle is also x2 this is true for all the particles and the net result is 2x2 a factor of x4. If we only double the weight but not the speed each particle remains the same and will be a factor of x1. 1x1 = 1 double the mass 1+1 = 2. This is how my funny head worked it out I hope it makes sense It could be wrong.
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JT, please tell 'em:
Would U rather crash into a stationary car at 100
or have a head-on with another car at 50, each?
The relative velocity is the same but the damage is twice in the first case, coz the (total) KE is twice.
Yes, I see what you're saying my first response was regarding only one object in motion. The second is the sharing of impact this is a different story. I do believe that the initial impact is the same but due to the cars having their own momentum this will reduce the overall damage to the front as the rear will take some of the load if both are in motion if we take the example of a car hitting a wall at 100 and the wall is still we hit at 100 if we are travelling at 50 and the wall is travelling at 50 that will be the same as hitting a still wall the wall has no rear collapse but cars do.
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KE and stopping distance go up exponentially, with speed"!
KE and stopping distance go up exponentially, with speed"!
If U double the speed, U quadruple the KE and the stopping distance.
Yes this I have already agreed with it is true. It is in agreeance with the factor of four.
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KE and stopping distance go up exponentially, with speed"!
Yes double the speed the energy goes up x4 double the speed stopping power goes up x4.
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I think that a head-on at 50, each, is equivalent to crashing into a solid wall at 50,
coz yes the other car is comin' at U but a wall will not crumple.
Well spotted.
If anyone is wondering if that's true, imagine putting a piece of paper between the two identical cars as they crash.
In principle, the paper gets squeezed and torn up down + sideways, but it never moves forwards or backwards (from the point of view of the vehicles). Each bit of it that is pushed one way by one car is pushed the other way by the other car.
Since the paper doesn't move, it acts like an infinitely stiff wall.
The really important difference is that the KE in a head on crash is shared between the two cars.
Since the wall (in the idealised limit) does not move, no work is done on it so all the energy is dissipated in one car.
So hitting a wall at 50 is pretty much the same experience as hitting another car also traveling at 50.
So, if you have the same energy in the crash, but only one car, you are in more trouble.
To get the same energy with 1 car hitting a wall, it would need to be travelling at 1.414 * 50.
The amount of damage done to the passenger is more nearly proportional to the energy than to the speed or the momentum. That's not a perfect model.
It's complicated.
If I fall off my push bike at 20 KPH I'm not likely to be severely harmed.
That's also true if you see me fall off while you are going past me in a car at 70KPH.
How much energy I have is frame dependent.
But if we consider my speed WRT the road, that gets rid of that problem (to a great extent).
There's 75 Kg of me.
20 KPH is 5.6 m/s
So 1/2 m v^2 tells me I would be carrying about 1.2KJ of kinetic energy.
But I dissipate millions of KJ in a day, so that much energy isn't the problem.
Part of the problem is how fast I need to shift that energy if I fall off (say a tenth of a second) implying a power of about 12KW or roughly 100 times how much power I normally dissipate.
Part of the problem is the force involved- That's harder to calculate because, essentially, I bounce a bit.
It's not a simple "it's the speed" or "it's the momentum" or whatever; it's a combination.
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Thank god for collapsible steering columns it helps to keep the skin on ones face. And seat belts.
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And don't forget the air bags, JT.
They say they are lubricated with talc, to make 'em come out easier,
and which afterwards looks like smoke, so U think U're on fire, for a sec!
Or is there really smoke from the explosive cartridge?
Thankfully I can't say as I have never been in a car accident and had an airbag go off but I have seen the results of a steering wheel on a persons face and it's like pealing one side of a orange.
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We seem to have drifted from the original question of why double the speed =4x the energy.
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That was answered in #2 above.
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Now do it to the parked car situation. One car parked (no KE). One going 100, so KE is 5000. After the hit, both cars are moving at 50, so KE is 2500 total. Total energy dissipated is 2500, shared between the cars so 1250 each. Same change in KE dissipated equally by both cars, so same damage as the slower speed head-on.
Your analysis assumes that the parked car doesn't have brakes.
On the other extreme, we can assume that the car is perfectly braked, or bolted to the ground. In this case, the whole KE is dissipated by the moving car.
In real life cases, they're mostly between those two extremes. So the OP's intuition is justifiable.
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On the other extreme, we can assume that the car is perfectly braked, or bolted to the ground. In this case, the whole KE is dissipated by the moving car.
No; the other car still crumples and that dissipates energy.
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We seem to have drifted from the original question of why double the speed =4x the energy.
Good point.
Imagine that you wanted to "harvest" the energy to do something useful like pull water out of a river for irrigation or something.
Consider hooking the car to a bucket on a rope over a pulley so that the car is slowed down by the tension in the rope.
If we allow the rope to be a bit elastic we can get round the sudden jerk when the rope goes tight.
So, to make the maths easy just imagine that the car is being slowed down by a constant force.
To make the maths easy (albeit an impractical example) consider the case when the car of mass 1000Kg is slowed down from about 30m/s to a halt by that force.
Then consider the case where it's slowed from 15m's to a halt (and then the general case where t is slowed down from a speed of V m/s.
Since energy is a conserved property (in this case; none is wasted as heat, for example), all the car's KE is converted into work done pulling on the rope.
So the work done tells you how much energy the car has.
You can also consider the question the other way- how far would you have to pull a rope at a constant tension to get the car up to a given speed.
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the KE and stopping distance go up exponentially, with speed!
If U double the speed, U quadruple the KE and the stopping distance
That is a square law = v2, not an exponential law = ev.
- Exponentials grow much more quickly than square laws
- Exponentials also start of with a non-zero value when v=0
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On the other extreme, we can assume that the car is perfectly braked, or bolted to the ground. In this case, the whole KE is dissipated by the moving car.
No; the other car still crumples and that dissipates energy.
I was describing two possible extreme cases. Ideally, the parking car is much stronger than cybertruck. Its crumple would be negligible.
That's why I said that real life cases are likely between those extremes.
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Both cars change velocity by the exact same amount in the same time, regardless of frame, because acceleration is absolute, not relative.
Someone who are free falling with their aeroplane don't accelerate according to the aeroplane. But they accelerate according to someone on earth.
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On the other extreme, we can assume that the car is perfectly braked, or bolted to the ground. In this case, the whole KE is dissipated by the moving car.
No; the other car still crumples and that dissipates energy.
I was describing two possible extreme cases. Ideally, the parking car is much stronger than cybertruck. Its crumple would be negligible.
That's why I said that real life cases are likely between those extremes.
You just re-defined a car as being a wall.
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but it just doesn't sound right to say SQUARELY.
Fine; The stopping distance rises quadratically with the speed.
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We disposed of the actual question some while back. The discussion is mostly about the corollary - why do people die in crashes?
Two reasons: gross internal disruption due to the sudden application of force by a non-penetrating object, or disruption of one or more critical organs by a penetrating object. The numbers are very variable, depending on the structure of the vehicle(s), but statistically (and there is no shortage of statistics) the probability of fatality correlates with the square of the closing speed.
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In many places you can restrict the range of vehicle speed to "a bit more than the speed limit" and , over that range the quadratic might fit fairly well.
Quite what one would do with that data is another question.
I guess you might get a PhD out of it.
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What's the purpose of that last column: e^v-1?
Are they just reminding us not to confuse it with e^(v-1),
which is the form I have seen/used?
To make the output value 0 when v=0.
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=83180.0;attach=32356;image)
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If we use 3 cars that are identical and crash one into a very hard and unforgiving wall head on at 100kph the damage will be the same as the two cars having a head on collision at a closing speed of 200 kph. If we consider solid narrow objects as point of a collision the damage will be far more server.
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On the other extreme, we can assume that the car is perfectly braked, or bolted to the ground. In this case, the whole KE is dissipated by the moving car.
No; the other car still crumples and that dissipates energy.
I was describing two possible extreme cases. Ideally, the parking car is much stronger than cybertruck. Its crumple would be negligible.
That's why I said that real life cases are likely between those extremes.
You just re-defined a car as being a wall.
Ideal parking car would behave like a wall when being hit. Fortunately, real life cars are not ideal. Just like the other extreme, where the ideal parking car has no friction with the road.
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acceleration is absolute, not relative.
Someone who are free falling with their aeroplane don't accelerate according to the aeroplane. But they accelerate according to someone on earth.
In Newtonian mechanics, which is what is being discussed in this thread, the aeroplane accelerates the same amount relative to any inertial frame, and thus the acceleration isn't frame dependent. The aeroplane doesn't define an inertial frame, but rather an accelerated reference frame.
Someone on earth don't define an inertial frame either.
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Because momentum is related to duration where as energy is just a total regardless of variables.
In the same time for double the velocity the energy needed to counter it is quadrupled due the body having twice the speed and covering twice the distance. To counter the faster body with the same rate of deceleration , the faster body will have covered 4 times the distance, so it takes 4 times the opposing force or energy.
If momentum is the effect a body will have on another in a set distance, the faster body has half the time to exert the mass, but conversely for time, it has double the distance to exert its momentum through, or in other word there is double the opportunity for mass to act due to the doubled distance, the mass dwells for double the distance.
Doubling the mass for the same energy increaces the momentum.
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Because momentum is related to duration where as energy is just a total regardless of variables.
How should we interpret this statement? Is total volume becomes energy? Or total intensity?
Energy stored in a battery is often expressed in kWh. It means that energy is also related to duration.
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In general, objects get deformed when their parts receive non-homogeneous force. A water baloon gets deformed when laid down on the floor or hung to the ceiling because the floor or the string only put force to some parts of the baloon.
In a free falling balloon, every part of it experiences the same gravitational force, hence it doesn't get deformed.
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If U couldn't avoid a head-on, collision, would U rather have a full
head-on or a single side one,
I think an impact to the side will wash off some of the energy but that could be worse for a person on that side as there could be more penitration in that aria. A T bone is the worst impact as there is very little structior to protect one.
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Because momentum is related to duration where as energy is just a total regardless of variables.
How should we interpret this statement? Is total volume becomes energy? Or total intensity?
Energy stored in a battery is often expressed in kWh. It means that energy is also related to duration.
Joules is also expressed as time dependant. But it is a total. Momentum is a quality.
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Because momentum is related to duration where as energy is just a total regardless of variables.
How should we interpret this statement?
I wouldn't try to interpret it.
It's nonsense.
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I not entierly sure Mr cat but it seems the culprit is in this " Why is it that if a car doing 100K crashes into a stationary car, it's a gonner, and yet if I have a head-on with another car doing 50 each, I would expect to walk away, unscathed, in my big car "
It depends on how one read it possibly but are you assuming that there is a difference between those two scenarios, in the kinetic energy experienced by the driver? As if one could assume one of those cars, regardless of which one you choose, as representing something unmovable, as a rock? In which case the ´kinetic energy' experienced then will be 'halved', represented by just one side, no matter which side you choose?
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Heh, missed the second page. It seems that you do? Assume that the the momentum of something isn't there if it is of a speed, equal to what it collides with?
Is that correct?
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Both cars use earth as their relative frame of no motion. and both cars are moving at a same speed relative earth. You put up a rock in front of any of those cars and the kinetic energy will exist, being the same for both occasions, assuming the cars to be identical clones :) as well as the speed etc.
So that kinetic energy must exist as a momentum for both cars and will transform into kinetic energy at a collision. So it should be the same as if you collide with that rock at a hundred, or crash head-on, doing fifty, into that other car, it too doing fifty although in the opposite direction.
But it is weird, momentum and kinetic energy. You could define something else than earth as your 'stationary point', some patch of space that earth swish by in its 'relative motion' through the universe. At least in relativistic terms. Then vectors and speeds relative that motion will come in and play a role for how that collision will be interpreted etc. But it won't change the kinetic energy involved in the 'system' colliding. So suddenly it's not relative anymore, or is it?
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So that kinetic energy must exist as a momentum
That can't make sense; it has the wrong units.
So it should be the same as if you collide with that rock at a hundred, or crash head-on, doing fifty, into that other car, it too doing fifty although in the opposite direction.
No.
See above.
Hitting an oncoming car which is doing 50 is the same "experience" as hitting a wall at 50.
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How can that be BC?
What about the momentum?
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And how do would I get to a kinetic energy without a momentum involved BC?
Hmm, okay, depends on definitions. https://www.sarthaks.com/454279/a-can-kinetic-energy-of-a-system-be-changed-without-changing-its-momentum
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I will need to ponder that one.
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Not here though. It will take too much place.
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I will need to ponder that one.
HI Yor-on you see a hard surface like a concrete wall or a 100 ton rock has no give in it so a car hitting it at 50 is the same as two cars colliding with a closing speed of 100 as both cars will share the impact fealing only there Owen deceleration. The two cars combined have double the amount of crumple zone so double the amount of give and double the distance to stop all amounting to halving the damage.
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You're thinking of inelastic collisions relative elastic, if I get you right JT?
But that's not what I got stuck on :)
Practically it may come out that way, but using definitions as kinetic energy and momentum I don't find those two situations equivalent, and that's my headache.
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How can that be BC?
It hasn't changed.
https://www.thenakedscientists.com/forum/index.php?topic=83180.msg656048#msg656048
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You're thinking of inelastic collisions relative elastic,
Maybe if you think of it like this if you roll a rubber ball at a hard wall it will bounce back if you roll two rubber balls at the same speed at each other they will bounce back the same amount even though the closing speed is doubled both balls equally share the collision. The hard wall did not share.
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That one was very nice JT, intuitive. But what I don't find equivalent are the initial conditions. In the first case both kinetic energy and momentum differs from the other.
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The paradox is due to the fact that the driver is not part of the car, but essentially a floating body travelling at the same speed as the car.
Ignoring crumple time, the damage caused to the driver is due to the fact that he continues to move when the car has stopped. So if he was initially moving at 100 kph, the energy dissipated when he hits the dashboard will be four times the energy at 50 kph. Crumple zones are really only effective if you are tightly belted to the chassis, so you hit the belt as the car deforms, not a hard surface when it has stopped.
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That one was very nice JT, intuitive. But what I don't find equivalent are the initial conditions. In the first case both kinetic energy and momentum differs from the other.
I think I see where you may be confused say each car is travelling at 50k if we double the speed of the cars the kinetic energy will go up to x4 but in the event of the two cars colliding even when the speed is doubled the kinetic energy is not changed as each car is a separate energy to its self the two cars are as 1x1=1 not 1+1=4 each car has its Owen momentum to deal with and it is not shared as double. The impact stays as one, not 2x and not 4x Energy only goes up for the individual object when the speed is incrested not by combining. However, by combining two objects travelling in the same direction we will increase the energy of both combined.
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An example of a different kind the car is travelling at 50k a truck with a big solid bumper is travelling at 50k a head on in this scenario is very different for the car as the truck will force the car backwards that will increase the level of energy to the car but not by 4x certainly not equal but possibly the force on the car could be in the order of 3x why not equal because the car is experiencing a force that is past its internal inertia by being reversed in motion only slightly reduced by the bumper of the truck collapsing a small amount. If you were travelling down the road at 50k and a 100 ton concrete block was travelling at 50k and it was a head on impact then yes the force of the collision on the car will be 4x as the concrete block will have no give and the cars direction will be subjected to a force that is equal to that of doubling the speed this is the big difference concrete block has no give and the car is not only stopped but forced in the reversed direction at 50k. This gives the car a total of 100k impact with no shared absorption. This is x4 impact.
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That one was very nice JT, intuitive. But what I don't find equivalent are the initial conditions. In the first case both kinetic energy and momentum differs from the other.
The ke and momentum are saying the same thing.
If you look at the eg I gave of the person jumping from a building, keeping ke, momentum & speed constant the killer is acceleration/deceleration. Alan & BC have said the same thing in different ways. Accident investigators reckon that the crash that killed Diana put 70-100g on her body and that tore a major artery from her heart.
KE is easier to see the relationship with speed v but less so with deceleration. However, as BC says ke is the work done accelerating/decelerating an object to v:
F x d = 1/2 mv2
If we have a crumple zone of d that stops the car then the force is proportional to v2
Now look at momentum. Although it is only mv the force is due to the rate of change of momentum, usually expressed as F = ma.
To see relationship between speed and a take an eg of car hitting a child (light so car won’t slow). The child will be accelerated to v in the width of its body and in time t and at 2v the time will be halved. If you look at acceleration units = m/s2 so if you halve the time (double the speed) you see the force is square law against speed just as in KE. It’s all saying the same thing.
As KT says, momentum also plays a part if car hits juggernaut head on. Car occupants are accelerated forward by their own momentum, but the juggernaut’s greater momentum pushes the car back increasing the acceleration on the occupants.
Survivability is interesting. Most researchers say the turning point is 43mph and above that the chance of survival drops exponentially. The reason is that the materials used to decrease acceleration- crumple zones, seatbelts, airbags - have limited ability to absorb energy. If you look at the fireman’s blanket eg I gave, a person from the 10th floor is likely to tear the material.
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If you look at the eg I gave of the person jumping from a building, keeping ke, momentum & speed constant the killer is acceleration/deceleration. Alan & BC have said the same thing in different ways. Accident investigators reckon that the crash that killed Diana put 70-100g on her body and that tore a major artery from her heart.
How the force/acceleration is distributed matters. You can accelerate in 100g free fall while not feeling anything.
In general, objects get deformed when their parts receive non-homogeneous force. A water baloon gets deformed when laid down on the floor or hung to the ceiling because the floor or the string only put force to some parts of the baloon.
In a free falling balloon, every part of it experiences the same gravitational force, hence it doesn't get deformed.
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How the force/acceleration is distributed matters. You can accelerate in 100g free fall while not feeling anything.
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In a free falling balloon, every part of it experiences the same gravitational force, hence it doesn't get deformed.
Yes, this the big difference I try explain to people.
In an acelerating car the back of the seat pushes the atoms of the back forward, but the rest of the atoms eg stomach want to go as they where and the back nerves feel a similar sensation to lying on the ground. As you say, freefall and car acceleration are very different - important difference when discussing car crashes!
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Thank god for collapsible steering columns it helps to keep the skin on ones face.
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Thank god for collapsible steering columns it helps to keep the skin on ones face.
Not really. The airbag is designed to deploy and stop you hitting the steering wheel. Most steering wheel injuries, which still occur with collapsible columns, are due to the driver sitting too close to the wheel so the bag doesn’t have time to deploy fully.
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Thank god for collapsible steering columns it helps to keep the skin on ones face.
Not really. The airbag is designed to deploy and stop you hitting the steering wheel. Most steering wheel injuries, which still occur with collapsible columns, are due to the driver sitting too close to the wheel so the bag doesn’t have time to deploy fully.
A malfunctioning airbag can be very dangerous and lead to law suits.
https://www.classaction.com/takata-airbags/lawsuit/
Plus this highly scientific and relevant video
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A malfunctioning airbag can be very dangerous and lead to law suits.
A malfunctioning anything can be very dangerous and lead to law suits.
Seems obvious.
Plus this highly scientific and relevant video
True. Highly relevant if you intend to buy a car with the airbag underneath the seat.
By the way, black suits you ;D
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A malfunctioning airbag can be very dangerous and lead to law suits.
A malfunctioning anything can be very dangerous and lead to law suits.
Seems obvious.
I don't think a malfunctioning remote control will lead to a dangerous situation, injury or lawsuits, any injury will be due to either user error such as throwing it at something, or a battery malfunction. Wardrobe malfunction however can.
https://www.hollywoodreporter.com/business/business-news/men-black-3-lawsuit-wardrobe-malfunction-331034/amp/
Sing along Colin,
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I don't think a malfunctioning remote control will lead to a dangerous situation, injury or lawsuits, any injury will be due to either user error such as throwing it at something,
If the item doesn’t have sufficient safety warnings a lawsuit can result. Each remote control should have a label saying “do not throw this at anyone”. Similarly airbags apparently need a warning (for some people at least) saying “do not sit on this airbag).
However, this is drifting off topic so, to get back:
The reason airbag and seatbelt are there to prevent you hitting the steering column is that the column needs to be strong and not fail during the stress of driving. So, hitting it can still cause serious injury including broken wrists, internal injury etc.
PS black still suits you, singing less so :D