[Bored chemist]

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.

[Bored chemist]

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.

[evan_au]

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 = e^v.
- Exponentials grow much more quickly than square laws
- Exponentials also start of with a non-zero value when v=0


Exponential_growth.png (4.27 kB . 277x170 - viewed 3287 times)

[hamdani yusuf]

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.

[hamdani yusuf]

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.

[Halc]

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.

[Bored chemist]

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.

[Bored chemist]

but it just doesn't sound right to say SQUARELY.

Fine; The stopping distance rises quadratically with the speed.

[alancalverd]

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.

[Halc]

but it just doesn't sound right to say SQUARELY.
...
BC has reminded me it's QUADRATICALLY.

Right, so next time, in order to prevent the bending of the nail, be sure to hit it quadratically on the head.

[Halc]

statistically (and there is no shortage of statistics) the probability of fatality correlates with the square of the closing speed.

But as this thread has shown (to everybody but the deniers), closing speed with a wall is worse than the same closing speed with a similar mass vehicle or say a fire hydrant. There's more to it that just the one factor.

Apples to apples, it is a very loose correlation indeed. A crash into a wall by a typical passenger car at a closing speed of say 160 km/hr has almost identical probability of fatality as one at twice that speed. Nothing near 4x the probability. A quadratic curve cannot correlate with a curve confined by a finite range, except over a limited portion of the curves.

I picked 160 because it's about as fast as I've ever driven, with a diesel car no less. In my mirror I spotted another car who shortly blew by me like I was standing still. I guess it was an optimal road for that sort of thing.

[Bored chemist]

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.

[hamdani yusuf]

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.

[Just thinking]

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.

[hamdani yusuf]

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.

[hamdani yusuf]

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.

[Petrochemicals]

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.

[hamdani yusuf]

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.

[hamdani yusuf]

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.

[Just thinking]

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.