# What does physics say about Car collision damages?

• Carphysics
In summary: I forget what it was, a small car. The large-end saloon had more momentum, I'm guessing.In summary, the car with more momentum will sustain more damage when it rear-ends a stopped car.

#### Carphysics

Thanks for looking into my thread. I find various threads suggest to use Kinetic energy/conservation of momentum to explain car collision.

Moving car generate/carry more energy compared to stopped one.

I find when a car (car1) (moves with 10-15 miles/hr) rear-ends stopped vehicle (car 2), the stopped car (car2) sustain more damage compare to moving one (car1) .

Car 1 has kinetic energy and car 2 has 0 kinetic energy.

Does the Kinetic energy of car 1 contribute for more damage to car 2?Is there a way to explain the above situation using physics?

Welcome to the PF.
Carphysics said:
I find when a car (car1) (moves with 10-15 miles/hr) rear-ends stopped vehicle (car 2), the stopped car (car2) sustain more damage compare to moving one (car1) .
Why do you say that? At the PF, we require good references for scientific claims. And I can say that in general that is not true. All kinds of factors contribute to damage, including the design of "crumple zones" and the weights and heights of the two vehicles.

What is your background in physics and mechanical engineering so far? What is your plan for your education going forward? This is an interesting subject, but there is a lot of learning that goes into understanding crash physics...

The general case for collisions is that a more massive object will maintain structural integrity better than a less massive object.
It doesn't matter much which object is moving and which is stationary, the lighter object will always be the one more likey to disintegrate.
In terms of road vehicles you could have a ten ton truck hitting a motorbike, or else have the motor bike hit the truck.
Either way it's bad news for the guy on the bike.

berkeman
rootone said:
you could have a ten ton truck hitting a motorbike

Why'd you have to use that example...

rootone said:
The general case for collisions is that a more massive object will maintain structural integrity better than a less massive object.
General case? It might be true under certain assumptions about the objects, like that both are cars. But it's hardly a general case for all collisions.

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Think about how the collision energy is dissipated.Design is all about that, eg modern cars all but disintegrate to use up the collision energy and save the occupants.

Fun simple way to learn is dropping a shielded egg, what's the best shield and why.

A.T. said:
General case? It might be true under certain assumptions about the objects, like that both are cars
.
You're right of course. the density of the objects involved will have a lot to do with it well.
My 'general case' assumed objects of roughly similar density.

The question is too hard to deal with without using a simpler question first, I think. PF keeps getting queries about traffic accidents and heavyweight punches to the head and there never is a satisfactory answer. That's why rich people employ highly paid 'expert' witnesses who make statements which are only based on experience and recorded evidence from previous collisions. A Physicist would not get a look in.
The basics of momentum conservation will always apply. The simplest model would involve, say, two cylindrical buffers of exactly the same low (zero) density and non-resilient (or, later on, partly elastic material) and the same cross sectional area but different lengths. They each have a mass on the opposite ends from the impact. This deals with the complication of distributed mass and complicated details of structure.
They meet end-on (constrained in some sort of smooth track, to stay on the same axis). During the impact, they will both always experience the same force on them. The strain (percentage compression) on each cylinder will be the same if the masses are the same. (You have effectively just one long cylinder of bungee).The result will be that they both end up stationary and the acceleration of each mass will be the same. You could calculate the final amount of compression of each buffer. Change the ratio of the masses and the initial velocities and you could do the same thing. Getting more and more realism, you would introduce different materials for each side.

rootone said:
The general case for collisions is that a more massive object will maintain structural integrity better than a less massive object.
It doesn't matter much which object is moving and which is stationary, the lighter object will always be the one more likey to disintegrate.

I'm not sure this is necessarily the general case unless you're talking about significant differences in mass (as per the example you used above). Many eons ago I hit a car that stopped at a junction in front of me - he did... I didn't. It was a fair old thump but nothing ridiculous. I was driving my dad's car - a large-end saloon - and he was driving a Renault 5 (UK small P.O.S ). After getting out and inspecting his rear bumper which secretly I was pretty relieved about - thinking I may even get away without telling my dad as it looked like a simple bolt-off replacement job - I turned around and looked at my dad's car. It looked like a cartoon car that had been in a crusher - the crumple zones had done exactly what they said on the tin - crumpled beyond all recognition.

So going back to the OPs question, I don't think you can generalise - you need to factor in relative masses, where the cars connected (e.g. crumple zones or not), at what angle, what speed, and a whole host of other things before you can predict damage.

One thing to point out though; for the purpose of the collision, using the ground as the reference frame for calculating kinetic energy (per the OP) is a poor/misleading choice. The kinetic energy lost in the collision would be calculated by first calculating the final speed of the crushed vehicles (assuming they basically move together) and using that as the rest frame.

For equal mass vehicles at 15 mph, it would mean you can figure each to be moving toward the other at 7.5 mph.

Note, you can solve the problem either way, but considering only one to be "moving" has led the OP to believe its "higher" kinetic energy gives it some sort of preferred status in the collision, when in reality they are equal.

berkeman
russ_watters said:
The kinetic energy lost in the collision would be calculated by first calculating the final speed of the crushed vehicles (assuming they basically move together) and using that as the rest frame.
That's certainly another factor consider but in most (at least, many) accidents. the drivers are actually braking, even whilst the vehicles are in contact and moving over the road - coming to a halt. Crushing and braking are happening at the same time and the amount of KE that the brakes and the skidding tyres are dissipating must be significant. I imagine that ABS is doing its best even during the impact time.
It far too broad a subject to expect to be dealt with with any simple equations. It may be that accelerometers, installed in cars, could help in analysing accidents as they happen. Engine data on modern cars is, I believe, stored for a short time so we could, at least know more about the actual circumstances of accidents, rather than just the evidence of drivers and witnesses.

sophiecentaur said:
That's certainly another factor consider but in most (at least, many) accidents. the drivers are actually braking, even whilst the vehicles are in contact and moving over the road - coming to a halt. Crushing and braking are happening at the same time and the amount of KE that the brakes and the skidding tyres are dissipating must be significant. I imagine that ABS is doing its best even during the impact time.
Given the short distance and time of an impact - and enormous forces/accelerations, I would not expect the braking force to play a significant role. However:
It far too broad a subject to expect to be dealt with with any simple equations.
Yes. Particularly, the behavior of the car as it deforms is extraordinarily complicated and based on the proprietary specifics of the design of the car. No 3rd party has any hope of modeling/predicting the crash behavior of a car for anywhere close to the cost of buying the car to destroy -- which is why that's how it is done.
It may be that accelerometers, installed in cars, could help in analysing accidents as they happen. Engine data on modern cars is, I believe, stored for a short time so we could, at least know more about the actual circumstances of accidents, rather than just the evidence of drivers and witnesses.
There are all of those things:
http://www.edmunds.com/car-technology/car-black-box-recorders-capture-crash-data.html

Thanks for chiming in and sharing your insight. I made this observation in couple of accidents situation. I am wondering whether any phenomena behind it. So I am here. As many folks wonder about weights of the cars on my posting.

car1 - 1999 Ford Expedition weight 7000 lbs

Car 2 - 1999 Toyota Camry weight 3120 lbs

Car1 weight is more than 2 X car 2 weight.

I hope this helps.

Carphysics said:
As many folks wonder about weights of the cars on my posting.

car1 - 1999 Ford Expedition weight 7000 lbs

Car 2 - 1999 Toyota Camry weight 3120 lbs

Car1 weight is more than 2 X car 2 weight.

I hope this helps.
Since typical crash tests involve a crash into a fixed barrier, energy absorbed has to be proportional to weight in order for smaller and larger cars to suffer similar levels of damage and pass their crash tests. In real-world crashes, the cars split the energy loss, so the larger car will sustain roughly proportionally less damage. In your example, the larger car sustains less than half as much damage as the smaller car.

the key point in car collisions is clearly not damage sustained to the vehicle or design would be a no brainer.

the key areas are damage to the occupants and cost of protecting them while having a clean, safe, economical, functioning vehicle.

Ohanian text has a great interlude on the physics of vehicle collisions with real collision data, role of vehicle mass, speed... Ohanian also includes the key equations in COM coordinates and a rather neat toy mathematical model of a vehicle under typical/general crash forces.

sophiecentaur

## 1. What is the main principle of physics that explains car collision damages?

The main principle of physics that explains car collision damages is Newton's laws of motion. This law states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. In the case of a car collision, the external force is the impact of one car hitting another.

## 2. How does the speed of the cars involved affect the damages in a car collision?

The speed of the cars involved in a car collision greatly affects the damages. According to the physics of collisions, the force of impact is directly proportional to the speed of the objects involved. This means that the higher the speed of the cars, the greater the force of impact and the more severe the damages are likely to be.

## 3. What role do the mass and weight of the cars play in car collision damages?

The mass and weight of the cars also play a significant role in car collision damages. According to Newton's second law of motion, the force of an object is equal to its mass multiplied by its acceleration. This means that the heavier the cars involved, the more force will be generated upon impact, and the more severe the damages will be.

## 4. How does the angle of impact affect the damages in a car collision?

The angle of impact also plays a role in determining the damages in a car collision. The force of impact is greatest when the cars collide head-on, as this results in a direct transfer of momentum. However, if the angle of impact is more glancing, the force of impact will be less, resulting in less severe damages.

## 5. Can the design and structure of a car affect the damages in a car collision?

Yes, the design and structure of a car can affect the damages in a car collision. Cars with advanced safety features, such as airbags and crumple zones, are designed to absorb and distribute the force of impact, reducing the damages to the car and its passengers. Additionally, the structural integrity of a car can also play a role in how well it withstands a collision and how much damage it sustains.