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two cars crashing at 50mph = 1 car crashing at 100mph?

The formula for kinetic energy is:

F = ½ m * v^2

So if a car of a fixed mass is hitting a wall, the total force applied to the wall (in an inelastic equation) will be equal to the force above.

If that same car were to be halted in the exact same spot by another car going in the opposite direction using an equal force, then the force would be exactly the same.

If you look at a car going 100 mph into a wall, notice how the velocity component is square and therefore the forces applied would be much greater.

So you are correct: The Mythbusters analogy for two cars hitting each other at 50 mph is NOT equivalent to one car hitting a wall at 100 mph. Rather it would be more correct to say that two cars hitting each other at 50 mph is more equivalent to one car hitting a wall at 50 mph.

However, it isn’t entirely accurate to say that two cars hitting each other at 50 mph is similar to one car hitting a stationary car at 100 mph. As you can see the forces are far greater at that speed. However, in reality it completely changes the dynamic of the crash. One major limiting factor is the coefficient of static friction of the stationary car will limit how much force the stationary car can apply back to the moving car. The maximum force the stationary car can apply back to the moving car will be far less than the force of the moving car as the tires can hold only so much force before they break loose. The 100 mph car will plow into the stationary car, but will end up pushing it very far and the coefficient of dynamic friction will act as a dampener (or airbag) for the moving car and will help distribute the force over a longer period of time. Two moving cars crashing into each other will be more of an impact (relatively speaking) where the force will immediately peak, whereas a car hitting a stationary car will have a much longer and drawn out force curve relative to time.

Thanks for the equation, yea I'd love to have them do this test and see how the cars end up looking like. It might be more damage than two cars crashing at 50mph each, or might not. :smile:

Is it? I thought it's just:
Force = Mass*Acceleration

Should be linear, no?

Bryan - our resident mechanical engineer, provided the equation: Force = ½ mass * velocity ^2 , so it's not linear.

I have a headache.

How about avoiding crashing into a wall and head on with other cars.

Makes sense gentlemen?

LOL then mythbusters would be boring and we'd have no fun! :D
 
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.....LOL then mythbusters would be boring and we'd have no fun! :D

I liked the one that they did on the BATMAN suit made by Universal Designs.

I will neither confirm nor deny that I own either or both BATMAN Begins & Dark Knight.

adam.jpg
 
Thanks for the equation, yea I'd love to have them do this test and see how the cars end up looking like. It might be more damage than two cars crashing at 50mph each, or might not. :smile:

It would be very interesting because you are going to have significantly higher kinetic energy (way more than double as you mentioned) however, the reactive forces of a stationary car is very limited as the tires will only provide so much resistive forces. Too many variables (coefficient of restitution, deformation of materials, coeficient of static and dynamic friction of the tires etc.) to really be able to accurately model and say for sure. Only one way to find out! Got 2 spare cars? :biggrin:

Bryan - our resident mechanical engineer, provided the equation: Force = ½ mass * velocity ^2 , so it's not linear.

Whoops, I should clarify, the equation is for Kinetic Energy:

KE = 1/2 m * v^2

which is what we are interested in. Just wanted to clarify lest I get called out for incorrectly writing:

Force = 1/2 m * v^2

since energy is not techincally a force.
 
No, the kinetic energy of the system is doubled (exactly). It's not "much more than double" - it's just purely doubled.

Not sure if you mean if you are comparing the kinetic energy of one car travelling at 50 mph two cars travelling at 50 mph or one car travelling at 50 mph to one car travelling at 100 mph.

If you are comparing one car travelling at 50 mph to two cars travelling at 50 mph, then yes the total kinetic energy is doubled.

If you are comparing one car travelling at 50 mph to one car travelling at 100 mph, then the kinetic energy is quadrupled since the equation for kinetic energy is ½ * mass * velocity^2
 
Thinking more about this:

valid comparison scenarios:

1) 1 car traveling at 50mph, crashes into a solid wall also traveling at 50mph. Compare to 1 car traveling at 100mph crashing into stationary solid wall.

2) as per above, 2 car traveling at 50mph each crashing into each other. Compare to 1 car traveling at 100mph crashing into stationary vehicle.

A wall does not distribute or absorb energy like a car, so it seems to me Mythbusters made a huge flaw comparing 2 cars crashing at 50mph each, to a car traveling at 100mph crashing into a solid unmoving wall...

Any engineers or any one care to comment?? I think Mythbusters need to fix this test and do it right per my scenarios above.


Im an engineer, ive been over this 100 times. If your going 50mph in an NSX, and you have a head on collision with another NSX, also going 50mph, it is NOT the same as crashing one NSX into a wall at 100mph, as far as body damange to your NSX goes.. It is roughly the same as crashing one NSX into a wall at 50mph. I think of it this way, a solid wall stops your NSX dead. The only way an incoming car can stop you dead is if it matches your mass and velocity. If the car you were hitting was doing 30mph, you would impact at point A, and come to a complete stop at point B, located X distance away, which denotes a less severe crash.

The question is what denotes a 50mph crash, technically it would be hitting a solid wall. Obviously hitting a wall that was doing 50mph, while you were doing 50mph, would be worse than hitting a stationary wall while you were doing 50mph. Im not even sure what the question is anymore but what i posted above it infact correct, the idea behind the mythbuster test is to compare swerving right and hitting a tree (immovable) or swerving left into oncoming traffic. The intuitive thinking is that oncoming traffic would result in twice as much damage, but infact it would be roughly the same as with the tree collision.

In reference to kinetic energy, in the head on collision scenario, yes, the total energy of the system is double than that of the wall collision, but BOTH cars are absorbing the energy, as apposed to the wall where all the energy is absorbed by one car. So there is twice the energy but twice the absorption- resulting in 50mph damage for both cars, as seen in the test
 
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Not sure if you mean if you are comparing the kinetic energy of one car travelling at 50 mph two cars travelling at 50 mph or one car travelling at 50 mph to one car travelling at 100 mph.

If you are comparing one car travelling at 50 mph to two cars travelling at 50 mph, then yes the total kinetic energy is doubled.

If you are comparing one car travelling at 50 mph to one car travelling at 100 mph, then the kinetic energy is quadrupled since the equation for kinetic energy is ½ * mass * velocity^2
I'm saying neither (both of your examples are correct though).

I'm saying that one car traveling at 100mph has double the kinetic energy of two cars traveling at 50 mph. That's why I used the word "system".
 
I agree with Vega$ NSX.

Car hits wall at 100 mph. Wall exerts same amount of force to stop it.

Car hits car is essentially the same thing. Car 1 at 50 mph hits Car 2 at 50 mph. both forces cancel out since they are equal and opposite; therefore only 50 mph force exerted to stop each vehicle.

Makes perfect sense to me.
 
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