But the real question (actually there are two big questions) is what about safety? This is actually a pretty tough question to answer. The problem is that collisions depend on so many things. If this is too difficult a question to answer, change it. That is the physicist way.

## Simplified Car Model

To explore the difference between crashing a car at 70 mph and 85 mph, I will use a model. This car doesn’t have a crumple zone, it has a huge spring on the front. Here is a diagram.## Work Energy

The work energy principle says that the work done on an object is equal to its change in energy. If I take the spring and car as my system, then there is no work done on it during the collision. The car will decrease in kinetic energy and increase in spring-potential energy. This can be written as:_{2}will be zero (because it is stopped) and U

_{1}will be zero because the spring is not compressed yet. The kinetic energy and spring potential can be written as:

*k*is the spring constant. A higher

*k*means a stiffer spring. Also,

*s*is the distance the spring is compressed. Putting these expressions into the work-energy principle, I get:

## Force and Acceleration

What about the acceleration of the car as it crashes into the wall? Here is a force diagram for the car while it is crashing.## How About Some Values

I think I can do this without picking a mass of the car. Suppose that I have a car going 70 mph (31 m/s) and it crashes into a wall with a spring compression of 1 meter (I just randomly picked that). What would the value for*m/k*be?

The other problem is that the useful acceleration data really needs a time. A human can withstand super high accelerations as long as the time interval is short enough. So, what is the acceleration as a function of time? Acceleration depends on position, but position depends on velocity and velocity depends on acceleration. How about a quick numerical plot? First, this is the velocity of the car as it collides.

**UPDATE:**I was wrong (as pointed out in the comments). The table above says that the time is in minutes, not seconds. Dooh! Anyway, looking again at Wikipedia’s human tolerance page – it lists 50 g’s as pretty much fatal. So, this is still bad.

Here is a plot of accelerations for different starting velocities.

- This is just a model using a spring to simulate the crushing of the car.
- The above graph shows the acceleration of the car. The person inside would have a different acceleration. Just imagine an air bag inside. The person would actually move forward more than the car (and decrease the acceleration). The person is not rigidly attached to car (at least I hope not).
- Driving is dangerous. Driving is especially dangerous if there are walls in the road. I would just avoid any road like this.

Follow @rjallain on Twitter.

http://www.wired.com/wiredscience/2011/04/crashing-into-wall/

## Δεν υπάρχουν σχόλια:

## Δημοσίευση σχολίου