Modelling Car Impact: Predicting Obstacle Movement and Displacement

[Harmony]

I am trying to model the following situation:

Let say i have an obstacle with known mass, and I know the coefficient of static and dynamic friction between the obstacle material and the floor. A car traveling at a fixed velocity is to impact the obstacle. For simplicity i will first consider the simplified case where the car engine is turned off just before the impact begin. In this case it is assumed that the obstacle is a rigid body. I would like to know whether the obstacle would move, and what is the displacement if it does move. How should I model this situation? What additional information should I assume if the current information is in suffice?

Thanks in advanced.

 

[Stonebridge]

You need to consider the nature of the collision. What happens to the car during the collision? Does it crumple or is it rigid? If it crumples, by how much?
This will determine the (average) force required to stop the car because it will determine its deceleration. This force, in turn, will determine what happens the obstacle.

 

[Harmony]

I know that real car would crumple, and it is hard to estimate to what extend would a particular vehicle crumple in an impact. For simplicity, i would assume rigid body case first. In such case how can i proceed with my modelling?

 

[fss]

Deciding what the object's coefficients of kinetic and static friction are would be fairly important.

Just a general warning; collision modelling of any real-world scenario is very difficult.

 

[Stonebridge]

You still need to decide what happens to the car. In particular, how much energy is lost in the collision. (How elastic is it?)
A perfectly elastic collision is not realistic for a car crash.
The resulting motion of the car and obstacle is governed by conservation of momentum and the kinetic energy before and after.
As for crumpling.
A little research on Google will surely find you some values for the typical amount of crumple in the bumper/fender? of a typical car. It would even be possible to make an informed guess, surely?

 

[Harmony]

You still need to decide what happens to the car. In particular, how much energy is lost in the collision. (How elastic is it?)
A perfectly elastic collision is not realistic for a car crash.
The resulting motion of the car and obstacle is governed by conservation of momentum and the kinetic energy before and after.
As for crumpling.
A little research on Google will surely find you some values for the typical amount of crumple in the bumper/fender? of a typical car. It would even be possible to make an informed guess, surely?

I have done some googling online, and there are fair bit of journals and articles describing how to define the contact force and the changes during the collision. Haven't manage to look through all of those thoroughly, but from first glance, the articles on impact modelling that i have read didn't seem to consider the friction between the colliding particle and the road.

Surely i have to consider the effect of friction when i formulate the linear momentum conservation formula? Collision between two body on ice and two body on rough sand would be pretty different? And how should i take account of the effect of friction when i use the conservation of linear momentum formula?

 

[Stonebridge]

In the case of the obstacle
*the coefficient of static friction with the surface will determine the minimum size of the force applied horizontally in order to just move the object.
*once it starts moving, the coefficient of dynamic friction will determine the motion.
Taking the first part first:
The force applied to the obstacle by the car is determined by the magnitude of the deceleration of the car. [F=ma]
The deceleration of the car is, in turn, determined by
*how fast it was traveling before impact
*how long it takes to stop
How long it takes to stop will depend on how far it travels before it stops. This will be determined by how much it crumples.

There are a number of possible scenarios for the collision.
1) the car crumples and stops, the obstacle doesn't move
2) the car crumples and pushes the obstacle along with it before it stops (they effectively stick together)
3) the car crumples and stops, the obstacle moves away from the car before stopping
4) the car rebounds off the obstacle
Exactly what happens will depend on the relative masses of the car and obstacle, the initial speed of the car, the coefficient of static friction between then obstacle and ground and the coefficient of dynamic friction between then obstacle and ground.
And of course, the "elasticity" of the front of the car.
It might be a good idea to assume that the maximum mount of crumple of the car is equal to about the length of the front compartment with the engine.
If you assume that this is designed to crumple completely if the car hits a solid wall at, say, 30 mph (or whatever it is) and that a typical car's mass is 1.5tonne (or whatever it is) you can estimate the deceleration and force involved from F=ma.