# Homework Help: Car Crash o.O

1. Jul 28, 2004

### Try hard

A typical car with a dummy crashed into a wall, what is a suitable parameter for the head of the crash test dummy(with and without restraints) as a function of time? and how do i estimate the forces acting on the head in the two situations? Thanks a lot

2. Jul 29, 2004

### maverick280857

You could use impulse, you know...

$$\Delta G = \int_{t_{i}}^{t_{f}} F dt$$

What do you mean by

What do you want to measure?

Cheers
Vivek

3. Jul 29, 2004

### HIGHLYTOXIC

I dun think u can measure that by any measure...Impulse wont do it...
Impulse wud solve it only in a case of a particle, I dun think it can be applied in this case...The solution depends a lot on what u want to measure..

I think it requires complex calculations (dun assume it right, coz most of my ideas arent!!)..

Hey maverick, impulse will definately act on the head, but whether it will be considered a conventional case needs to be examined...have ya tried some calculations on it?

4. Jul 29, 2004

### maverick280857

Okay I see the problem you folks have visualizing a dynamic variable when you've used it so far only for a particle and not for an extended body. Well, the conventional definition lacks the rigour of complexity, so it would be better if I write it to express the net impulse vector of the center of mass of the extended body (in this case, it is the head). On impact, the head moves forward (sort of rotates about a "hinge" in the neck). The center of mass of the head evidently moves as well and may execute a circular arc about the fixed hinge (or a curvilinear motion...).

Assuming in this case that the mass of the head is constant (i.e. the inflow of fluids into the brain and outflow of fluids is more or less equal during impact) the calcululations, higlytoxic, are fairly straightforward IF you can take into account the mass distribution in the head.

What do you mean??

Of course, it always does!

What do you mean by conventional case? Of course, the calculations will be complex because we're not dealing with an elementary motion of the system under consideration here...it is a kind of superposition of elementary motions leading to what is called a complex motion.

Of course, calculation of impulse or any dynamic variable in this case cannot be done by just plugging in the value under the integral and integrating as I pointed out earlier. However, you can (experimentally) determine quantities through graphs by subsequent interpolation, data point extraction and/or a least square analysis (and more generally, experimental methods).

Cheers
Vivek

5. Jul 30, 2004

### HIGHLYTOXIC

"I dun think u can measure that by any measure..."

Well...I was thinking whether it wud be possible to actually calculate the force on the head...Vivek, you are right when you say that the motion wud be a bit kind of circular, but it wud be translational too...But I think there are far more factors that must be taken into consideration (IMO)..Coz the hinge in the neck will also move, so will the body and the head...

However, we can find the acceleration of the centre of mass easily...

6. Jul 30, 2004

### maverick280857

Hello highlytoxic (Abhishek)

Well I didn't say that it would be circular. I said it would be sort of circular or more complex (please read my post again).

Finding the center of mass motion is also not easy my friend . It seems easy theoretically while solving problems (textbook ones) but complex superpositions of translational, vibrational and rotational motion in the bulk leads to nonidealities and you can never be accurate in an experiment anyway (the finest detail measurements too have errors for a reason more fundamental than experimental limitations: the Heisenberg Uncertainty Principle).

What we're dealing with here is experimental determination. The simplest way of thinking about it would be to get a set of finitely spaced readings of some easily measurable dynamic variable. Then you could plot it on a graph, linearize the data set or do a best fit/least square approximation using a computer and finally use approximate mathematical models to get an answer.

Cheers
Vivek