momentum of the bus, what would you tell the judge??

Question

You are a professional witness in a lawsuit. What do you tell the judge? (Read the following scenario.)


You are on an RTD Stretch Bus (the long busses with the accordion in the middle. The bus is fully
loaded with fuel and people. You are traveling at 30 mph when a miniVan pulls in front of the bus as it travels
in a similar direction; the van is traveling 20 mph. The bus driver slams on the brakes, but there is black ice so the bus gracefully slides right into the van sending the van flying ahead. Three passengers, upon realizing their opportunity to make some quick cash, start crying of back and neck pain.

Mass of bus + passengers + fuel is about 66,600 [lb] or 30,200 kg.
Mass of van is about 2,000 kg.

Forensics estimates from the bending of the lightpole that the van was moving at an uninhibited speed of about 35mph when it hit the pole after sliding on ice.

I want to hear what you ideas about this, so please help, and REAL answers...please THANKS

Answer 1

I guess the first thing I would want to do is compute the acceleration that the passengers underwent to see if it was sufficient to cause trauma.

I also did a bit of research. There has been much study done about the physics of whiplash in collisions. There is good data about collisions in the 30 mph range, so this is relevant.

http://www.greatrix.co.uk/Pub3.htm

It looks like there has to be around 4g to cause soft tissue injury

Using conservation of momentum assuming little kinetic energy lost to friction prior to collision (this also is worst-case scenario)
Estimate the speed of the bus after collision
30.2*30+2*20=2*35+30.2*v
v=29 mph

The delta v of the bus is
1 mph

1 mph = 1.46666667 feet per second

1.46667 = a*t
If delta v is 1 mph, this is well below the delta v of 5 to 9 mph necessary to cause injury
let's look at the acceleration w/r/t g

t=300 ms a=0.15 g
Given that the average is about 1/2 the peak (see reference), this is still too small to be likely to cause injury by an order of magnitude.

j