# Q & A: Car crash?

Q:
If an object weighing 6400 lbs struck an immobile object weighing 3200 lbs and pushed it 84 feet at what rate was the 6400 lbs object moving? How about changing the weight of the 6400 lb object to 8800 lbs?
- Jennifer (age 16)
Neoga IL USA
A:
Jennifer-

It sure sounds like someone is preparing for a court case involving a traffic accident. Unfortunately, we can't help out too much here, because some information is missing.

If a moving object bumps into a stationary object and they then stick together (it sounds like this is the situation) they will continue moving forever, unless some other force acts on them. In your case, they came to rest (with respect to the Earth), so they probably had friction with that object- say friction between tires and a street. To answer your question, one then needs to know the coefficient of friction between the tires and the street or dirt or whatever. That depends a lot on conditions, so even if our guesses about what you're asking about are right, we can't give an accurate answer.

Let's say, just for further guessing, that the friction was between dry rubber and dry concrete (that would mean that the parking brakes are on on the stationary object, or that it is being pushed sideways to keep the tires from rolling, which would make for a very different friction scenario). The coefficient of friction between dry rubber and dry concrete is about 0.8. Then the combined objects decelerated at about 8 m/s^2. It's not hard to solve that they were travelling at about 20 m/s right after colliding. Since in a collision momentum is conserved (not enough time for outside forces to change it) the 6400 lb object (truck?) would have been travelling at 30 m/s before the collision. That's 108 km/hr, or about 66 mph. If the big object weighed 8800 lb, its initial speed would have been about 27 m/s, or about 60 mph.

What was the speed limit?

Mike W.

(published on 10/22/2007)