Re: How do I calculate the impact force on a wall from a 10,000 pound automobil

Tommy,

As is the case in many situations, the answer is, "It depends." From Newton's second law, we know that force is equal to mass times acceleration (F=ma). We know the mass (10,000 lbs in the example you asked about), so now we need to determine the acceleration.

The acceleration (or deceleration in this case because we are slowing down when we hit the wall) is equal to the change in velocity (speed) divided by the time it takes to change speed (Dv/Dt). So first of all, the force is going to depend on how fast the automobile is moving when it hits the wall. Let's assume for now that the vehicle is moving at 40 mph.

Next, we need to know how much the vehicle slows down, and how long it takes to slow down. This gets to be the tricky part. If we're hitting a wall, we can probably assume that the vehicle comes to a complete stop, so the change in velocity is -40mph. Now, the amount of time it takes to slow down will depend on a lot of things. Does the wall give in at all when it gets hit, or does it stay perfectly rigid? How much does the vehicle "crumple" when it hits the wall? These are factors which are pretty hard to determine without doing some testing. But when a vehicle hits a large stationary object like a wall, it's going to slow down VERY fast. I'm going to make a guess and say that the vehicle comes to a stop in 1/10 of a second. Again, the actual time it takes could be faster or slower depending on what vehicle and what wall we're talking about, but that is a fairly good guess for this example.

Now we have everything we need to know. So F = ma and a = Dv/Dt. (By the way, for those not familiar with some of the symbols normally used in math and physics, D is the greek symbol delta and when used in equations like this means, "the change in..". So Dv means the change in velocity.) Therefore, F = m Dv/Dt = (10,000lbs) * ( 40mph) / (0.1 sec) * (.0455)= 182,000 lbs! That last .0455 is a unit conversion since pound-miles per hour per second probably doesn't make much sense to most people. Anyway, that's a lot of force, and now you can see why car crashes can be very dangerous and very destructive. So drive safely!

Your Mad Scientist,
Mike Scannell