# Weird physics statement in driver safety manual

1. Mar 31, 2012

### hvla

Hi everyone,

I'm taking an online "Driver Safety" course and came across this gem:

"Here is an example of how disastrous the force of impact can be:

If you weigh 100 pounds, are traveling at 30 mph, and hit a stationary object, the force of impact is 3000 pounds (mass multiplied by acceleration). "

Now I'm currently a medical student and its been a while since I took introductory physics, but that statement seems fishy to me. They appear to be using pounds both for the mass and the weight, whereas I thought that pounds were a measurement of weight. But then I looked on Wiki and found that there are many different definitions of the term 'pound.'

Also, it looks like they just multiplied the pounds by the speed in mph, which makes absolutely no sense. Overall the statement confuses me and I was hoping someone with a better grasp of physics could make some sense of it, and maybe improve my grasp of physics in doing so.

2. Mar 31, 2012

### Bill_K

Interesting! Is this number wrong? Or just a numerical coincidence? Let's see. The first thing to do is convert the speed 30 mph to feet/sec. Multiply by 5280 feet/mile and divide by 3600 seconds/hour. Answer: 44 feet/second.

Next we have to assume something about how a car absorbs the impact when it strikes a stationary object. The velocity will change over a very short distance, namely the amount your front bumper and hood will crumple. Let's say 1 foot.

For uniform acceleration the relationship between velocity, acceleration and distance is v2 = 2as. Solve for a: a = v2/2s. In our case, a = (44)2/2 = 968 feet/sec2. The normal acceleration due to gravity is 32 feet/sec2, so this is about 30 g's. In other words, the force you'd feel would be 30 times your normal weight, or 3000 pounds. They were right!

Was it a coincidence? Well, try working it out for some other speed, say 60 mph, and see what happens.

3. Mar 31, 2012

### jim hardy

no wonder seat belts are made of such strong fabric.

4. Mar 31, 2012

### hvla

So using 60 mph as an example, that is 88 ft/sec2. Assuming constant acceleration and a stopping distance of 1 foot, and using v2 = 2as, I get a deceleration of 3872 ft/sec2 or a force of 121 g's. For our 100 pound (now quite dead) person, that corresponds to 12,100 pounds!

So the numbers appearing the way they did for the original problem was an interesting numerical coincidence, dependent on the person's weight, the speed of the vehicle, and the stopping distance.

Thanks for the help!

5. Mar 31, 2012

### xxChrisxx

It's a fairly arbitrary figure. And only seems to be making the point that higher speed = bigger crash.