# If a 235 lb person falls 2 stories in an elevator

1. Oct 4, 2004

### Orbit

I have a situation wherein a 235pound 30 year old man claims that he was in an elevator at our company and that the elevator free-fell 2 stories and injured his knee.

However, the man is claiming that his total injury is a bruise (but he wants a lot of money from us). I'm having a hard time believeing he would not have been more hurt if this happened the way he says it did and thus I question his entire story. I wnat to be able to go to my boss with some science to justify spending more money to fight this claim - if I'm wrong i just assume find out here.

Can someone help me out with determining how fast this guy would have been falling in miles per hour or even feet per second.

I am merely an associate lawyer and I'm really having a hard time converting meters per second into miles per hour and I know the 235 pound is relevant to how hard he would hit, but I'm not sure how it works into the equation and I need to be able to explain this in terms that my boss will understand. I'm figuring two stories is about 20-25 feet (right?).

Red

2. Oct 4, 2004

### Tide

Is there any other evidence to support a claim that the elevator fell?

With freefall, the speed at the bottom in miles per hour is

$$v = 5.47 \sqrt H$$

But that is only half the problem. The amount damage and injury also depend on important details like the construction of the elevator and the type of cushioning or buffering.

3. Oct 4, 2004

### chroot

Staff Emeritus
There are many points that must be considered.

1) Let's take care of the basics first. Converting between units is a pain -- so don't do it! Let google do it for you:

2) It is not speed that causes injury -- it is acceleration, the change in speed over time, that causes injury. Even if the man fell a large distance, he would not be hurt unless the elevator car came to an abrupt stop. If the car came to an abrupt stop, he would hit the floor hard, experiencing a large change in speed over a short time. If instead the elevator car came to a gentle and gradual stop due to its brakes engaging, the acceleration would be mild, spread over time, and any injury would be minimal.

In short, even if the elevator did fall freely for two stories, that knowledge is irrelevant. The only bit that's relevant is how abruptly the car stopped falling.

I am not qualified to be an expert witness in elevator designs, but I believe the majority of elevators in service today use both electromagnetic and mechanically-actuated braking systems, both of which should respond faster than two stories, and both of which are designed to slowly bring the car to a stop. An abrupt stop requires large forces and would as dangerous to the cables and other supporting structures as to the occupants.

You would do well to contact an elevator technician, particularly one who is knowledgeable about the building's equipment, and ask him how quickly the elevator car decelerates (in m/s^2) when its brakes are engaged. From this information, you can determine how much force was applied to the man, and the likely severity of the resulting injury.

3) Let's work the numbers you requested.

The speed of a body falling freely in the Earth's gravitational influence is

$$v = \sqrt{2 g h}$$

where $g = 9.8 m/s^2$ and h is the distance fallen.

Plugging in the numbers, the man would have been travelling at a little over 12 m/s, or a little over 27 miles per hour, after falling 25 feet.

If the elevator fell freely for two stories, say 25 feet, the 235 lb man inside it would have gained about 8,000 joules of kinetic energy:

8,000 joules is about as much energy as a 60W light-bulb burns in two minutes. It's certainly enough to hurt a person very badly, particularly if they happen to fall in a position which applies a lot the force to a particular joint.

4) You might want to speak to the prosecution's medical doctor to determine the severity of the injury.

5) Welcome to physicsforums!

- Warren

4. Oct 4, 2004

### cogito²

Talk to another lawyer.

5. Oct 5, 2004

### Orbit

Thank you all so much

Thank you for your advice it was very helpful and pretty dang close to what I figued his velocity would be.

He is claiming that the elevator came to a sudden stop, but there is no other evidence to support this contention, plus his injuries are at most slight (probably pre-existent). This is why I initially questioned his story.

Thank you all for your time and brains.

Red