BS: The physics of a fall

Subject: BS: The physics of a fall
From: Mrrzy
Date: 19 Apr 07 - 02:04 PM

Help, you math and physics people.

Say I weigh 85 kilos, and usually walk at about 5 km/hour. But I was running down the stairs when I tripped, so I'm assuming I was going faster than that. And speeding up as I hit.
Upon tripping, I landed - with all my mass times acceleration- on about 3 square centimeters of shin, on the edge of a concrete step - no give at all. So:

How much energy was actually transferred to my leg in the fall?

Now, I basically have a tremendous bruise - my entire lower leg is swollen and the bruising extends to my ankle and half-way up my thigh. The swelling looked for all the world like somebody had shoved an American football into my leg, with the stitching being the little scrape on my shin. All the rest of the injury is inside my leg - I had to have crutches for the first time in my life, I missed several days of work and now that I'm back, it's swelling and painful again (RICE therapy doesn't work at the office). So:

Is it possible that the hydrostatic (lipostatic?) force from all that energy being transferred suddenly to my leg caused something more like a blast injury than a boo boo (the bruise on my shin)?


Thank you all for your kind and thoughtful analysis.

Subject: RE: BS: The physics of a fall
From: Ebbie
Date: 19 Apr 07 - 03:24 PM

I don't know the scientific formulae- but commiserations anyway.

Subject: RE: BS: The physics of a fall
From: Greg B
Date: 19 Apr 07 - 03:31 PM

"How much energy was actually transferred to my leg in the fall?"

Enough.

Subject: RE: BS: The physics of a fall
From: Sorcha
Date: 19 Apr 07 - 03:38 PM

I'm surprised you didn't break at least the shin bone, let alone something else! Hope you mend fast!

Subject: RE: BS: The physics of a fall
From: Jean(eanjay)
Date: 19 Apr 07 - 03:39 PM

work done/energy = force x distance

Somebody else's turn now!

Subject: RE: BS: The physics of a fall
From: Amos
Date: 19 Apr 07 - 03:40 PM

Had it been a free fall, it would have accelerated at 32 ft/sec per second of time falling. You were pretty close to the ground at the low end, but suppose you were moving at 7000 meters per hour, 116.6 m per minute, about 2m per sec. If your fall took .5 seconds, which seems reasonable, the increase would be about 4.9 m/sec, so assume your final velocity on impact was 6.9 m/sec.   

If I recall basic physics correctly, which is always problematical, kinetic energy = 1/2 mass * v^2. This would equate to 42.5 * 47.61 or about 2023 joules of energy. About 675 joules per square cm.

I hope John H will come check my work, though. Insult to nerves can sometimes cause reaction in a region rather than a single point of impact in my experience. I would be more inclined to attribute it to nerve insult and shock than to transmitted hydrostatic pressure.


A


A

Subject: RE: BS: The physics of a fall
From: Slag
Date: 19 Apr 07 - 03:47 PM

Correction: 32 ft per second SQUARED as this is acceleration. Add to the speed of forward momentum. Roughly 15 to 20 miles an hour max. Enough to bruise a bone.

Subject: RE: BS: The physics of a fall
From: Jean(eanjay)
Date: 19 Apr 07 - 03:59 PM

Per second per second is the same as per second squared.

Subject: RE: BS: The physics of a fall
From: TIA
Date: 19 Apr 07 - 04:08 PM

Total energy = kinetic + potential

=(1/2*m*v^2)+(m*g*h)

or

=1/2*m^2*v^2*g*h

where

m=mass
g=980 cm/s^2
h=height of point where fall began above step where fall ended
v=velocity of faller at point where fall began

Plug and chug for numerical answer.

It'll still hurt like hell.

Subject: RE: BS: The physics of a fall
From: Slag
Date: 19 Apr 07 - 04:28 PM

Right. Check your post. I think you omitted the second "per second,"

Subject: RE: BS: The physics of a fall
From: MMario
Date: 19 Apr 07 - 04:34 PM

g - 10 m/sec*sec to keep it in the terms posted

but the answer you want is that yes, the force would be spread through the tissues and cause damage outside of the site of actual impact.

Subject: RE: BS: The physics of a fall
From: catspaw49
Date: 19 Apr 07 - 04:35 PM

Did you go to a doc about this? Check for breaks or hairline fractures? That type of fall and the associated bruising might also bear a look at a deep vein thrombosis which can also cause clot problems........

Spaw

Subject: RE: BS: The physics of a fall
From: Rapparee
Date: 19 Apr 07 - 04:35 PM

Put ice on it. Keep it elevated, and for Crissakes, see a doctor!

Subject: RE: BS: The physics of a fall
From: Jean(eanjay)
Date: 19 Apr 07 - 04:39 PM

Slag, it was Amos' post I was referring to. He wrote 32 ft/sec per second.

Subject: RE: BS: The physics of a fall
From: Jean(eanjay)
Date: 19 Apr 07 - 04:43 PM

.....not that it really matters. I don't know why I mentioned it; I must be bored tonight!

Subject: RE: BS: The physics of a fall
From: Amos
Date: 19 Apr 07 - 04:51 PM

Appreciate the defense.


A

Subject: RE: BS: The physics of a fall
From: Bee
Date: 19 Apr 07 - 05:03 PM

Ouch.

If you haven't seen a doctor, do - and again...ouch!

Subject: RE: BS: The physics of a fall
From: Wolfhound person
Date: 19 Apr 07 - 05:04 PM

Bruising is internal bleeding. You want to get it checked out *now*, and for goodness sake keep it up and rested. *Don't * overdo it or you'll risk all sorts of complications

I did something similar a few years back and now have a permanently torn thigh muscle. After 6 weeks I had to have a pint of excess and misplaced fluid drained from the injured area.

I don't do physics, though, sorry

Paws

Subject: RE: BS: The physics of a fall
From: Mrrzy
Date: 19 Apr 07 - 05:09 PM

The ER docs were very nice - they are the ones who prescribed RICE (Rest, Ice, Compression, Elevation) - but I've come back to work where I sit a lot with my leg down. I asked about thrombisis and they said not to worry - but man, my calf is FILLED with decomposing blood. And it's crawling up my leg in the most glorious technicolor.

Hurt like I couldn't have imagined - but then stopped hurting, I continued my walk to dinner, had dinner - and then tried to get up again and literally could not walk.


Anyway, back to the physics - always let g=10 or your students hate you.
I'll try TIA's formula when I have more brains...

Subject: RE: BS: The physics of a fall
From: catspaw49
Date: 19 Apr 07 - 06:20 PM

No, not back to the physics, back to the doctor.   Don't let this go Myrrz.......I could tell you about sister Connie but it would take too long for all the details. Just go check back and let them evaluate what is happening now.

Spaw

Subject: RE: BS: The physics of a fall
From: Rowan
Date: 19 Apr 07 - 06:43 PM

The others have done the physics but my (somewhat similar) experiences suggest to me that what you may be experiencing is usually called a subperiostial haematoma. A haematoma is basically a spectacular bruise. The periostium is the membrane surrounding the bone tissue, so a subperiostial haematoma is a bruise under the periostium.

Yours sounds more spectacular than most but RICE is the trick. If you do it repeatedly (as I did when training and competing in IV Judo many years ago; lots of vigourous ankle blocks that were more like batterings) the shin bone develops a rough feel. This was also a sign of tertiary syphyllis in times past but I've successfully avoided such parasites. And I can report that the roughness of the shin caused by repeated subperiostial haematomas gradually smoothes out again.

All the best.

Cheers, Rowan

Subject: RE: BS: The physics of a fall
From: leeneia
Date: 19 Apr 07 - 07:48 PM

"but I've come back to work where I sit a lot with my leg down."

Here's what to do, Mrrzy. Pretend that your employers FORBADE you to elevate your leg. If you are like most people, that will motivate you to elevate it, and it will get better faster.

Subject: RE: BS: The physics of a fall
From: Bill D
Date: 19 Apr 07 - 07:55 PM

.......(and be sure to pray a lot...*grin*)



take care.. and give up the trampoline lessons for awhile...

Subject: RE: BS: The physics of a fall
From: JennieG
Date: 19 Apr 07 - 08:26 PM

Ouch!

Plus what Bill D said about the trampoline lessons....and I would add tango lessons too.

Cheers
JennieG

Subject: RE: BS: The physics of a fall
From: TIA
Date: 20 Apr 07 - 09:30 AM

Other factors that would be important are:

The area of the bruise since stress is force per unit area. One would probably rather be hit with large (blunt) object rather than a pointy or sharp one of equal weight and acceleration.

Coefficient of restitution (or "give") of the step. A steel step with no "give" will hurt a lot more than a carpeted one.

Made for great mental entertainment thinking about fall physics on the train last night. Thanks for falling Mrrzy.

Subject: RE: BS: The physics of a fall
From: Amos
Date: 20 Apr 07 - 10:02 AM

Using TIA's formula:

m        85        kg
v        1.5        m/s
g        9.8        m/s/s
h        2        m
m^2        7225        
v^2        2.25        

m^2v^2gh        318622.5        
/2        159311.25 joules

or about 53Kjoules per square centimeter.


I think this is high. But I don't have time at the moment to track down the error.

A

Subject: RE: BS: The physics of a fall
From: MMario
Date: 20 Apr 07 - 10:07 AM

h would be smaller because it would calculate from the height of center of mass.

Subject: RE: BS: The physics of a fall
From: Amos
Date: 20 Apr 07 - 10:26 AM

OK, so 1 m instead of 2 m for "h", and you still get an awfully high number.


A

Subject: RE: BS: The physics of a fall
From: MMario
Date: 20 Apr 07 - 10:32 AM

well - it's concentrated. 3 square centimeters is probably less then 1 % of the area that normally supports that mass

Subject: RE: BS: The physics of a fall
From: Amos
Date: 20 Apr 07 - 10:50 AM

Actually, it is probably incorrect to compute all the impact as focusing on the point of contact. A lot of that energy is dissipated across the whole area of the accelerated mass whether it is still moving or had its own impact _after_ the ankle hit the stairs.

A

Subject: RE: BS: The physics of a fall
From: Mrrzy
Date: 20 Apr 07 - 11:28 AM

Well, it sure FELT like the impact was focused! And I saw my regular doc today, one week later, and he said just to watch for infection if the little scrape riding like a flea on an elephant on top of the swelling gets red.
But he agreed with my theory that it was the lipostatic pressures as the energy whoomed around inside my leg that caused the huge swelling and bruising... so I'm wondering, if I were thin and still weighed this much, same fall, do you think it would have broken the bone? Never been so happy to be padded!

Subject: RE: BS: The physics of a fall
From: Mrrzy
Date: 20 Apr 07 - 08:04 PM

Helpful wonderful physicists, I have more data, and thus (of course! I'm a scientist) another question. Pretty please? Love you all!

Update: There is a large collection under my ankle that is newish, and obviously seeped from somewhere, so I took another look in the full-length mirror (rather than looking at my leg, you see; made me wonder if individual tigers know they're striped) and saw amazing wave-form patterns in the bruising that strongly support my blast-being-transferred-through-a-lipohydrostatic-medium theory. I can't draw in html so bear with me.

Recap: The impact site is on the front of my shin going top-o-centrically from the middle of the shin (in the vertical dimension) outwards and downwards about 5 cm, usually less than a cm wide and possibly slightly deeper and wider at the top. It has gone from a kind of skinned-knee-ish scrape to dark thick flat mostly numb stripe that looks for all the world as if it had had stitches, which it didn't. It sits on a little pillow of swelling whose bruising has now turned yellow, which makes it absolutely repulsive. The nurse actually called it Dreadful.

Anyway, the point is that I hit pretty much in parallel to the plane of the shinbones, at an angle that sent the blast inwards and upwards.

The greatest area of swelling, which still looks pretty bad, goes upward and inward from the impact site to the very top of my calf, and doesn't wrap around to the side or up into my knee.

The dark bruising on the inside of my left calf and around to the shin on that side, that seemed to me to go pretty much from above the knee to the ankle, turned out to go all the way to the sole of my foot but* - critical datum here- *is darker in thin stripes that are parallel to the impact scrape and equally spaced, like ripples in a pond. Of Mrr.

The huge and still very purple bruise in my popliteal region (relax - back of the knee, down you scoundrels) turns out to be counter-coup, the injury from the blast going right through me to the other side. You get this in brain injuries too - shake like a bowlful of jelly, we do, and our insides rattle around inside our outsides and whack against the other side - the other inside of our outside, that is. Ya folla?

The bruising that was creeping from my outer lower left (neither shin nor calf- what IS that part called?) up the outside of my thigh in a kind of arc around my knee joint also resoleved into parallel stripes going outward from the impact site. That is, what I was seeing as a vertical stripe of bruising (when standing up and my knee isn't bent) turns out to be a series of parellel-to-the-impact-area stripes that together comprise a vertical set of bruises running together in my perception.

I love data. They sure distract you from actuality when you want them to, without taking you out of reality at all!

OK, so, here's the next question: the stripes from the blast petered out in about, say, a half meter either side of the impact, anywhere the blast had a half-meter to travel in. When it didn't, as in directly through my leg across the knee from it, looks to have been the worst damaged after the shin itself. But now, can we verify our calculations of the blast strength?
And once it's in joules or something meaningful to you helpful physicists, can you translate that into either kilocalories (it was like your shin at 17 big macs in basically 0 seconds) or square meters of area cleared if you were in helpful rather than destructive demolitions?

Subject: RE: BS: The physics of a fall
From: folk1e
Date: 20 Apr 07 - 08:43 PM

The problem with the figures in previous posts is that whilst they "look" accurate they are not!
If you are going to take acceleration (due to gravity) it is only aplicable in a free fall situation. If you were to jump 2m in the air the acceleration would determine your speed when you "hit the floor"! As you were running when you "tripped" the acceleration would be reduced.
Your body mass did not stop when your knee came into contact with the step, but slowed as your body crumpled up.
Your arms would be flailing round and therefore alter the effective body mass.
As you came into contact with the step your shin absorbed some of the energy of the impact by compressing and bending.
Unfortunately the many forces involved quickly become so complex that an accurate figure is not attainable! If you doubt this you only have to look at slow motion video of bodily contacts, for example in the film "Rocky"! The body can change shape dramatically for short periods of time!
Still hurts though!!

Subject: RE: BS: The physics of a fall
From: Amos
Date: 20 Apr 07 - 08:45 PM

I can't confront doing this problem. Every timne I think about it I flinch!! :D


A

Subject: RE: BS: The physics of a fall
From: Amos
Date: 20 Apr 07 - 08:52 PM

I don't think she needed a physicist to tell her it hurt.

A

Subject: RE: BS: The physics of a fall
From: Mrrzy
Date: 20 Apr 07 - 09:20 PM

Sympathy is also gut.

Subject: RE: BS: The physics of a fall
From: Rowan
Date: 20 Apr 07 - 11:59 PM

Mrrzy, "Sympathy!!!!!"

And some distractions?
The colourations you've described do indeed sound as though hydrostatic pressure waves were cruising through whatever soft tissue was there to take them. The parallel stripes probably indicate locations of particular muscles, which would be more likely than tendon to conduct pressure waves (tsunamis?) down into the foot and past the knee into the thigh.

I gace up on trying the physics for the reason outlined by folk1e. And I agree, it DOES hurt.
But it will go away and the colour transitions will take some time to complete.

Cheers, Rowan

Subject: RE: BS: The physics of a fall
From: kendall
Date: 21 Apr 07 - 08:51 AM

Just think how lucky you are. If you were elderly, it could have been your finish.

Subject: RE: BS: The physics of a fall
From: Mrrzy
Date: 21 Apr 07 - 02:52 PM

Absolutely, Kendall! The luckiest I've probably been, if you want to look at it that way!
Not to mention it's a great story...

Subject: RE: BS: The physics of a fall
From: Slag
Date: 21 Apr 07 - 04:28 PM

All that pretty black, blue, purple, yellow brown and green(not gangrene)will migrate to the bottom of your foot and around the edge somewhat. What fun!

As long as you are doing physics, don't forget air resistance, the Coriolis effect, celestial gravitational alignments, tension strength of bone, tissues, etc. tension and tensile strength of the material encountered, any retrograde motion you were able to effect, if any. Good Luck!

Subject: RE: BS: The physics of a fall
From: Mrrzy
Date: 22 Apr 07 - 01:26 PM

The Coriolis effect must be why I was turning as I fell, LOL! Lessee - I'm in the northern hemisphere...
(better get off the painkillers soon, eh?)

Subject: RE: BS: The physics of a fall
From: TIA
Date: 22 Apr 07 - 11:08 PM

In which direction did they wrap the leg?

Subject: RE: BS: The physics of a fall
From: Mrrzy
Date: 22 Apr 07 - 11:39 PM

Hee hee! I have to go flush now!

Subject: RE: BS: The physics of a fall
From: Stilly River Sage
Date: 23 Apr 07 - 06:57 PM

About 10 years ago I fell by tripping on a raised section of sidewalk, and landed smack on the front of my right knee and my hands so fast I was hardly aware I was falling until I landed. Hurt like hell, took ages to get over. I probably should have taken it to a doctor. Condolences to anyone with something as painful as that.

SRS

Subject: RE: BS: The physics of a fall
From: Naemanson
Date: 23 Apr 07 - 07:17 PM

I agree with all that's been said. You have my sympathy. I am just getting over corrective surgery on my wrist after a fall.

Maybe we should go back to just before the fall. What were you doing? Hurrying. Why? That's for you to consider. Result? Injury. Lesson? Don't run, don't hurry, stay calm, and let others take the falls.

Subject: RE: BS: The physics of a fall
From: Amos
Date: 23 Apr 07 - 08:05 PM

I think we'd all be mnuch happier if we went back before the Fall.

:D

A

Subject: RE: BS: The physics of a fall
From: Mr Happy
Date: 23 Apr 07 - 09:08 PM

What's a square second??

Subject: RE: BS: The physics of a fall
From: Rowan
Date: 23 Apr 07 - 09:20 PM

Surely a square second is the untrendily conventional supporter of a duellist?

Subject: RE: BS: The physics of a fall
From: Mr Happy
Date: 23 Apr 07 - 09:25 PM

.........& if your ankle's affected, surely the calculation should be in foot pounds!!

Subject: RE: BS: The physics of a fall
From: Mrrzy
Date: 23 Apr 07 - 09:40 PM

I do wear hats, but that's toque, not torque.

Not hurrying, just going down the steps to go out to dinner with one of my twins. I was kinda tripping down the stairs like pretty Peggy-O, I guess!