[Blindmath] physics/mathematics problem; have a solution?

Mon Dec 19 08:00:26 UTC 2011

Okay, i understand.

Here's the truth, the whole truth, nothing but the truth... hee hee, the 
"hole" truth"

I've been digging drainage holes in my yard to direct downspouts to.  One of 
them I dug and put all sorts of safety items atop it so no one would fall 
into it.  I was especially worried about my son who is quite bouncy and 
jumpy and runs really fast without looking.  My son is sighted, FYI.

A neighbor of mine was moving and sold me a lovely rocking chair and end 
table.  She also gave me some fun things like a full spectrum sun lamp and 
more, but I digress.

The issue was that, in order to open the gate to get to her yard through the 
alley behind my house, I had to remove all of my safety devices covering the 
hole.  Yes, the hole was, basically, directly in front of the back gate. 
*sigh*  Can you now see why I wanted to keep this as anonymous as possible?

I took most of the goodies from her house to mine and remembered to stay 
clear of the four foot deep and four foot diameter hole.

She and I sat and chatted for a while (she's moving to a senior home and is 
quite sad about leaving the independance of her lovely little home in our 
peaceful neighborhood).  I took the sun light and told her I'd be right 
back.  She was, by that time, in a big hurry to go to an appointment.  I 
needed to write her a check for the goodies she sold me and my checkbook was 
at home.

I hurried home and, well, forgot about the f***ing hole I put in front of my 
back gate and promptly fell in it.

Basically, I had both arms above my head holding the lamp and was hurrying 
as fast as any blind person can while encumbered by a heavy item.  When I 
walked into the hole I fell straight down.  My right rib cage hit the edge 
of the hole (at about 4 feet from the sole of my shoe) at an instant before 
both of my feet landed in the hole.

I would be happy to describe the noises I heard at that point and the 
severity of having the wind knocked out of me and my pride hurt to a severe 
degree, but that is probably not a requirement for figuring out the force 
placed upon my right rib cage.

So, the soil that approximately 20" (probably more like 14") of my right rib 
cage hit was, well, not very soft.  Also, my ribs are kinda flexible like 
most human ribs are.  Are those the missing parameters you were looking for 
to solve the problem?

I was kind of hoping someone could just outline what a  uniform mass of 170 
pounds would experience with a direct vertical drop travelling at 2.5 miles 
an hour at the four foot point of the mass (disregarding elasticity of the 
materials involved, but there ya go).

You now know way more than you wanted to, I'll bet.  *grin*

I appreciate your mathematical description of an anonymous and inflexible 
mass who did the same thing I described.  I might have lost my intellectual 
ability to figure such a problem out after losing oxygen for so long.

It's been a while since i've had the wind knocked out of me and forgot how 
scary that is...

just for your information, I did jump out of the hole and recovered my pride 
like a cat who just emberrassed itself by not landing on its feet.  I don't 
know if you've seen that from a cat, but it is the "stand up proud, look 
around, and do a few licks on each shoulder" to make sure no one is actually 
within distance to have seen the mishap.  All that while trying to get my 
breath back.  yeesh.  Pride can be such a silly thing.

Okay, just one more comment... since you asked for details... I had strained 
my achilles tendon a couple of weeks before that.  I was basically bed 
ridden for days.  It was one of the first days in weeks that I felt like I 
had the strength to carry heavy things around again.

My ribs took so much of the force that my feet landed perfectly flat in the 
bottom of the hole.  I did absolutely NO further damage to my achilles.  It 
could have been much worse.  Probably could have broken some legs if I would 
have stepped into the hole differently.

Anyhoo, now that my pride is recovering and I'm back to my normal "i'm blind 
but i can do anything" attitude, I'm interested in the physics and 
mathematics of the situation.  Also, my back is so effed up now that my ribs 
are semi healed, I need to go to the doctor.  I didn't go to the doctor 
because I didn't think they could do anything about cracked ribs.

I wasn't really thinking about the back damage or the internal damage that 
might have happened at that point.  I just braved it with tylenol and 
ibuprofren.  sigh.  I hope to grow up some day.  *smile*

Anyhoo, if you've got any idea what the force on my ribs would have been, I 
would sure enjoy bragging about it to my doctor so he'll feel sorry for me 
and send me to a chiropractor or something.

Best,
David

David Engebretson
Support at PeaceWeaverHosting.com - "We know what our name means"
----- Original Message ----- 
From: "Richard Baldwin" <baldwin at dickbaldwin.com>
To: "Blind Math list for those interested in mathematics" 
<blindmath at nfbnet.org>
Sent: Sunday, December 18, 2011 9:30 PM
Subject: Re: [Blindmath] physics/mathematics problem; have a solution?

>A quick off the top of my head assessment tells me that there is a missing
> term.
>
> The force required to stop the mass is equal to the mass times the 
> negative
> acceleration.
>
> The negative acceleration is equal to the change in velocity from impact
> velocity to zero velocity in a given amount of time. Since we don't know
> the time interval over which the velocity changed, we can't compute the
> acceleration. If the time interval was zero (impossible), the required
> force would be infinite.
>
> It seems that a work/energy solution might be more appropriate than a
> force/mass solution, but even there, we would need to know something about
> the behavior of the system at the point of impact.
>
> Dick Baldwin
>
>
> On Sun, Dec 18, 2011 at 11:14 PM, David Engebretson Jr. <
> davide at soundandscience.com> wrote:
>
>> Physics problem - have a solution?:
>>
>> Imagine a 68" object with a mass of 170 pounds travelling at 2.5 miles 
>> per
>> hour (assume the mass is evenly distributed in the object in motion). The
>> mass drops four feet and all of the momentum and other forces are placed 
>> in
>> a single point on the object at 4 feet. Assume, also, that the bottom of
>> the mass lands at the bottom of the four foot hole at the same time the
>> impact upon the mass is inflicted upon the mass (ignore any loss of 
>> energy
>> due to the landing of the mass in the bottome of the hole - the landing 
>> and
>> the impact are ALMOST instantaneous).
>>
>> What is the amount of force that the mass absorbs at the time of impact?
>>
>> You can also assume the mass is 20" wide at the "point" of impact.
>>
>> In summary:
>> The mass drops four feet travelling 2.5 mph. The impact area is 4 feet up
>> from the bottom of the mass. The impact point is a single line 20" wide.
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>
>
>
> -- 
> Richard G. Baldwin (Dick Baldwin)
> Home of Baldwin's on-line Java Tutorials
> http://www.DickBaldwin.com
>
> Professor of Computer Information Technology
> Austin Community College
> (512) 223-4758
> mailto:Baldwin at DickBaldwin.com
> http://www.austincc.edu/baldwin/
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