Remember that Potential Energy = mass x gravitational constant x height above the first floor of your house. Also remember that Kinetic Energy = 1/2 x mass x velocity x velocity. At bottom of stairs, fourteen feet below the second floor, calculate the velocity of a 6.21 slug man sliding down the stairs before the first floor stops him from moving. Neglect wind resistance. Do not consider frictional forces, as the edges of the stairs are smooth and the Brooks running pants coefficient of friction is below 0.05. Remember that the acceleration of gravity is 32.2 ft per second per second. For extra credit, calculate the force imparted to the first floor, using Newton's second law F = d(mV)/dT, and state your assumptions as to the dT term, giving your best estimate of the deceleration time. Papers will be accepted until midnight tomorrow, and grading will be on the SOL curve for the Commonwealth of Virginia.

Force = busted ass bone

Yep, enough force to bust your ass pretty well!
Depending on who's around, a nice bruised ego as well.

Feel better!

Okay, so you hit the floor at around ~30 ft/s. But it is a bit harder to determine the full force exerted on the floor since you need the size of the "impact" membrane and the deflection of the floor to fully approximate the deceleration and determine the force. If memory serves, it is a fourth order partial diff. eq. But 2800 ft-lbs is nothing to sneeze at.

I was designing human impact windows for psych facilities this past year and we only require 2000 ft-lb impacts to meet spec. (I have a 300 lb dead blow pedulum at work for this, never considered just setting the test window up at the bottom of the stairs)

Ken

Probably didn’t take much to bust his ass, it was already cracked.

quote:

Originally posted by KenS:...If memory serves, it is a fourth order partial diff. eq. ...

Partial differential equations, and trig integration, are the reasons I switched to accounting half way through college. Accounting has only add, subtract, multiply, and divide.

I don't think it matters much, so long as the first floor was there to break your fall. The main thing is that you did eventually stop.

Okay, the extra credit.

We'll assume the floor (or wall) at the bottom didn't budge. We'll also assume you wound up in a nice 3 foot pile, so your "smoosh" distance was 3 ft at an average velocity of 15 ft/sec ( from 30 ft/ s to 0 ft/s). That means your deceleration time was .2 sec or an average deceleration of 75 ft/s/s and your force of impact was around 465 lbs.

Ken

You only need the diff eq. if you are take flexure of the impacted surface into account for design purposes.

Dang, you guys are smart.

quote:

Originally posted by bushpilot:
Dang, you guys are smart.

Nah, just lucky enough to write about it.

I am still alive this morning. My upper back area is sore. My right buttock is sore. My elbows are sore.

The calculations offered have been checked against the Virginia physics SOL (standards of learning) answer key, and each of you may matriculate to the next grade level. Congratulations.

In the meantime, I will repair to the kitchen for my first cup of coffee and twelve pages in my "90 Day Bible." We are almost finished reading from cover to cover in 90 days.

Sorry, late for the quiz. Don't you have to know the angle of impact to calculate the extra credit?

Knowing that Newton's Law states that for every action there is an equal and opposite reaction, the floor, and by extension the ground beneath it, and the entirety of planet Earth must have reacted in some infinitesimally small way.

So it could have been worse.

Half as much than falling twice as far.

quote:

slug man sliding down the stairs

Is this a trick question? They didn't provide the viscosity in centipoise of slug-man's slime.

On a more serious note, hope you're feeling better soon.

quote:

Originally posted by 220-9er:
Half as much than falling twice as far.

Actually, a quarter as much as falling twice as far, assuming he didn't reach terminal velocity.

quote:

Originally posted by Fenris:

quote:

Originally posted by 220-9er:
Half as much than falling twice as far.

Actually, a quarter as much as falling twice as far, assuming he didn't reach terminal velocity.

His post proves that his velocity wasn't terminal.