[TheForge] Re:Mass vs. acceleration vs. soil (A Novel)

[Thomas A. Troszak]

> From: Peter Fels And Phoebe Palmer <artgawk@thegrid.net>
> I've been giving a lot of thought  to the foundation to go under the
> hammer, as you might imagine.
> My tentative plan is to dig deep and pour a couple of yards of
> reinforced concrete, put in a layer of timbers topped with another yard
> of concrete. On top of that I plan to stack alternating layers of
> plywood, cork, steel, rubber,  4"wood slab and more timbers.
> The theory is that different layers of materials will tend to damp
> different frequencys of vibration and the cold shut effect will be
> compounded by having all those different layers.

Dear Peter and Phoebe,
No, no, no, no, no. Please read the following.  :)

>From: GHS <ghs@execpc.com>
>Tom Troszak, are you out there? This arrangement sounds much like the
>one that gave me so much grief. I lost your explanation or I would just
>post it here.


Dear Peter and Phoebe and Mike,

The solution is very simple, but perhaps not simple to explain why. There
are two distinctly different things happening here, what is going on in the
hammer, and what is going on in the soil.

First, what is going on in the hammer:  Think of the anvil as a mass
floating in space, because that is what it is. When we strike the anvil with
a mass (such as the ram) the anvil accelerates in space as a ratio of the
mass of the ram (and the the velocity of the blow), vs. the mass of the
anvil.   

An analogy: Ever played croquet? You know how you can "launch" your
opponent's croquet ball clear out of the game if your ball is touching it,
by smacking your ball with the mallet. The blow from your mallet accelerates
your ball (which decelerates the mallet) which then strikes the opponent's
ball (which decelerates your ball) and accelerates the opponent's ball clear
out of the yard (about thirty feet).

Now think of the mallet as the "ram", your ball (under your foot) as the
"anvil", and the opponent's ball as the "soil". If the mass of the "anvil"
(the ball under your foot) is nearly the same as the "ram" (the mallet), it
will accelerate to nearly the same velocity as the "ram" (the mallet), and
pass that acceleration on the the "soil" (the opponent's ball) at high
speed. 

Let's try the experiment again, but substitute a bowling ball for the
"anvil" under your foot. The 16 lb. bowling ball "anvil" has a mass about
thirty two times greater than the 1/2 lb. mallet "ram".

Smack the bowling ball with the mallet, and it will accelerate, but only to
1/32 of the velocity of the mallet, so when the bowling ball "anvil"
collides with the "soil" (the opponent's ball), it does so at only 1/32 of
the original velocity of the mallet, so that the "soil" (the opponent's
ball) only launches about 1/32 as far (about a foot).

The total energy of the blow of the hammer ram is not "absorbed" by the
anvil, it is transformed into a lower velocity of acceleration of the anvil.
Since the anvil is accelerating more slowly, the the soil is "struck" more
slowly, and the resulting "shock wave" has less velocity.

Still with me?

Ok, try these Mind Experiments (but don't actually do them, I cannot me held
liable for injuries):

Take your favorite 2 lb. hammer and smack the palm of your hand. Ouch.
(remember I said don't really do this, just think about it)

Now place your palm on one end of a brick and smack the other end of the
brick with the hammer. Ouch.

Now place your palm on one end of a two foot long pine 2x4 and smack the
other end of the 2x4 with the hammer. Ouch.

Place your palm on one side of a piece of plywood, and smack the other side.
Ouch.

Place the end of the 2x4 against the end of the brick, palm at one end,
hammer at the other. STILL Ouch.


Now change things a little:

Place your palm on one side of your anvil and smack the other side. Ting. No
ouch.  

Why?

The wood and bricks (concrete, croquet balls,) etc, are fairly rigid, yet
not very dense, so they conduct high velocity shock waves fairly
efficiently. If you have ever held a board while someone was nailing on it
you know what I mean. They do no (or very little) good as absorbers of shock
waves because they participate in the propagation of the shock wave with
great enthusiasm. 

What to do? Slow down the velocity of the shock wave at the source: the
anvil. The heavier the anvil, the slower the wave, as in the croquet
experiment. One caveat: the anvil has to be one big fat piece, not a stack
of loose plates. Why?

If you set a row of billiard balls about 1/4 inch apart (or even touching)
and shoot the first ball... craaaack and the last ball shoots away nearly as
fast as the first was shot. Same goes for those little hanging ball
bearings, or a row of dominoes, empty freight cars in a train or whatever.
The acceleration is transferred from object to object with little loss of
velocity as each object accelerates with the nearly same velocity, and the
shock (actually acceleration) wave passes right along.

Now place the bowling ball (left over from the croquet experiment) gently on
the billiard table, and shoot it with a billiard ball. Click. Yep, the
bowling ball moved, but probably too little to even see. Just like the
anvil.

Ok, enough of analogies. Firmly bolt your power hammer to a single thick
plate of steel, say a minimum of 20 times the mass of the ram.   If you have
a 100 lb hammer, then use a 2000 lb. plate minimum.  More is definitely
better, up to about  35/1 ratio. The hill (as well as the wine glasses on
your pantry shelves) will not even know your hammer is there. Save all that
digging.

Question: If all 1,000,000,000 Chinese stood up on chairs and jumped off at
the same instant, would Peter's house slide into the sea?

Answer: No, but that is a different question for another time...

I hope this is helpful.

Tom Troszak