[TheForge] heavy hammers (Was Hammer Handles)
Peter Hirst
saltydog335 at aol.com
Sun Jan 11 17:46:34 EST 2009
Ok lets dispense with the qualitative and go to the numbers.
First, the momentum of the small hammer would be 200, not 2,000. 1 lb x 200
ips = 200 lb-ips . That's one one-hundredth of the momentum of the big
hammer, not one-tenth. Your analysis suggests that the larger hammer would
then do one hundred times as much work on the little cube as the smaller
hammer would. But would it? Maybe. But why? because just the act of
lifting it puts tremendous potential energy into it. Just resting the
10,000 pound weight on the workpiece with no movement at all would squish it
flat at forging heat. Zero momentum. In my example, I disregarded the
potential energy of lifting the different weights becaus at reasonable
weights say 2.5 to 5 lb hammers, the difference is negligible. This is
where using an extreme example skews the result. YOur larger hammer is
delivering its kinetic energy plus its static weight of 10,000 lbs. Its the
energy required to lift that weight -- which is released in addition to the
momentum of 2" per second velocity -- that does the extra work on the piece.
That's why its easy to intuit a huge difference in result. The difference
in static weight of two hand held hammers-- or even 2.5 lb hammer and a 100
lb power hammer, is not much, so I disregard it in my example. But it makes
a huge difference in your example. To take that out of your example,and
reduce the analysis only to kinetic energy versus momentum, you have to
picture the setup working horizontally. Now you have a 10,000 lb hammer
moving horizontally at 2" per second -- a little over 1/10 of a mile per
hour -- versus a 1 pound hammer moving at 200 inches per second, a little
over 11 miles per hour. Picture say a 16 penny nail driven half way into a
very sold post. A 10,000 pound truck coasting only, not under any power but
momentum, hits the nail -- and only the nail -- square with its front bumper
at point 0ne 0ne ( .11 ) mph, 2" per second. Now picture the one pound
hammer hitting that nail at eleven miles per hour 200 ips. A hundredfold
difference in momentum, no difference in energy. Under your theory, the
truck would have to drive the nail 100 times deeper than the hammer blow.
DO you think it would? OK, now lets go back to qualitative. Ever see the
damage a really slow moving vehicle does to a tree? say at 5 mph? I've
gotten away with a number of such collisions in my lifetime without a mark.
Hit the same tree with a hammer, and you'll at least leave a dent. Put it
another way: would you rather get hit by the truck moving at one tenth of a
mile per hour, or the hammer moving at 11 mph?
----- Original Message -----
From: <sos at frii.com>
To: "Blacksmithing List Sponsored by ABANA" <theforge at mailman.qth.net>
Sent: Sunday, January 11, 2009 12:54 PM
Subject: Re: [TheForge] heavy hammers (Was Hammer Handles)
>> Steve: two things wrong with this. First, you are ASSUMING, rather than
>> proving, that momentum is the key. But energy is the key to doing work,
>> by definition. second, if your arm can handle it is a hypothesis
>> contrary
>> to fact: your arm CAN'T handle it.
>>
>> Your analysis demonstrates that an arm moving very fast can create as
>> much momentum as a huge hammer moving very slowly.
>
> I'm not assuming anything about momentum. I set up two cases with the same
> kinetic energy but quite different momentum and asked what the result
> would be. You could do it the other way around, but the cases wouldn't be
> as dramatically different without the squared term. It doesn't really
> matter what my arm can handle, this is a thought experiment. The purpose
> is to try and tie the discussion back to the real world (instead of
> arguing about exactly what k.e. and momentum do). It is often instructive
> to consider extreme examples.
>
> Do you think that the 1 pound hammer moving at an ordinary hand hammer
> rate of speed will do as much to a 1" cube of steel? The one pound hammer
> will make some dents in the surface, the 10,000 pound hammer will squish
> the cube like a hydraulic press--maybe down to 2/3 or 3/4" of an inch, in
> one blow. The numbers are different enough that this seems pretty clearly
> to support momentum over k.e.
>
>> I saw a discussion recently between a mechanic and a physist recently on
>> this analysis. The mechanic claimed that everyone from Newton to
>> Einstein
>> was wrong about conservation of energy, and no matter how hard he tried,
> the
>> physicist could not get the guy to understand the difference between
>> momentum and energy. If momentum were the key, no lighter power hammer
>> could as hard or harder than a heavier hammer, but many do.
>
> Why not? If you hit faster with a lighter hammer, you should do the same
> amount of deformation. This applies whether k.e. or momentum is the key.
>
>> Ask any ballplayer what the key to slugging is: bat speed or weight.
> (ANd dont try
>> the loaded bat argument: that increases the area of the sweet spot, not
> the
>> energy delivered to the ball. That's why the corked bat is just as
>> illegal
>> as the leaded bat, and way more popular: it incrreases speed AND sweet
> spot).
>
>> ----- Original Message -----
>> From: <sos at frii.com>
>> To: <mspencer at tallships.ca>; "Blacksmithing List Sponsored by ABANA"
>> <theforge at mailman.qth.net>
>> Sent: Sunday, January 11, 2009 9:16 AM
>> Subject: Re: [TheForge] heavy hammers (Was Hammer Handles)
>>
>>
>>> Mike, how about a thought experiment.
>>>
>>> I'm taking a wag and saying that during forging your hammer moves at 200
>>> inches per second (~0.1 seconds for the blow from shoulder to anvil).
>>> You
>>> probably have a lot better number, the exact value isn't crucial.
>>> Cases:
>>> 1. 10,000 pound hammer, falling at 2" per second: mv=20,000
>>> pound-seconds
>>> (don't give me slugs, you know what I mean), mv^2=40,000 pound-second^2
>>> 2. 1 pound hammer, falling at 200" per second: mv=2,000 pound-seconds,
>>> mv^2=40,000 pound-second^2
>>> I think it is pretty obvious that #1 is by far preferred, if your arm
>>> can
>>> handle it. This makes me think that momentum is the key rather than
>>> kinetic energy.
>>> But I always had trouble with those two.
>>>
>>> Steve
>>>
>>>>> Movement of metal results from the amount of energy delivered in the
>>>>> blow. [snip longish discussion]
>>>>
>>>> Well, that's something I've been thinking about and haven't been able
>>>> to come up with a conclusion or computation that satisfies me.
>>>>
>>>> Kinetic energy (a scalar) is 1/2 m v-squared and momentum (a vector)
>>>> is mv. "Get a bigger hammer" is excellent advice when driving out a
>>>> stuck part because what you want is to max out momentum, not energy.
>>>>
>>>> Things are not nearly so clear when talking about forging. In
>>>> particular, the collision is inelastic, i.e. more like dropping a
>>>> bearing ball onto wet clay than like dropping one onto an anvil face.
>>>>
>>>> I *think* "get a bigger hammer" is good advice (within your physical
>>>> limits or power hammer budget) for forging, too, but I can't quite get
>>>> a grip on the physics.
>>>>
>>>> In addition, the "collision" may be thought of as between the hammer
>>>> (mass, say, 1 kilo) and the earth (mass around 6x10^24 kilos) with the
>>>> hot iron between them. Do I have to carry 10^24 around through the
>>>> computations (and keep track of changes in the velocity of the earth on
>>>> the order of 10^-24) to get the right result?
>>>>
>>>> So: energy is absolutely conserved. Momentum is conserved in elastic
>>>> collisions but what about inelastic ones? If you drop, say, a 1
>>>> kg. bearing ball into a big block of wet clay, you can calculate the
>>>> momentum of the ball just at impact. A moment later, though, nothing
>>>> is moving. [1] No v, no momentum. The energy is conserved by
>>>> conversion
>>>> to heat but what happened to the momentum?
>>>>
>>>> I actually buttonholed a physics profs [2] during one of my gigs at
>>>> MIT and asked him to explain this. He could never get beyond the
>>>> textbook examples where momentum, as well as energy, is conserved and
>>>> even became quite heated about conservation of momentum rather than
>>>> explaining why it *appeared* to me not to be conserved. At that
>>>> point I gave up. Who am I to disagree with Isaac Newton? But the
>>>> textbook examples don't seem to apply to calculations about hammering
>>>> hot, soft iron on an anvil solidly fixed to the earth.
>>>>
>>>> Starting from the engineering end, there are a lot of data tables
>>>> about forging, drawing, rolling and the like but they're empirical,
>>>> i.e., engineers measure what happens under certain industrial
>>>> conditions.
>>>>
>>>> Ho hum. :-) Anyhow, think about momentum, too.
>>>>
>>>>
>>>> - Mike
>>>>
>>>>
>>>> [1] Okay, the earth with ball attaches is theoretically now moving,
>>>> oh, say, 10^-24 m/s faster in the direction the ball was
>>>> moving. That doesn't seem like a useful piece of new knowledge. :-)
>>>>
>>>> [2] One of the more junior ones, who was heard to pronounce that he
>>>> was more interested in education than research. This is a
>>>> career-limiting attitude at MIT but I thought it would be just
>>>> right for my questions. Oh well.
>>>>
>>>> --
>>>> Michael Spencer Nova Scotia, Canada .~.
>>>> /V\
>>>> mspencer at tallships.ca /( )\
>>>> http://home.tallships.ca/mspencer/ ^^-^^
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>>>>
>>>
>>>
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>>
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