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Posted by Tozetre on July 10, 2008, 11:33 am
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> of the blow; it's a squared function, I think. =A0(Energy =3D weight X sp=
eed
> squared, or something like that). =A0----I always get confused about the
> difference between weight and mass---
On the surface of the Earth, weight and mass are pretty much
interchangeable in conversation.
Weight =3D mass * acceleration (of gravity)
1kg of mass is 1kg of mass on the moon, but on the moon it only has
1/6kg of weight, since there's less acceleration. Being "weightless"
is what happens when one's "perceived weight" is zero- that is, when
there's nothing pressing up against us. At the top of a rollercoaster
curve, we have no upward acceleration- in fact since we started the
uphill climb our acceleration has been downward, but our velocity has
been upward. At the top, our imparted upward velocity runs out, so we
hover for a moment before gravity takes us back down again. In
freefall, while we've got full downward acceleration (at 9.8m/s^2) and
probably velocity (0 to start falling, increasing as we fall), we
don't feel the effects much because we don't feel anything pressing
against us to give us physical cues about our attraction to Earth-
until the end, anyway. So even an object in freefall on Earth (or at
rest on the ground afterwards) has an unchanging weight because the
force of gravity is always acting on it. In space, nothing's
attracting the object, so its mass is the same but its weight is 0
because it has no acceleration.
So, the weight of a hammer remains constant at the surface of the
Earth because its mass doesn't change and gravity's always pulling on
it. Its perceived weight (by itself, not us) is zero at the top of the
stroke, and all the way down if we just let it fall- but its objective
weight remains the same (1 lb, 2 lb, 5 lb) because gravity's still
working on its mass (W =3D mass (1 lb) * 9.8 m/s^2). The energy with
which it strikes the iron depends on how fast it's going when it hits;
if it falls for one second, its velocity will be 9.8m/s and its energy
will be 9.8 joules per kilogram; presumably your hammer falls for less
time than that. A 2lb hammer is roughly 1 kg; the acceleration is
constant, so 1/2 a second fall in Earth's gravity imparts 4.9 Joules
to the hammer. When the hammer hits the iron, that energy is
transferred to the iron- and then to the anvil, and some of it is
reflected back up to the hammer. Hot iron will absorb more of the
force and reflect less, which is why it deforms and the hammer doesn't
bounce back into your face unless you bang it against your anvil. Now,
this only calculates gravity's effect; your arm pushing down on the
hammer as it falls imparts more energy yet, because it's increasing
the net acceleration downward, like a roller coaster in reverse. When
you pull the hammer up, downward acceleration is 9.8 m/s^2, and upward
acceleration (your lifting) is higher than that, giving you a net
acceleration (at least at the start) upward, and a net velocity upward
until the hammer or coaster reaches the top (as it slows, it has net
acceleration downward). At the top, your arm starts giving the hammer
more acceleration downward, which adds to gravity. This means that the
hammer is going faster than 4.9m/s when it hits the anvil, which means
it's imparting more than 4.9 Joules to the hot iron.
Speed his how fast something is going (20 m/h).
Velocity is how fast something is going and in which direction (20 m/h
heading east).
Acceleration is how fast something is speeding up or slowing down (0
to 60 in 3 seconds).
Mass is how much of something there is (2 pounds on Earth, the moon,
or in space).
Weight is how much force gravity is giving an object (2 pounds on
Earth, 4 ounces on the moon).
Force is how much it's going to hurt when it hits you. (2 pounds of
mass hitting your thumb at 4.9m/s hurts just as much in space as it
does on Earth. The difference is that on Earth you can drop it, but in
space you have to swing it.)
A trip hammer weighing 65 pounds and falling for 1/4 a second (9.8 m/
s^2 * 1/4 =3D 2.45 m/s) imparts (2.45 Joules/kg * 30kg =3D) ~73 Joules. To
hit with the same force using a 2 pound hammer a smith would need it
to be traveling at 73 m/s. A boxer can punch about 8 m/s, and I think
our hammers aren't as fast as that. If we assume we can get the speed
up to 4m/s, then we're imparting about 20 Joules per blow. For
comparison, 1 Joule is roughly what it takes to lift a small apple 3
feet in the air (and the same force you'd feel when that apple hit you
coming back down). If you took 20 small apples, compressed them into a
small area, and dropped them 3 feet onto your hand, that's about how
much it ought to hurt when you smack your hand with a hammer- seems
about right to me.
Keep in mind that while the calculations are out of science texts, the
numbers (1/4 a second, 4m/s) are rough guesses. Also, I'm not a
physicist, so take my assertions with a grain of salt.
/endsciencelesson
/relurk
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Posted by Carl West on July 10, 2008, 1:21 pm
Please log in for more thread options When Tozetre put fingers to keys it was 7/10/08 11:33 AM...
>> ... it's a squared function, I think. (Energy = weight X speed
>> squared, or something like that)...
OK, so this _is_ the formula? The speed at impact is the important part,
the acceleration is only important 'cause that's how we get the speed.
Got it.
So I can explain to a student that if they can _swing_ the hammer
instead of _pushing_ it, and get it going twice as fast, they'll hit
with four times the force?
I can say "Force equals Speed squared times Mass"?
Hrmmm... I know the formula F=MA, but now it seems flawed because it
doesn't include time, and A requires time. I'm missing an assumption,
Yes? It's been a long time since I studied this stuff.
> A boxer can punch about 8 m/s, and I think
> our hammers aren't as fast as that. If we assume we can get the speed
> up to 4m/s, then we're imparting about 20 Joules per blow.
Speaking of swinging...
The boxer's punch is a fairly linear thing, thrown that way because it's
harder to block. If you get to swing your arm through an arc you can get
a lot more speed on your hand. Add a handle with a weight on the end and
swing _that_ and I bet it gets going pretty darn fast. 4m/s is only
about 9mph. I _know_ my hammer head is going faster than that.
--
Carl West
http://prospecthillforge.com : The Blacksmithing Classroom
Reduce. Reuse. Recover. Refurbish. Repair. Repurpose. Recycle.
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Posted by Todd Rich on July 10, 2008, 1:58 pm
Please log in for more thread options (snip)
> I can say "Force equals Speed squared times Mass"?
> Hrmmm... I know the formula F=MA, but now it seems flawed because it
> doesn't include time, and A requires time. I'm missing an assumption,
> Yes? It's been a long time since I studied this stuff.
Yes. If A has a time component, F has it as well.
Start out with distance. 8 meters
Add a time component. Speed = Distance over time
Or 8 meters per second.
Add in another time component, and you have Acceleration.
Add in the mass to get the force with F=MA.
Add in distance again, and you get work.
Add in time again to work and you get Power.
Here is a refresher if you are interested
http://en.wikipedia.org/wiki/Elementary_physics_formulae
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Posted by John O. Kopf on July 10, 2008, 7:13 pm
Please log in for more thread options Carl West wrote:
> When Tozetre put fingers to keys it was 7/10/08 11:33 AM...
>
>>> ... it's a squared function, I think. (Energy = weight X speed
>>> squared, or something like that)...
>
> OK, so this _is_ the formula? The speed at impact is the important part,
> the acceleration is only important 'cause that's how we get the speed.
> Got it.
>
> So I can explain to a student that if they can _swing_ the hammer
> instead of _pushing_ it, and get it going twice as fast, they'll hit
> with four times the force?
>
> I can say "Force equals Speed squared times Mass"?
>
> Hrmmm... I know the formula F=MA, but now it seems flawed because it
> doesn't include time, and A requires time. I'm missing an assumption,
> Yes? It's been a long time since I studied this stuff.
>
>
>> A boxer can punch about 8 m/s, and I think
>> our hammers aren't as fast as that. If we assume we can get the speed
>> up to 4m/s, then we're imparting about 20 Joules per blow.
>
> Speaking of swinging...
> The boxer's punch is a fairly linear thing, thrown that way because it's
> harder to block. If you get to swing your arm through an arc you can get
> a lot more speed on your hand. Add a handle with a weight on the end and
> swing _that_ and I bet it gets going pretty darn fast. 4m/s is only
> about 9mph. I _know_ my hammer head is going faster than that.
Assuming a solid anvil/target, the force applied by the hammer is the
mass of the hammer times the (de-)acceleration of the hammer (change of
velocity) Assume a 4-lb hammer *DROPPED* onto the anvil - it will have
2x the force of a 2 lb hammer dropped the same distance. *SWING* the
same hammer, and you'll have a lot more velocity to slow down; the
slowing from full-speed to stop will take about the same time, and
impose a lot more deceleration (= force) A 50-lb "Little-giant" will
probably move about as fast as a good swing, but must decelerate 50 lbs,
and so applies a lot of force. Also, if the hammer bounces, it must be
decelerated and then re-accelerated in the opposite direction - more force.
John Kopf
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Posted by Tozetre on July 11, 2008, 8:38 am
Please log in for more thread options (my apologies for re-answering some questions)
> >> ... it's a squared function, I think. =A0(Energy =3D weight X speed
> >> squared, or something like that)...
>
> OK, so this _is_ the formula? The speed at impact is the important part,
> the acceleration is only important 'cause that's how we get the speed.
> Got it.
Short answer; nope, the formula for calculating the force that's going
into hot iron is; energy =3D (how heavy the hammer is) times (how fast
it's going).
Long answer; Newton's second law is F=3Dma, but this means; the rate of
change of momentum of a body is proportional to the resultant force
acting on the body and is in the same direction. In other words, once
you stop accelerating something (and it's moving at a constant
velocity), it has no more F, or *rate of change* of momentum.
Acceleration is not speed squared, either; m/s is speed, and
acceleration is m/(s^2), not (m/s)^2. I think what we want is
something more like his explanation of impulse, that the impulse
granted an object is force F exercised over time. Other posters have
stated this with more clarity than I did.
> a lot more speed on your hand. Add a handle with a weight on the end and
> swing _that_ and I bet it gets going pretty darn fast. 4m/s is only
> about 9mph. I _know_ my hammer head is going faster than that.
True! I forgot about pivots and levers, sorry. Well, like I said I was
picking those numbers out of thin air.
> Also, if the hammer bounces, it must be
> decelerated and then re-accelerated in the opposite direction - more for=
ce.
Nope. The amount of force available doesn't change, just where it goes
and what its direction is. It's like a wave in a pool; when the wave
hits the edge it gets reflected back. Some of its energy is imparted
to the wall, and the rest goes back into the water. Your wave is now
smaller and heading in the opposite direction, right? but just because
it switched doesn't mean it's going to capsize boats. Same thing with
a hammer; you swing, it hits, it bounces back. It may bounce back
higher than it started, because you gave it more energy than gravity
alone, but it doesn't have more energy coming off the anvil than it
did coming down. My apologies if you didn't mean that and I'm holding
forth on something you already know.
> Yeah, I wish this was the same for air pressure.
Living nearer the mountains, here, elevation 2000ft. Advantages:
easier to find coal mines. Disadvantages; less air to burn it with. I
feel your pain.
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