Question for you physicists

[danzibr]

Suppose you are chopping wood. What is more important: the force or momentum? It seems to be momentum, but I'm not good at physics. I mean... if there's a sudden jerk that seems not as potent as something moving with great velocity but 0 acceleration.

[Gwyn chan 'r Gwyll]

mv versus ma?

I'd guess Force.

[Reluctance]

In a physics sense, force. That's more due to how physics-speak is different from layperson-speak.

More practically, though, there's a reason the classic executioner swings overhand rather than putting the blade against the person's neck and pushing down hard. While you could get a lot of speed over a small distance in a small amount of time (think a bullet), that would take exceptional force. It's easier to apply a more moderate force over more time, which takes more distance. The fact that you have more assistance from gravity when you start the weight higher doesn't hurt either.

[Spiryt]

Suppose you are chopping wood. What is more important: the force or momentum? It seems to be momentum, but I'm not good at physics. I mean... if there's a sudden jerk that seems not as potent as something moving with great velocity but 0 acceleration.

I don't think that you really got that one well, to be honest....

Acceleration has not much to do with impact here.

I won't really be getting into describing movement of body and axe here, because it's pretty complicated, and I'm terrible at physics, so I don't really get.

However, your question, is pretty weird one - why some 'comparison' between force and momentum?

Forces that different parts of body will work with, will have direct effect on momentum of axe, and moving parts of the body.

As far as force of impact goes, it depends on wood, among other thing, in the first place.

If you drop 2 kg of axe on some hard wood, it will decelerate quickly.

Thus, according to the equation - F = m * a - force unleashed upon piece of wood, axe etc. will be greater, because change of velocity will be violent.

Compared to chopping the hypothetical huge lump of butter, which won't stop the axe too much - thus force of impact won't be great, due to lower deceleration value.

Somebody with better engrish physics can probably put it together better.

[danzibr]

force unleashed upon piece of wood, axe etc. will be greater, because change of velocity will be violent.
Of course, I was thinking of it from the axe's point of view. Thanks.

[ShadowHunter]

The question doesn't really make sense, force and momentum are linked.

In general, far more general than F=ma, F(t) = dp/dt, where p=momentum=mv - basically if you've changed the momentum of something, you've applied a force. (if mass is constant then you get F(t) = m*dv/dt, which will equal a(t), a isn't necessarily constant, but until you learn calculus you can't deal with it)

Alternatively and equivalently, you can think of it as applying a force over a distance to do work on the axe and give it kinetic energy. Basically I can apply more force over a shorter distance or less force over a longer distance to reach the same kinetic energy(at a long enough distance gravity will be a sufficient force and I can just drop it, like a guillotine). OR I can apply less force to a heavier axe (since KE=1/2mv^2), or more force to a lighter axe, and so on.

When possible, considering things from an energy perspective tends to help understand things fundamentally. "Force" in Newtonian physics can be difficult to picture, and we use the term informally to mean different things too much, which makes it even harder.

[thubby]

if this is from your teacher, it sounds more like a "i dont care what you say, just argue it well" thing than anything else.

[ShadowHunter]

The topic was about chopping wood, yet clearly I somehow read it as about executing people. Same idea!

Quote:
Originally Posted by Spiryt View Post
force unleashed upon piece of wood, axe etc. will be greater, because change of velocity will be violent.
Of course, I was thinking of it from the axe's point of view. Thanks.


Problem with that train of thought, if I swing the axe HARDER and cut clean through the wood, the axe will decelerate less, yet clearly there was not less force involved. If I don't have enough energy to cut the wood, the axe will hit and decelerate to 0 very quickly. That's because the wood applied a force on the axe (a la Newton's third law). If the wood cannot apply enough force to stop the axe, it yields. Sure, there is less deceleration of the axe, but it's because MORE force was applied to the axe (or the axe was heavier or it was swung over a longer period...).

Beyond that you'll have a hard time treating this with basic Newtonian physics. You've chopped or seen wood chopped and you'll try to intuitively apply ideas (fracture mechanics and yield strength!) that aren't really being addressed here.

[Spiryt]

The topic was about chopping wood, yet clearly I somehow read it as about executing people. Same idea!

Quote:
Originally Posted by Spiryt View Post
force unleashed upon piece of wood, axe etc. will be greater, because change of velocity will be violent.
Of course, I was thinking of it from the axe's point of view. Thanks.


Problem with that train of thought, if I swing the axe HARDER and cut clean through the wood, the axe will decelerate less, yet clearly there was not less force involved. If I don't have enough energy to cut the wood, the axe will hit and decelerate to 0 very quickly. That's because the wood applied a force on the axe (a la Newton's third law). If the wood cannot apply enough force to stop the axe, it yields. Sure, there is less deceleration of the axe, but it's because MORE force was applied to the axe (or the axe was heavier or it was swung over a longer period...).

Beyond that you'll have a hard time treating this with basic Newtonian physics. You've chopped or seen wood chopped and you'll try to intuitively apply ideas (fracture mechanics and yield strength!) that aren't really being addressed here.

Well, looking like that, you can also hit wood less hard but at good angle, velocity and at rigth place, and split it with lesser forces involved all around.

So because all that wood chopping would get complicated, I used lump of butter and wood as kind of "extreme" examples....

Well more extreme would be block of marble or steel, then hitting it with axe would result in tremendous, probably wrist shattering force of impact. :smallwink:

[Heliomance]

Pretty sure what actually matters here is neither the force, nor the momentum, but the kinetic energy and thus the energy transfer on impact.

[Mephit]

OP's question need clarifying because it's anyone's guess what his exact question is.


More practically, though, there's a reason the classic executioner swings overhand rather than putting the blade against the person's neck and pushing down hard.

This is probably the most straight to the point answer if I read your question right. The momentum the axe has at the time of impact will be lot more important than the force you're applying to the axe at that moment. That's because the wood needs to apply (and therefore undergo) a lot more force to reduce the axe's momentum than to counteract the acceleration you're giving the axe.

[danzibr]

The question doesn't really make sense, force and momentum are linked.

In general, far more general than F=ma, F(t) = dp/dt, where p=momentum=mv - basically if you've changed the momentum of something, you've applied a force. (if mass is constant then you get F(t) = m*dv/dt, which will equal a(t), a isn't necessarily constant, but until you learn calculus you can't deal with it)[...]
I don't see how force and momentum being linked has anything to do with the question not making sense. By almost exactly the same reasoning, you could say something like, "The question 'Is velocity or acceleration more important if you wish to travel' doesn't make sense because velocity and acceleration are linked." Of course velocity is the more important of the two. You could try to argue if you know velocity then you know acceleration, and if you know acceleration then you know velocity (up to addition of a constant), but to me that's as silly as bringing in distance and jerk as functions of time. Also, I teach Calculus at a university.

And no, this is not for homework or something silly. Well, perhaps something silly, but not related to my schooling.

Let me ask a different question: which would lead to more destruction of wood?

a) axe moving at 1 m/s and accelerating at 10m/s^2;
b) axe moving at 10 m/s and accelerating at 1 m/s^2.

[Telonius]

I think acceleration matters a bit more than velocity here, because it takes time for the axe to cut through the wood. (Not much time, but time). If acceleration is positive, we can assume that some force is acting on the axe to accelerate it. During the time it takes for the axe to cut, that force would still be acting on the object. Same way if the acceleration were negative.

Put it another way; suppose you have the axe an inch from the wood, and strap a rocket booster to it. It's going 50 miles an hour when it hits, but has a giant amount of acceleration. It might chop right through. But say it had been going a hundred miles an hour, an inch before it hit, but then had a rocket pointed in the other direction. If the wood weren't there, the axe would have stopped in another inch anyway. The momentum at the point of impact in both cases is the same; mass of the axe times 50 miles an hour. But the force (mass times acceleration) is very different.

[Spiryt]

I don't see how force and momentum being linked has anything to do with the question not making sense. By almost exactly the same reasoning, you could say something like, "The question 'Is velocity or acceleration more important if you wish to travel' doesn't make sense because velocity and acceleration are linked." Of course velocity is the more important of the two. You could try to argue if you know velocity then you know acceleration, and if you know acceleration then you know velocity (up to addition of a constant), but to me that's as silly as bringing in distance and jerk as functions of time. Also, I teach Calculus at a university.

And no, this is not for homework or something silly. Well, perhaps something silly, but not related to my schooling.

Let me ask a different question: which would lead to more destruction of wood?

a) axe moving at 1 m/s and accelerating at 10m/s^2;
b) axe moving at 10 m/s and accelerating at 1 m/s^2.


I don't think that acceleration really matter much at all here.

If axe is moving at 1 m/s it has really fraction of Kinetic energy and momentum of faster axe.

That high acceleration means that somebody pretty much didn't speed axe up fully so far.

So ignoring other stuff, about body mechanics etc. :

No one chops would if he's still at 'speeding up' phase.

He chop it at about thigh level, when axe, arms, etc. are already moving quick.

[ShadowHunter]

I don't think that acceleration really matter much at all here.

If axe is moving at 1 m/s it has really fraction of Kinetic energy and momentum of faster axe.

That high acceleration means that somebody pretty much didn't speed axe up fully so far.

So ignoring other stuff, about body mechanics etc. :

No one chops would if he's still at 'speeding up' phase.

He chop it at about thigh level, when axe, arms, etc. are already moving quick.

Think of a block of jello, just because it is easier for me to picture. The axe with the greater acceleration is having the greater force applied to it (assuming same mass). That force, applied over the distance of the swing (it is really rotational motion but that is ok!) imparts kinetic energy to the axe. Presumably you don't just let go at impact, you keep applying that force. However the jello will be supplying a resistive force. If that force is greater than the driving force behind the axe, it will decelerate, possibly even stopping. Basically that force is being applied while the axe is in the jello and stunting the growth of its kinetic energy (or dragging it towards 0 if it is great enough)

Therefore, it is possible that the axe that hits slower but is driven with more force will penetrate deeper than the axe that hits faster with less force. It will have more kinetic energy but it will be depleted faster.

The question of which goes deeper depends on the material.

I think my original statement was wrong. Of course in fairness, if you ask me which is important for a trip, acceleration or velocity, I could argue that given the appropriate initial conditions both do contain all the information! In fact, ask for a plot of position vs time and give me whatever you want, jerk, change in jerk, I think as long as you have the initial conditions (and you will need more and more) you can get it. :-)

[Heliomance]

I don't see how force and momentum being linked has anything to do with the question not making sense. By almost exactly the same reasoning, you could say something like, "The question 'Is velocity or acceleration more important if you wish to travel' doesn't make sense because velocity and acceleration are linked." Of course velocity is the more important of the two.

That depends on the scales involved, actually. In interplanetary or interstellar travel, for example, acceleration becomes a lot more important because the velocities involved are so huge, it takes seriously non-trivial time to reach them. It doesn't matter what your maximum velocity is if you don't have the acceleration to reach it before you get to your destination.

[ShadowHunter]

I think we are all kinda answering different question. What you said makes sense.

if the question is "a ship travels across the galaxy, which quantity really represents what it did; acceleration or velocity?" I would say the same as before - both equivalently describe the motion. As it pertains to the axe, which quantity should I look at? If I look at the axe's momentum over time or the forces acting on the axe, you can describe what happened. But that really wasn't the nature of his question, and his rephrasing cleared it up

[Spiryt]

Think of a block of jello, just because it is easier for me to picture. The axe with the greater acceleration is having the greater force applied to it (assuming same mass). That force, applied over the distance of the swing (it is really rotational motion but that is ok!) imparts kinetic energy to the axe. Presumably you don't just let go at impact, you keep applying that force. However the jello will be supplying a resistive force. If that force is greater than the driving force behind the axe, it will decelerate, possibly even stopping. Basically that force is being applied while the axe is in the jello and stunting the growth of its kinetic energy (or dragging it towards 0 if it is great enough)

Therefore, it is possible that the axe that hits slower but is driven with more force will penetrate deeper than the axe that hits faster with less force. It will have more kinetic energy but it will be depleted faster.

The question of which goes deeper depends on the material.


Well, yeah, additional acceleration certainly does help, but it's pretty hard to imagine how much can it help with pretty sudden change of "medium" from air to piece of wood.... All in all I would say that if energy and momentum are low in the first place, applying great force, achieving great acceleration won't help much, cause movement will be violently halted anyway.

All this force applied by muscle will probably work to move around some other stuff, and muscles won't be able to apply it anymore - without further motion possible.

[Erloas]

I'm also going to go with the group that says the question doesn't really make sense. Mostly because there is no practical way to separate the two ideas in this scenario and still have it be practical example. The important part is what the speed is when the ax head hits the wood, if the ax takes 10 minutes or 1/2 a second to get to that speed makes no difference. From a practical standpoint, given the relatively small distance the ax has to gain speed, the acceleration has to be high to hit with any force.

A more practical question would be does increasing the speed of the ax or increasing the weight of the ax give you more cutting power. And from a body mechanic standpoint, its weight to a certain point and then it drops off. Even a very small weight can only get moving so fast by the body, and you can increase mass faster then you decrease speed, up until the point where you can't swing it at all. Part of that is because gravity helps a lot and it isn't negatively affected by mass.

There is also a question of if you are talking about cutting a log across the diameter or splitting the log. And in those cases the shape and angle of impact are much more important factors (when factoring in human limitations of speed and mass).

[Spiryt]

Most 'practical' question is the mechanics of the swing, or 'technique' to give axe most support, and obviously the bulk and strength of chopping fellow.

But original question seemed more abstract and theoretical to me. :smallwink:

[Mando Knight]

You're looking for impulse, by the way. First integral of force with respect to time.

[averagejoe]

More important for what? In causing wood to split, force is more important by definition (http://earthobservatory.nasa.gov/Glossary/index.php?mode=alpha&seg=f&segend=h). In fact, one might say it is of sole importance.

When a person chops wood in the way you probably mean, the force comes from the change of momentum imparted to the axe. There are, however, other ways one could impart an equal force - by balancing sufficient weight on the wedge, for example, though such a solution would be slow and unwieldy. So, I suppose you could say momentum is more important in that it's the only practical method for a human to apply sufficient force to split wood.

I'm fairly sure my understanding of this is correct, yet I'm still not sure I've answered your question.


I don't see how force and momentum being linked has anything to do with the question not making sense. By almost exactly the same reasoning, you could say something like, "The question 'Is velocity or acceleration more important if you wish to travel' doesn't make sense because velocity and acceleration are linked." Of course velocity is the more important of the two. You could try to argue if you know velocity then you know acceleration, and if you know acceleration then you know velocity (up to addition of a constant), but to me that's as silly as bringing in distance and jerk as functions of time.

Okay, but I'm still not sure I understand why velocity is more important for travel. You say, "Of course it is," and that's the only proof you offer, but it's not obvious to me. Even leaving aside that, "More important," is still rather vague, I really have no idea how one would determine definitively that velocity is more important for traveling.


Let me ask a different question: which would lead to more destruction of wood?

a) axe moving at 1 m/s and accelerating at 10m/s^2;
b) axe moving at 10 m/s and accelerating at 1 m/s^2.

I assume the speeds given are at the moment of impact, since they're accelerating. Also assuming that the forces causing these accelerations are constantly applied through the entire chop.

I suspect that a) would result in more destruction of wood. Initially b) would be higher, until the frictional and normal forces from the wood imparted to the axe became enough to stop the acceleration. The a) case would have the axe moving more slowly through the wood but more able to maintain penetration. Think of the difference between hitting a watermelon with a hunk of metal and putting that watermelon under a hydraulic press. Hitting it will cause it to instantaneously shatter, much more quickly than the press would shatter it, but the hitter will still have fairly large chunks of watermelon left, where as the press would reduce it utterly to paste. It is a similar concept.

[Spiryt]

Well, machine's for log splitting, that pretty much work by slow moving press that applying pressure constantly doesn't really destroy wood much.

In fact a hard axe blows often tend to send small pieces fly around leaving quite a mess.


http://www.youtube.com/watch?v=f9qlcg_95u0&feature=related

It's usually the log that's being pushed against the blade though.

[averagejoe]

Well, machine's for log splitting, that pretty much work by slow moving press that applying pressure constantly doesn't really destroy wood much.

In fact a hard axe blows often tend to send small pieces fly around leaving quite a mess.


http://www.youtube.com/watch?v=f9qlcg_95u0&feature=related

It's usually the log that's being pushed against the blade though.

Well, the question was imprecise, and the meaning could be interpreted multiple ways. I thought of, "Destroy more wood," as, "Cut further through." The fact that one process transmits its energy more effectively is not, I think, in the spirit of the question.

[The Extinguisher]

From what I understand, he's asking if all other things being equal, what change in parameter gives the larger result. In short, which is increases faster z(m) or z(F).

So in short, how is the fictional "ability to cut wood" parameter affected by force or momentum, assuming the other was equal. Is that right?

[Anarion]

Just a couple points. First, although force is the main quantity of importance, it's really pressure that decides whether you cut the wood or not. Imagine just taking a large circular hunk of metal and pounding it into the wood. It's never going to split the wood (might crush it flat or cause splintering along the grain though). The splitting has to do with the fact that the axe or sawblade is very thin and applying its force to one small area of the wood and the mechanical properties of wood allow it to split fairly easily (compare glass for rather different mechanical properties).

Then this becomes a deformation problem: there is a certain minimum amount of force that is required to actually cause the wood to deform. It's easier to think of this with something like a metal beam since it deforms evenly unlike wood, which splinters. If you have a metal beam, you can pound and pound and it does nothing, but once you pass the amount of force required to deform it, it keeps on deforming until the force stops (that's what happens in a car wreck).

Now, having said all that, figuring out force during an inelastic collision is kinda hard. If somebody asked me to solve this problem for how fast I need to swing an axe to cut the log (and let's be honest, that's the quantity you have physical control over), I would do it via conservation of energy.

You can look up the minimum force to split wood, and the amount of distance through the wood you need to go, which gets you the work required (this probably requires calculus because I'd bet a lot of money that the force going through wood is not a constant function). Work will be equal to the kinetic energy you apply, so then you just divide by M, multiply by 2 and take the square root and you have the velocity to swing the axe at.

[averagejoe]

Just a couple points. First, although force is the main quantity of importance, it's really pressure that decides whether you cut the wood or not. Imagine just taking a large circular hunk of metal and pounding it into the wood. It's never going to split the wood (might crush it flat or cause splintering along the grain though). The splitting has to do with the fact that the axe or sawblade is very thin and applying its force to one small area of the wood and the mechanical properties of wood allow it to split fairly easily (compare glass for rather different mechanical properties).

Well, yes, but presumably the axe head and swing motion are the same in each case, so force and pressure are essentially equivilant concepts for the purpose of this problem.

[Mando Knight]

Well, yes, but presumably the axe head and swing motion are the same in each case, so force and pressure are essentially equivilant concepts for the purpose of this problem.

Which leads back to impulse and energy. The initial force at the interface between the axe and the wood depends on the impact velocity. After that the cut is defined by the stress function (it's essentially a Mode I fracture, though the material isn't as easily modeled as metals).

Swinging an axe is a rather front-loaded procedure compared to a hydraulic splitter or similar device, so whether you integrate with respect to time (impulse) or distance (energy) doesn't really matter for this question... what matters is that your initial force depends on the velocity and mass at the interface, and the function of the force as it cuts through the wood will depend on the properties of the wood and how much force you can put into the axe after it hits. A mechanical splitter will keep applying a fairly constant pressure, but a human woodcutter's axe will quickly slow down after impact.

[averagejoe]

Which leads back to impulse and energy. The initial force at the interface between the axe and the wood depends on the impact velocity. After that the cut is defined by the stress function (it's essentially a Mode I fracture, though the material isn't as easily modeled as metals).

Swinging an axe is a rather front-loaded procedure compared to a hydraulic splitter or similar device, so whether you integrate with respect to time (impulse) or distance (energy) doesn't really matter for this question... what matters is that your initial force depends on the velocity and mass at the interface, and the function of the force as it cuts through the wood will depend on the properties of the wood and how much force you can put into the axe after it hits. A mechanical splitter will keep applying a fairly constant pressure, but a human woodcutter's axe will quickly slow down after impact.

Yeah. This is what I was trying to say, only in more general terms. A hydraulic press is a rather extreme example, but it illustrates the idea of great force caused by something other than high velocity very nicely.