studiot

Sorry to hear that. Don't think I saw that video but it sound as though the author was trying to be 'clever' and complicated. I recommend sticking to the ball and string. To get the ball going as you say you start off by dragging it in a line with the string. You then give it a second yank sideways to the motion to divert it from that line into a curved path. You repeat this as many times as necessary to get it swinging round. The first initial pull is linear and the tension in the string has no special name. The sideways pull is still tension but is now called centripetal force. But this is where the problems start. No inertia was not 'given to the ball', it is an inherent property of the ball (or any other piece of matter). It cannot be given to anything, and equally it cannot be taken away. Inertia is measured by mass. It is not momentum, but as swansont said backalong, it is one part of momentum, the other being velocity. You haven't made any comment or asked any questions about momentum in my post 37 ? This was meant to be encouraging BTW.

The force in the string at the other end is called the anchoring, tying or fixing force. Are you quite clear which end is which and which direction the forces act in a string?

tar, I just read and commented in the centrifugal thread and I thought you had cracked it. You seem to have forgotten that 1) It is possible for a body to loose all its momentum, whilst its KE remains unchanged. 2) It is possible for a body to gain double its momentum, whilst its KE is unchanged. Does that sound like they are directly related? Yes they are related, they both belong to or are attributable to the same body. But that is not quite the answer you are seeking.

Francis Sears (with and without Zemansky) books always offered a clarity of understanding missing IMHO from their great rivals and successors at this level, (Resnick and Halliday). +1

It is a pity some fool chose to formalise the definition of the word action in physics, he was a jerk. I can't now say that there are several mechanisms that action (in the general english sense) can be transferred from one place to another and impulse would certainly be one of them. But impulse is tricky and not the main subject of this thread. That is why I have discontinued our cordial discussion on that subject here. However I would be happy to continue in a brand spanking new thread, designed expressly for that purpose, if you so wish. We could discuss examples of fire hoses, jack-in-the-boxes and sledge hammers and the impulse-momentum theorem there. Perhaps tar might also read it and derive something of value.

Perhaps you mean multistage pumps? Here is an extract from the Grundfoss centrifugal water pump design manual. This speaks for itself

Since when was scrolling a valid integration technique? There it is, writ large at the head of their page, like a banner for all to see. An indefinite integral that needs an arbitrary constant to complete the integration. But that is irrelevant to the point I made that the impulsive force has a beginning and an end. That is what makes it different from say, gravity.

I have these two images in my head. The first is of a graceful skater spreading her arms wide ashe she travels the ice into a turn. Then bringing her arms in close to her body thus speeding up her rotation rate. Moment of momentum is conserved. The second is of a hairy Orc from Lord of the Rings sharpening a huge knife on an enormous grindstone, sparks flying everywhere. He is sweating profusely from having to work really hard as he presses the knife firmly against the edgge of the stone, maintaining the moment of momentum lost to friction.

I'm sorry? here is a screenshot from the link you gave. How is the Wiki integral the same as mine?

Unless parts of a body or system of particles possess linear momentum there can be no "moment of momentum", and even then there may be none because it means that the angular momentum is the sum of the products of all the linear momenta with their lever arm about some axis.

Don't forget that angular momentum is not the same as linear momentum. The dimensions are different. Linear momentum MLT-1 Angular momentum ML2T-1 The extra L is why the old and alternative name for angular momentum is moment of momentum, which some consider more descriptive and less confusing.

Is this a sort of is there a sound of a tree falling in the wilderness if there is no-one there to hear it question? If so, is this Science? What do you understand "information" to mean.

Perhaps I was just being kind to Wikipedia? Defining impulse as the indefinite integral of Fdt is meaningless. Impulse is properly defined as the definite integral [math]I = \int_{t2}^{t1}F.dt[/math] The point is that it has a begining and and end. The disturbance travelling through the elastic media does not necessarily have either.

Well I said I was no expert.

I am sorry to complicate matters for you tar, but Strange's discourse on Impulse is incomplete. Impulse is intended for impact forces, not for disturbances travelling in elastic media, and subject to different laws of propagation. A simple example ( I seem to be trying to find a lot of these) Think of a block of sponge and and block of wood of similar density placed against a wall. Now apply an impulse ( with a hammer or billiard ball ?) to the sponge and to the wood and consider how the 'push' is transmitted to the wall. It is the reaction force from the wall on the two blocks that prevents bodily movement of the block under the impacts. There are two stages. The first stage the impactor strikes and the block deforms locally and elastically under the strike. The sponge is deformation much slower and softer so the impulse is less. The rate of deformation depends on the characteristics of both the impactor and the block material, but is much slowerr than the speed of sound in the blocks. This is the mechancial impulse. The local is transmitted through the blocks as an elastic wave disturbance from molecule to molecule until the last molecule at the other end pushes against the end wall. This is not called an impulse and travels at the speed of sound in the material of the block.

Good question ajb and I am no expert in this field so anything I propose would be speculation. However I see a parallel with the mathematics of chemical reaction kinetics. If two substances, A and B, react then most reaction rates are proportional to the concentrations of the two reagents. This is because for two molecules to meet and react they must be in the same place at the same time. Statistical kinetic considerations yield equations proportional to the concentrations. ie the higher the concentration the greater the chances of molecule A meeting molecule B and reacting. If we extend that to more reacting molecules, say C, the chances of three molecules being in the right place at the right time is reduced compared for only two and so on..... The other consideration that occurs is that there is les scope for error in single cell fission than two cell fusion and even more scope for error if a third...fourth.. are required to play an input.

It's a nit, I know. But for the rope to trail it's velocity must change, therefore it is accelerated, therefore it must be subject to force (=pull).

Can't quite agree with this. The rope changes its velocity as it trails after the weight. It doesn't move bodily sideways keeping as straight as it did when it was aligned taught along the radius. And it is unfair to claim that circular motion requires an acceleration force because there is a change of velocity direction, but not say the same for the rope after release.

Mad or not you need Bernoulli to understand how the difference between the operation of a positive displacement and a centrifugal pump. In particular you need to be able to pick the correct answer in this question. https://www.youtube.com/watch?v=Dvs_AV4JYdw

Hello Robittybob, I notice you have skillfully avoided my fresh look (post425). And BTW if you let the rope slip you have released the tension, and therefore the centripetal force. You have also just agreed that if there is no centripetal force there is no centrifugal force. So whatever pulls the rope through your hands is not centrifugal force.

I'm not sure what you mean by mutually exclusive. Yes they are different and they account for different properties, but sometimes and only sometimes there is a direct connection. This is rather like mass and volume. For a solid an increas in volume means an increase in mass. But for a gas an increase in volume may simply mean a decrease in pressure. Both roughly indicate the something about the amount of matter and how it will behave in specific circumstances. I assume you mean what we call Newton's Cradle? Raise the left hand ball and let it drop back. The dynamics runs like this: You have two objects, one ball and a group of three balls. At the moment of impact the 3ball has zero momentum and KE and the 1ball has a certain KE and a certain momentum. At impact you now have a single object a group of four balls. This object has the total original momentum and KE. If you watch very carefully the group does in fact start to move, but the impulse travels through the balls at the speed of sound. That is hundreds of times faster than the original ball was travelling, and of course the 4ball will travel at 1/4 the 1ball speed given the same momentum. So the difference is enhanced by the regrouping of the balls. The centre two balls have something to restrain them but there is nothing beyond the right outer ball so it carries off the momentum and KE, leaving a group of three behind. Momentum is thus preserved. You should analyse this with momentum first to get the new velocity and then work out the KE at the new speed. What happens to the 'lost energy' you ask? Well you hear some of it in the clack sound and some of it remains distributed in elastic deformation of the 4ball until again the fact that the outer ball is unrestrained and allows it to accept the KE from the elastic recovery and end up with all the cake. That's the simplified version. Remember an impulse is a (large) force applied for a short time. Only momentum can be converted to force not energy, and it take force to accelerate the stationary balls. That is why we take the momentum balance as the primary and work the KE out to suit. During the exchange the energy doesn't disappear it suffuses all the balls (without direction) as elastic stored energy and is returned to supply the motion KE. You can be very complicated and calculate all the exchange forces as each ball deforms elastically in turn and you will get the same answer.

Let us take a fresh look at why not. Let us consider a body moving in a circle (or part of one), of radius R. Now we postulate a force, C, pushing this body radially outwards. There are two possibilities for the source of this force. 1) Something external to the body. 2) Something within the body itself. No names no pack drill at this point, just go with the flow. The weight on a string clearly has no external agents acting on it so that should eliminate (1). So consider (2). Well if the body moves itself out to a large radius either A) It must increase or maintain its rotational speed. B) It must reduce its rotational speed. (B) leads us to the situation that the body is rotating but pushing forever outwards. As it does so it continually slows down its rotation until it stops alltogether. As soon as it stops the outward force ceases and the bodies Kinetic Energy has magically disappeared to nothing. So B violates the conservation ov energy. So what about (A) Well if the rotational speed remains constant or increases then the tangential velocity increases and the Kinetic Energy increases without limit, all internally from an object. So (A) also violates conservation of energy, in the other direction. Which leads to the conclusion such a force cannot exist.

The Bernoulli family were certainly your friends as far as centrifugal pumps and pipelines are concerned, although they never explained the workings of such pumps, which were first introduced in the 15th century. http://en.wikipedia.org/wiki/Bernoulli_family

There is much confusion about the workings of centrifugal pumps and this thread shows that even normally accurate experts are confused by this machine. About the only completely correct posts were the original question about inlet and outlet sizes and John Cuthber's observation that volume out must equal volume in for an incompressible fluid like water. It was also correctly observed that some pumps have equal inlet and outlet pipes sizes, particularly positive displacement types that operate in an entirely different manner and have no need of the change of size. The plain fact is that the size change is an essential part of the workings of a centrifugal pump and must occur. The actual outlet size will depend upon where the expansion occurs, it is often largely included in the casing. Needless to say the operation of a centrifugal pump has nothing to do with 'centrifugal force' and in fact the centripetal force the fluid is subject to impedes the pump action and must be overcome by the mechanics of the pump.

No, v is the velocity at time any time t. It is the general solution giving the velocity as a function of time or (nearly) the answer to the first part of your question. It remains to substitute the boundary conditions to obtain values for the constants. I gave the formula for the hyperbolic tangent before. The inverse tangent is [math]tanh^{-1}x = \frac{1}{2}ln\left ( \frac{1+x}{1-x} \right )[/math]