Von Helmholtz, working on a similar hypothesis, but with a frictional term introduced into his equations, obtained formulae which are applicable to cases of absorption.
When work is done against these forces no full equivalent of potential energy may be produced; this applies especially to frictional forces, for if the motion of the system be reversed the forces will be also reversed and will still oppose the motion.
The general theory of this kind of brake is as follows: - Let F be the whole frictional resistance, r the common radius of the rubbing surfaces, W the force which holds the brake from turning and whose line of action is at a perpendicular distance R from the axis of the shaft, N the revolutions of the shaft per minute, co its angular velocity in radians per second; then, assuming that the adjustments are made so that the engine runs steadily at a uniform speed, and that the brake is held still, clear of the stops and without oscillation, by W, the torque T exerted by the engine is equal to the frictional torque Fr acting at the brake surfaces, and this is measured by the statical moment of the weight W about the axis of revolution; that is T =Fr=WR...
This inquiry yielded (in 1867) the result 783, and this Joule himself was inclined to regard as more accurate than his old determination by the frictional method; the latter, however, was repeated with every precaution, and again indicated 772.55 foot-pounds as the quantity of work that must be expended at sea-level in the latitude of Greenwich in order to raise the temperature of one pound of water, weighed in vacuo, from 60 to 61° F.
Several important points were gained in the latter: the quadrantal deviation could be finally corrected for all latitudes; frictional error at the cap and pivot was reduced to a minimum, the average weight of the card being 200 grains; the long free vibrational period of the card was found to be favourable to its steadiness when the vessel was rolling.
Electrostatic machines are of two kinds: (I) Frictional, and (2) Influence machines.
A primitive form of frictional electrical machine was constructed about 1663 by Otto von Guericke (1602-1686).
- Frictional machines are, however, now quite superseded by the second class of instrument mentioned above, namely, influence machines.
There are some very evident disadvantages of excessive height; for instance, that the weight of an excessively high column of solid coke, ore and limestone tends to crush the coke and jam the charge in the lower and narrowing part of the furnace, and that the frictional resistance of a long column calls for a greater consumption of power for driving the blast up through it.
The reason why the frictional resistance would be further increased is the very simple one that the increase in the rate of production implies directly a corresponding increase in the quantity of blast forced through, and hence in the velocity of the rising gases, because the chemical work of the blast furnace needs a certain quantity of blast for each ton of iron made.
In short, to increase the rate of production by lengthening the furnace increases the frictional resistance of the rising gases, both by increasing their quantity and hence their velocity and by lengthening their path.
High, may be that this frictional resistance becomes so great as actually to interrupt the even descent of the charge, parts of which are at times suspended like a ball in the rising jet of a fountain, to fall perhaps with destructive violence when some shifting condition momentarily lessens the friction.
As regards frictional resistance, this smaller number of reversals of direction compensates in a measure for the smaller area of the Cowper flues.
This action and reaction between layers in relative motion is equivalent to a frictional stress tending to equalize the velocities of adjacent layers.
The Frictional Generation Of Heat In A Metallic Wire Conveying A Current Can Be Measured In Various Ways, Which Correspond To Slightly Different Methods.
This law applies to every body that is set in motion upon the surface of the rotating earth, but usually the duration of the motion of any body due to a single impulse is so brief, and there are so many frictional disturbances, that it is not easy to observe the results of this deflecting force.
The equation (5) when modified by the introduction of a frictional term becomes ~uxk*.
Neglecting frictional resistance we have, if R be the tension of the string, I~=Rb, mfi=mgR,
The slightest frictional forcessuch as the resistance of the aireven if they act in lines through the centre of the rolling sphere, and so do not directly affect its angular momentum, will cause the centre gradually to descend in an ever-widening spiral path.
The terms due to F in (33) are such as would arise from frictional resistances proportional to the absolute velocities of the particles, or to mutual forces of resistance proportional to the relative velocities; they are therefore classed as frictional or dissipative forces.
The validity of the recilirocal theorems of Helmholtz and Lord Rayleigh, already referred to, is not affected by frictional forces of the kind here considered.
The two great branches of electrical theory which concern the phenomena of electricity at rest, or " frictional " or " static " electricity, and of electricity in motion, or electric currents, are treated in two separate articles, Electrostatics and Electrokinetics.
The 3rd series (1833) he devoted to discussion of the identity of electricity derived from various sources, frictional, voltaic, animal and thermal, and he proved by rigorous experiments the identity and similarity in properties of the electricity generated by these various methods.
He also discovered similar successive orders of induction in the case of the passage of frictional electricity (Trans.
The maximum pressure is not uniform from the ground level to the roof but is greatest at the centre; it is diminished near the ground level by the frictional resistance of the ground, and at the eaves by the eddies formed by the air escaping over the roof.
This illustration gives some idea of the enormous increase of yield of such a well, if, by any means, we can get rid of the frictional sand, even from Artificial within the 16 in.
This result is mainly due to the reduction of frictional resistance to the passage of water through the sand in the immediate neighbourhood of the well, by washing out the finer particles of sand and leaving only the coarser particles.
Such a saltwater saucer of fresh water is maintained full to overflowing by the rainfall, and owing to the frictional resistance of the sand and to capillary action and the fact that a given column of fresh water is balanced by a shorter column of sea water, the fresh water never sinks to the mean sea-level unless artificially abstracted.
The pulley is secured to the shaft by conical keys, to give a frictional grip on both the shaft and the pulley; these keys may have their exterior surfaces eccentric to the shaft, with corresponding recesses in the nave, so that the pulley and keys virtually form one piece.
The frictional grip between the two surfaces prevents return motion of the worm shaft and the load remains suspended, but it may be lowered by turning the hand-wheel so as to overcome the friction brake.
The term "perfect gas" is applied to an imaginary substance in which there is no frictional retardation of molecular motion; or, in other words, the time during which any molecule is influenced by other molecules is infinitesimally small compared with the time during which it traverses its mean free path.
Unlike the frictional generation of heat due to the resistance of the conductor, which Joule (1841) Table I.-Thermoelectric Power, p=dE/dt, IN Microvolts At 50° C. Of Pure Metals With Respect To Lead.
The chemical action between metals in the solid state must be infinitesimal, and could only suffice to produce small charges analogous to those of frictional electricity; it could not maintain a permanent difference of potential at a metallic junction through which a current was passing.
There it becomes an effort tending either to move A upon B, or to move the body B itself, according to the frictional conditions.
Suppose B not to be fixed, but to be capable of moving against some third body C (which might, e.g., contain cylindrical bearings, if B were a drum with its shaft), itself fixed, - and further, suppose the frictional resistance between B and C to be the only resistance to B's motion.
Thus friction causes motion, for had there been no frictional resistance between the surfaces of A and of B, the latter body would have remained stationary, and A only would have moved.
Per second) there is a sensible increase of frictional resistance in many cases, most notably in those in which there is the most marked difference between the friction of rest and that of motion.
Whilst it is being paid out the portion between the surface of the water and the bottom of the sea lies along a straight line, the component of the weight at right angles to its length being supported by the frictional resistance to sinking in the water.
The factors Af (u-v cos i) and Bf (v sin i) give the frictional resistance to sinking, per unit length of the cable, in the direction of the length and transverse to the length respectively.
The relation between the b.h.p. and the torque on the driving-axle is 55 o B.H.P. =Tu., (9) It is usual with steam locomotives to regard the resistance R as including the frictional resistances between the cylinders and the driving-axle, so that the rate at which energy is expended in moving the train is expressed either by the product RV, or by the value of the indicated horse-power, the relation between them being 55 0 I.H.P. =RV (Io) or in terms of the torque 55 0 I.H.P.X€=RVe=TW (II) The individual factors of the product RV may have any value consistent with equation (to) and with certain practical conditions, so that for a given value of the I.H.P. R must decrease if V increases.
Assuming that the frictional resistance at the rails is given by the weight on the wheels, the total weight on the driving-wheels necessary to secure sufficient adhesion to prevent slipping must be at least 8.3 X5 =41.5 tons.
Alessandro Volta of Pavia discovered the electric battery in the year 1800, and thus placed the means of maintaining a steady electric current in the hands of investigators, who, before that date, had been restricted to the study of the isolated electric charges given by frictional electric machines.
The influence of temperature on the conductivity of solutions depends on (I) the ionization, and (2) the frictional resistance of the liquid to the passage of the ions, the reciprocal of which is called the ionic fluidity.
Soc., 1890, 48, 342) has demonstrated that it is quite unnecessary to assume either the directive force of Weber, the permanent set of Maxwell, or any kind of frictional resistance, the forces by which the molecular magnets are constrained being simply those due to their own mutual attractions and repulsions.
Opposed to the motive force producing the air current is the frictional resistance developed in passing through the mine workings.
If the tube is a perfect non-conductor, and if there are no eddies or frictional dissipation, the state of the substance at any point of the tube as to E, p, and v, is represented by the adiabatic or isentropic path, dE= -pdv.
In practice, however, there is always some frictional dissipation, accompanied by an increase of entropy and by a fall of pressure.
Motion is communicated to the rope by frictional contact with the drum,.
When these are held from turning, their frictional resistance may be adjusted by means of nuts on the screwed bolts which hold them together until the shaft revolves at a given speed.