Mechanical force

“ Induction of Force.—The inference of Mechanical Forces from phenomena has been so abundantly practised, that it is perfectly familiar among scientific inquirers. From the time of Newton, it has been the most common aim of mathematicians; and a persuasion has grown up among them, that mechanical forces,—attraction and repulsion,—are the only modes of action of the particles of bodies which we shall ultimately have to consider. ”

“ The mechanical force produced when a current flows in a conductor placed in a magnetic field forms the basis of the action of electric motors, and certain types of galvanometers and measuring instruments. The mechanical force is a mutual one, and tends to move the conductor and the field system in opposite directions. ”

“ In all these cases, if the bodies be disunited by mechanical force, they will separate at exactly the parts at which they had been united, so that after their separation no part of the one will adhere to the other; proving that the force of cohesion of the surfaces brought into contact is less than that which naturally held the particles of each together. ”

“ Whatever produces, or tends to produce, motion, or an alteration in its direction, is mechanical force, no matter from what force-centre it may start. When we can definitely determine the centre of vital force, as exercised in building up vital structure, not in wielding pickaxes, it is to be hoped we shall be able to distinguish, by the proper correlates, vital force from that which is mechanical. But the task is manifestly a hopeless one with the materialists. ”

“ In any machine, constructed in whatever manner to increase the force which I can exert, it is certain that what I gain in force I must lose in the velocity which I communicate. This is not a contingent truth, borrowed from and limited by observation; for a man of sound mechanical views applies it with like confidence, however novel be the construction of the machine. ”

“ For from hence are easily deduced the forces of Machines, which are compounded of Wheels, Pullies, Levers, Cords, and Weights, ascending directly or obliquely, and other Mechanical Powers; as also the force of the Tendons to move the Bones of Animals. ”

“ These are the principal examples of mechanical science; although some other portions of Physics, as Magnetism and Electrodynamics, introduce mechanical doctrines very largely into their speculations.
Now in all these sciences we have to consider Forces. In all mechanical reasonings forces enter, either as producing motion, or as prevented from doing so by other forces. Thus force, in its most general sense, is the cause of motion, or of tendency to motion ”

“ Of that class of mechanical agents by which motion is transmitted,—the lever, the pulley, the wedge, and many others,—it has been demonstrated, that no power is gained by their use, however combined. Whatever force is applied at one point can only be exerted at some other, diminished by friction and other incidental causes ”

“ It is this second type of resistance which we must consider, seeking to discover in what [152] proportion it is found in prisms and cylinders of the same material, whether alike or unlike in shape, length, and thickness. In this discussion I shall take for granted the well-known mechanical principle which has been shown to govern the behavior of a bar, which we call a lever, namely, that the force bears to the resistance the inverse ratio of the distances which separate the fulcrum from the force and resistance respectively. ”

“ A.--The mechanical powers are certain contrivances, such as the wedge, the screw, the inclined plane, and other elementary machines, which convert a small force acting through a great space into a great force acting through a small space. ”

“ Mechanical Advantage.—A lever often gives an advantage because by its use one may lift a stone or weight which the unaided strength of man could not move. If the lever is used in lifting a stone weighing 500 lbs., the force available being only 100 lbs., then its mechanical advantage would be 5, the ratio of w:f. In a similar way, the mechanical advantage of any machine is found by finding the ratio of the resistance or weight to the effort. ”

“ It is not always practicable to employ numerous hands for the purpose, nor is a steam-engine or other great source of power at all times available. But what are called the mechanical powers enable the forces at our disposal to be greatly increased. One man, by their aid, can exert as much force [Pg 100] as several could without such assistance; and when they are employed to augment the power of several men or of a steam-engine, gigantic weights, amounting sometimes to hundreds of tons, can be managed with facility. ”

“ This shows within what distinct limits machine-problems lie, and that they allow themselves to be readily separated from the general problems of Mechanics, as we have already maintained.
While the science of Mechanics examines motion caused in the most general cases by the action of mechanical forces, Machine-mechanics occupies itself with certain special cases only, with motions produced by a limited circle of means. It draws its first laws from the same fountain as Mechanics, to which, as the more comprehensive science, it is subordinate. ”

“ But the cases which we have more particularly in view are mechanical causes, the causes of the motion and of the equilibrium of bodies. In these cases, forces are conceived as capable of addition; and what has been said of the measure of causes in such cases, applies peculiarly to mechanical forces. Two weights, placed together, may be considered as a single weight, equal to the sum of the two. Two pressures, pushing a body in the same direction at the same point, are identical in all respects with some single pressure, their sum, pushing in like manner ”

“ The most obvious mechanical phenomenon in electrical and magnetical experiments is the mutual action by which bodies in certain states set each other in motion while still at a sensible distance from each other. The first step, therefore, in reducing these phenomena into scientific form, is to ascertain the magnitude and direction of the force acting between the bodies, and when it is found that this force depends in a certain way upon the relative position of the bodies and on their electric or magnetic condition, it seems at first sight natural to explain the facts by assuming the existence of something either at rest or in motion in each body, constituting its electric or magnetic state, and capable of acting at a distance according to mathematical laws. ”

“ Whilst in the first system, which we may call kosmical, the external measurable mechanical forces are opposed by similar external forces, in the second, the machine system, there are opposed to all external forces others concealed in the interior of the bodies forming the system, and appearing there,—and acting in exactly the required manner,—in consequence of the action of the external forces. ”

“ When energy has been stored in a fly-wheel, it can be withdrawn either as a small force acting over a great distance, or as a large force over a small distance. In the latter case the fly-wheel acts as a mechanical power, and in this form it is used in the very important machine to be next described. A model of the punching machine is shown in Fig. ”

“ In a machine of which each piece is to move with a uniform velocity, if the effort and the resistance be constant, the weight of each piece must be balanced on its axis, so that it may produce lateral pressure only, and not act as a reciprocating force. ”

“ Energy distributed between two Bodies: Projection and Propulsion.—Hitherto the effort by which a machine is moved has been treated as a force exerted between a movable body and a fixed body, so that the whole energy exerted by it is employed upon the movable body, and none upon the fixed body. This conception is sensibly realized in practice when one of the two bodies between which the effort acts is either so heavy as compared with the other, or has so great a resistance opposed to its motion, that it may, without sensible error, be treated as fixed. ”

“ This rule is true for all kinds of levers, blocks and tackles or pulley systems, automobile and bicycle gears, belt systems, cog systems, derricks, crowbars, and every kind of machine. In most machines you either put in more force than you get out and gain motion, or you put in more motion than you get out and gain force. ”

“ Yet this remarkable contrivance, with all its massive steel beams and chains and cog wheels, employs no other principles than the simple ones of lever and pulley and inclined plane that we have just examined. The power that must be applied to produce a given effect may be calculated to a nicety. The capacities of the machine are fully predetermined in advance of its actual construction. But of course this is equally true of every other form of power-transmitter with which the modern mechanical engineer has to deal. ”

“ When the power arm is longer than the load arm, the load is greater than the power; but when the power arm is shorter than the load arm, the power is greater than the load.
We may regard the strain on the balance as a power which supports the weight, just as we regard the weight to be a power producing the strain on the balance. We see, then, that for the lever of the first order to be efficient as a mechanical power it is necessary that the power arm be longer than the load arm. ”

“ Action and reaction being equal, the power exerted in raising or moving one heavy body must be exerted reversely against the earth, or other fixed body serving as a fulcrum to the lever, or for the attachment of one extremity of a tackle or series of pullies, or for the securing of the capstan spindle. Let the attachments of the machine and its object, however, be both afloat, and then any of the mechanical powers, like that of the wedge, will have an efficiency of double that of its ordinary operation where one part is a fixture. ”

“ However, we must remember that in mechanics, as in all walks of life, we cannot get “something for nothing.” If we multiply the pressure or force, we must pay for it in some way, otherwise we should be getting more work out of the press than we put in it, which is what the perpetual motion crank is ever trying to do. As the cross-sectional area of the plunger D is only 1/30th of that of the ram, the plunger must descend thirty inches to raise the ram one inch. ”

“ But to treat of Mechanics is not my present business. I was only willing to show by those examples the great extent and certainty of the third Law of motion. For if we estimate the action of the agent from its force and velocity conjunctly; and likewise the reaction of the impediment conjunctly from the velocities of its several parts, and from the forces of resistance arising from the attrition, cohesion, weight, and acceleration of those parts; the action and re-action in the use of all sorts of Machines will be found always equal to one another. ”

“ The strength of every part of the machine should be made proportional to the stress it is to bear: and therefore let every lever be made so much stronger, as its length and the weight it is to support are greater; and let its strength diminish proportionally from the fulcrum, or point where the greatest stress is to each end. The axles of wheels and pullies must be so much stronger as they are to bear greater weight. The teeth of wheels, and the wheels themselves, which act with greater force, must be proportionally stronger ”

“ In the selection of the subjects, the question of practical utility has in many cases been regarded as the one of paramount importance. The elementary truths of Mechanics are too well known to admit of novelty, but it is believed that the mode of treatment which is adopted is more or less original. This is especially the case in the Lectures relating to friction, to the mechanical powers, to the strength of timber and structures, to the laws of motion, and to the pendulum. The illustrations, drawn from the apparatus, are nearly all original, and are beautifully executed. ”

“ The next class of simple machines, which present themselves to our attention, is that which we have called the cord. If a rope were perfectly flexible, and were capable of being bent over a sharp edge, and of moving upon it without friction, we should be enabled by its means to make a force in any one direction overcome resistance, or communicate motion in any other direction. ”

“ It is easy to conceive, that when forces applied to mechanical instruments are in equilibrium, if the least addition be made to one of them, it will preponderate and overcome the effort. But the want of a perfect polish or smoothness in the parts of all instruments, and the rigidity of all ropes, which increases with the tension, are great impediments to motion, and in compounded engines are found to diminish about one fourth of the effect of the power. ”

“ The principles of the science of Mechanics were discovered by observations made upon bodies within the reach of men; as we have seen in speaking of the discoveries of Stevinus, Galileo, and others, up to the time of Newton. And when there arose the controversy about vis viva (Chap. v. Sect. 2 of this Book) ;—namely, whether the “living force” of a body is measured by the product of the weight into the 537 velocity, or of the weight into the square of the velocity;—still the examples taken were cases of action in machines and the like terrestrial objects. ”

“ If the brakes are applied to a train in motion, intense heat is generated in the substance of the brake. Now, the force employed by the brakesman is not equivalent to the heat generated. Where, then, is the balance of force expended? ”