Tension (mechanics)

“ Finally, let us remove the 28 lbs. from b, put on 56 lbs., and perform the experiment again; you see that even the 56 lbs. is raised up several inches. Here a tension in the rope has been generated sufficient to overcome a weight four times as heavy as a. We have then, by the help of inertia, been able to produce a mechanical power, for a small force has overcome a greater.
533. After b is raised by the chuck to a certain height it descends again, if heavier than a, and raises a. The height to which b is raised is of course the same as the height through which a descends. ”

“ The tension of the first rope is equal to the power; the second rope acts against twice the tension of the first, and therefore it is stretched with a force equal to twice the power: the third rope acts against twice this tension, and therefore it is stretched206 with a force equal to four times the power, and so on. In the system represented in fig. 126. there are three ropes, and the weight is eight times the power. ”

“ We must suppose that there is a pressure in the direction of the lines of force, combined with a tension in all directions at right angles to the lines of force. Such a state of stress would, no doubt, account for the observed effects of gravitation. ”

“ 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. ”

“ Just as the cord in our experiments cannot be straight when any force, however small, is pulling it downwards at the centre, so it is impossible by any exertion of force to straighten the long wire. Some further illustrations of this principle will be given in our next lecture, and with one application of it the present will be concluded.
21. One of the most important practical problems in mechanics is to make a small force overcome a greater. ”

“ A mechanical pressure not accompanied by an equal and opposite pressure, can no more be given by experience, than two unequal right angles. With the supposition of such inequalities, space ceases to be space, force ceases to be force, matter ceases to be matter. And this equality of action and reaction, considered in the case in which two bodies are connected so as to act on a single support, leads to the axiom which we have stated above, and which is one of the main foundations of the science of Mechanics. ”

“ Deflecting Force for Translation in a Curved Path.—In machinery, deflecting force is supplied by the tenacity of some piece, such as a crank, which guides the deflected body in its curved path, and is unbalanced, being employed in producing deflexion, and not in balancing another force. ”

“ At every point of the two equipotential surfaces and , let a tension = be applied, and at every point of the surface of no induction let a pressure = be applied. These forces will keep the figure in equilibrium. ”

“ 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 true source of the force lies in the inevitable roughness of all known surfaces, no matter how they may have been wrought. The minute asperities on one surface are detained in corresponding hollows in the other, and consequently force must be exerted to make one surface slide upon the other. By care in polishing the surfaces the amount of friction may be diminished ”

“ It has been confounded, under the common name of Mechanics, with the other science, Mechanics Proper, or Machinery, which considers the effect of force transmitted by Mechanism from one part of a material combination to another. For example, the Mechanical Powers, as they are usually termed, (the Lever, the Wheel and Axle, the Inclined Plane, the Wedge, and the Screw,) have almost always been treated with reference to the relation between the Power and the Weight, and not primarily as a mode of changing the velocity and kind of the motion. ”

“ Where great resistances have to be overcome, but where the distance through which the resistance must be urged is short, the lever or the screw is generally found to be the most appropriate means of [Pg 150] increasing power. When, however, the resistance has to be moved a considerable distance, the aid of the pulley, or the wheel and axle, or sometimes of both combined, is called in. The wheel and axle is the form of mechanical power which is generally used when the distance is considerable through which a weight must be raised, or through which some resistance must be overcome. ”

“ If we now proceed to investigate the mechanical state of the medium on the hypothesis that the mechanical action observed between electrified bodies is exerted through and by means of the medium, as in the familiar instances of the action of one body on another by means of the tension of a rope or the pressure of a rod, we find that the medium must be in a state of mechanical stress. ”

“ Hence, we learn that two equal and directly opposed forces counteract each other, and each may be regarded [Pg 6] as destroying the motion which the other is striving to produce. If I make the weights unequal by adding to one of them, the knot is no longer at rest; it instantly begins to move in the direction of the larger force. ”

“ The component across the direction of motion is a lateral pressure; the unbalanced lateral pressure on any piece, or part of a piece, is deflecting force. A lateral pressure may increase resistance by causing friction; the friction so caused acts against the motion, and is a resistance, but the lateral pressure causing it is not a resistance. Resistances are distinguished into useful and prejudicial, according as they arise from the useful effect produced by the machine or from other causes. ”

“ 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. ”

“ The resistance of a body to compression does not depend upon its hardness. Strike a diamond with a hammer and it flies to pieces, but wood does not. One is brittle and the other is tough.
The machinist can utilize this property by understanding that velocity enables a soft materialp. ”

“ But if the body, as is most usual, be subject to some resistance or restraint, it will either remain unmoved, its weight being expended in exciting pressure on the restraining points or surfaces, or it will move in111 a direction and with a velocity depending on the circumstances which restrain it. ”

“ We may in this way reduce any real structure to the case of a system of points with attractive or repulsive forces acting between certain pairs of these points, and keeping them in equilibrium. The direction of each of these forces is sufficiently indicated by that of the line joining the points, so that we have only to determine its magnitude. We might do this by calculation, and then write down on each link the pressure or the tension which acts in it. ”

“ 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. ”

“ 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. ”

“ In order to investigate the amount of power lost by winding the rope upon an axle of this size, I shall place a certain weight—suppose 56 lbs.—upon one hook f, and then I shall ascertain what amount of power hung upon the other hook e will be sufficient to raise f. There is here no mechanical advantage, so that the excess of load which e must receive in order to raise f is the true measure of the friction. ”

“ If there is the slightest displacement of the centre of gravity of the system from the axis of revolution a force acts on the shaft tending to deflect it, and varies as the deflexion and as the square of the speed. If the shaft is therefore to revolve stably, this force must be balanced at any instant by the elastic resistance of the shaft to deflexion. ”

“ If we consider any vertical section P, the forces exerted across the section by the portion of the structure on one side on the portion on the other may be reduced to a vertical force F at P and a couple M. The force measures the shearing stress, and the couple the bending moment at P ”

“ The driving and resisting efforts are represented by elastic links in the dynamic frame, and when the frame with its elastic links is drawn the stresses in the several members of it may be determined by means of reciprocal figures. ”

“ General Principles.—In order that the velocity of every piece of a machine may be uniform, it is necessary that the forces acting on each piece should be always exactly balanced. Also, in order that the forces acting on each piece of a machine may be always exactly balanced, it is necessary that the velocity of that piece should be uniform.
An excess of the effort exerted on any piece, above that which is necessary to balance the resistance, is accompanied with acceleration; a deficiency of the effort, with retardation. ”

“ Force is the name given in mechanics to whatever produces motion or pressure. This word is also often used to express the motion or pressure itself; and when the cause of the motion or pressure is not known, this is the only correct use of the word. Thus, when a piece of iron moves toward a magnet, it is usual to say that the cause of the motion is “the attraction of the magnet;” ”

“ 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 ”

“ If we assume that there is no other stress, then the magnitude of the traction in question is Ey/R, where E is Young’s modulus, and it is tension on the side where the filaments are extended and pressure on the side where they are contracted. ”

“ The condition that each piece of the structure is to be maintained in equilibrium by having its gross load, consisting of its own weight and of the external pressure applied to it, balanced by the resistances or pressures exerted between it and the contiguous pieces, furnishes the means of determining the magnitude, position and direction of the resistances required at each joint in order to produce equilibrium ”

“ In this case, there is something transmitted from my hand along the string to the weight in consequence of which the weight moves: that something is a force. I can also move the weight by pushing it with a stick, because force is transmitted along the stick, and makes itself known by producing motion. The archer who has bent his bow and holds the arrow between his finger and thumb feels the string pulling until the impatient arrow darts off. Here motion has been produced by the force of elasticity in the bent bow. ”

“ If a force be applied to a turning piece in a line not passing through its axis, the axis will press against its bearings with an equal and parallel force, and the equal and opposite reaction of the bearings will constitute, together with the first-mentioned force, a couple whose arm is the perpendicular distance from the axis to the line of action of the first force. ”

“ The greatest strain is on the shortest cord and the least strain on the longest. Here the force w lbs. produces three forces which, taken together, exceed its own amount. If I add an equal weight w, I find, as we might have anticipated, that the strains indicated by the scales are precisely double what they were before. Thus we see that the proportion of the force to each of the components into which it is decomposed does not depend on the actual magnitude of the force, but on the relative direction of the force and its components. ”

“ In one case the force of gravity will endeavor to destroy motion by opposing the lift of the arm, and in the other case the arm will endeavor to resist motion by opposing the pull of gravity. A book on a table is motionless and yet it is acted upon by two forces which are opposed to each other and hence balanced. The table furnishes a force which resists and balances the force exerted by gravity. ”