By Q. Makas. Winston-Salem State University. 2018.
Only when the old symptoms apcalis sx 20mg without a prescription, which had been eradicated or very much diminished by the last and the preceding medicines commence to rise again for a few days order apcalis sx 20 mg fast delivery, or to be again perceptibly aggravated apcalis sx 20mg line, then the time has most surely come when a dose of the medicine most homoeopathically fitting should be given. Experience and careful observation alone can decide; and it always has decided in my manifold, exact observations, so as to leave no doubt remaining. Now if we consider the great changes which must be effected by the medicine in the many, variously composite and incredibly delicate parts of our living organism, before a chronic miasm so deeply inrooted and, as it were, parasitically interwoven with the economy of our life as psora is, can be eradicated and health be thus restored: then it may well be seen how natural it is, that during the long- continued action of a dose of antipsoric medicine selected homoeopathically, assaults may be made by it at various periods on the organism, as it were in undulating fluctuations during this long-continued disease. Experience shows that when for several days there has been an improvement, half hours or whole hours or several hours will again appear when the case seems to become worse; but these periods, so long as only the original ailments are renewed and no new, severe symptoms present themselves, only show a continuing improvement, being homoeopathic aggravations which do not hinder but advance the cure, as they are only renewed beneficent assaults on the disease, though they are wont to appear at times sixteen, twenty or twenty-four days after taking a dose of antipsoric medicine. But vice versa also those medicines which in the healthy body show a long period of action act only a short time and quickly in acute diseases which speedily run their course (e. The physician must, therefore, in chronic diseases, allow all antipsoric remedies to act thirty, forty or even fifty and more days by themselves, so long as they continue to improve the diseased state perceptibly to the acute observer, even though gradually; for so long the good effects continue with the indicated doses and these must not be disturbed and checked by any new remedy. These great, pure truths will be questioned yet for years even by most of the homoeopathic physicians, and will not, therefore, be practiced, on account of the theoretical reflection and the reigning thought: ÒIt requires quite an effort to believe that so little a thing, so prodigiously small a dose of medicine, could effect the least thing in the human body, especially in coping with such enormously great, tedious diseases; but that the physician must cease to reason, if he should believe that these prodigiously small doses can act not only two or three days, but even twenty, thirty and forty days and longer yet, and cause, even to the last day of their operation, important, beneficent effects otherwise unattainable. Experience alone declares it, and I believe more in experience than in my own intelligence. But who will arrogate to himself the power of weighing the invisible forces that have hitherto been concealed in the inner bosom of nature, when they are brought out of the crude state of apparently dead matter through a new, hitherto undiscovered agency, such as is potentizing by long continued trituration and succussion. But he who will not allow himself to be convinced of this and who will not, therefore, imitate what I now teach after many yearsÕ trial and experience (and what does the physician risk, if he imitates it exactly? It seemed to me my duty to publish the great truths to the world that needs them, untroubled as to whether people can compel themselves to follow them exactly or not. If it is not done with exactness, let no one boast to have imitated me, nor expect a good result. Do we refuse to imitate any operation until the wonderful forces of nature on which the result is based are clearly brought before our eyes and made comprehensible even to a child? Would it not be silly to refuse to strike sparks from the stone and flint, because we cannot comprehend how so much combined caloric can be in these bodies, or how this can be drawn out by rubbing or striking, so that the particles of steel which are rubbed off by the stroke of the hard stone are melted, and, as glowing little balls, cause the tinder to catch fire? And yet we strike fire with it, without understanding or comprehending this miracle of the inexhaustible caloric hidden in the cold steel, or the possibility of calling it out with a frictional stroke. Again, it would be just as silly as if we should refuse to learn to write, because we cannot comprehend how one man can communicate his thought to another through pen, ink, and paper - and yet we communicate our thoughts to a friend in a letter without either being able or desirous of comprehending this psychico-physical miracle! Why, then, should we hesitate to conquer and heal the bitterest foes of the life of our fellowman, the Chronic diseases, in the stated way, which, punctually followed, is the best possible method, because we do not see how these cures are effected? Another antipsoric remedy which may be ever so useful, but is prescribed too early and before the cessation of the action of the present remedy, or a new dose of the same remedy which is still usefully acting, can in no case replace the good effect which has been lost through the interruption of the complete action of the preceding remedy, which was acting usefully, and which can hardly be again replaced. It is a fundamental rule in the treatment of chronic diseases: To let the action of the remedy, selected in a mode homoeopathically appropriate to the case of disease which has been carefully investigated as to its symptoms, come to an undisturbed conclusion, so long as it visibly advances the care and the while improvement still perceptibly progresses. This method forbids any new prescription, any interruption by another medicine and forbids as well the immediate repetition of the same remedy. Nor can there be anything more desirable for the physician than to see the improvement of the patient proceed to its completion unhindered and perceptibly. There are not a few cases, where the practiced careful Homoeopath sees a single dose of his remedy, selected so as to be perfectly homoeopathic, even in a very severe chronic disease, continue uninterruptedly to diminish the ailment for several weeks, yea, months, up to recovery; a thing which could not have been expected better in any other way, and could not have been effected by treating with several doses or with several medicines. To make the possibility of this process in some way intelligible, we may assume, what is not very unlikely, that an antipsoric remedy selected most accurately according to homoeopathic principles, even in the smallest dose of a high or the highest potency can manifest so long- continued a curative force, and at last cure, probably, only by means of a certain infection with a very similar medicinal disease which overpowers the original disease, by the process of nature itself, according to which (Organon, ¤ 5, Fifth Edition,) two diseases which are different, indeed, in their kind but very similar in their manifestations and effects, as also in the ailments and symptoms caused by it, when they meet together in the organism, the stronger disease (which is always the one caused by the medicine, ¤33, ibid. In this case every new medicine and also a new dose of the same medicine, would interrupt the work of improvement and cause new ailments, an interference which often cannot be repaired for a long time. Yet when a sudden great and striking improvement of a tedious great ailment follows immediately on the first dose of a medicine, there justly arises much suspicion that the remedy has only acted palliatively, and therefore must never be given again, even after the intervention of several others remedies. Nevertheless there are cases which make an exception to the rule, but which not every beginner should risk finding out. We may declare it once, that the practice of late, which has even been recommended in public journals of giving the patient several doses of the same medicine to take with him, so that he may take them himself at certain intervals, without considering whether this repetition may affect him injuriously, seems to show a negligent empiricism, and to be unworthy of a homoeopathic physician, who should not allow a new dose of a medicine to be taken or given without convincing himself in every case beforehand as to its usefulness. This is rare in chronic diseases, but in acute diseases and in chronic diseases that rise into an acute state it is frequently the case. It is only then, as a practiced observer may recognize - when the peculiar symptoms of the disease to be treated, after fourteen, ten, seven, and even fewer days, visibly cease to diminish, so that the improvement manifestly has come to a stop, without any disturbance of the mind and without the appearance of any new troublesome symptoms, so that the former medicine would still be perfectly homoeopathically suitable, only then, if say, is it useful, and probably necessary to give a dose of the same medicine of a similarly small amount, but most safely in a different degree of dynamic potency. To adduce an example: a freshly arisen eruption of itch belongs to those diseases which might soonest permit the repetition of the dose (sulphur), and which does permit it the more frequently, the sooner after the infection the itch is received for treatment, as it then approaches the nature of an acute disorder, and demands its remedies in more frequent doses than when it has been standing on the skin for some time. But this repetition should be permitted only when the preceding dose has largely exhausted its action (after six, eight or ten days), and the dose should be just as small as the preceding one, and be given in a different potency. Nevertheless it is in such a case often serviceable, in answer to a slight change of symptoms, to interpose between the doses of pure sulphur, a small dose of Hepar sulphuris calcareum. This also should be given in various potencies, if several doses should be needed from time to time. Often also, according to circumstances, a dose of Nux voinica (x) or one of mercury (x)** may be used between. A dose of medicine may also have been suddenly counteracted and annihilated by a grave error in the regimen of the patient, when perhaps a dose of the former serviceable medicine might again be given with the modification mentioned above. Thereby the remedy seeing to take a deeper hold on the organism and hasten the restoration in patients who are vigorous and not too sensitive. Indeed it is hardly ever needed in chronic diseases, as we have a goodly supply of antipsoric remedies at our disposal, so that as soon as one well selected remedy has completed its action, and a change of symptoms, i. Nevertheless in very tedious and complex cases, which are mostly such as have been mismanaged by allopathic treatment, it is nearly always necessary to give again from time to time during the treatment, a dose of Sulphur or of Hepar (according to the symptoms), even to the patients who have been before dosed with large allopathic doses of Sulphur and with sulphur-baths; but then only after a previous dose of Mercury (x). Where, as is usually the case in chronic diseases, various antipsoric remedies are necessary, the more frequent sudden change of them is a sign that the physician has selected neither the one nor the other in an appropriately homoeopathic manner, and had not properly investigated the leading symptoms of the case before prescribing a new remedy. This is a frequent fault into which the homoeopathic physician falls in urgent cases of chronic diseases, but oftener still in acute diseases from overhaste, especially when the patient is a person very dear to his heart. Then the patient naturally falls into such an irritated state that, as we say, no medicine acts, or shows its effect,* yea, so that the power of response in the patient is in danger of flaring up and expiring at the least further dose of medicine.
This could occur only if agonist 3 was capable of ~l receptor activation in the heart generic apcalis sx 20mg otc. Direct cardiac stimulation could occur with norepinephrine (agonist 3) but not with methoxamine (agonist 2) buy apcalis sx 20mg overnight delivery, which is a selective alpha adrenoceptor agonist apcalis sx 20 mg amex. Explanations to Figures 11-4-2 through 11-4-11: Drug Identification from Effects on Heart Rate and Blood Pressure. Figure 11-4-2: The effects of Drug R are changed by treatment with either an alpha or beta- blocker, so Drug R must have activity at both receptors (choices C, D, and E are ruled out). A pressor dose of epinephrine would be "reversed" by an alpha- blocker, not just decreased! Figure 11-4-3: The effects of Drug U are changed by treatment with the alpha-blocker, but not by the beta-blocker. Drug U must be an alpha-activator with no beta actions-the only choice is phenylephrine. Figure 11-4-4: The effects of Drug S are changed by treatment with the beta-blocker, but not by the alpha blocker (choices A, B, and C are ruled out). Note that option A would have been a possibility but one would have to assume a low-dose of epinephrine. Figure 11-4-5: The effects of Drug H are changed by treatment with either an alpha- or beta- blocker, so Drug H must have activity at both receptors (choices C, D, and E are ruled out). Figure 11-4-6: Mecamylamine blocked reflexed tachycardia induced by Drug X, which dropped blood pressure by vasodilation. Note that the alpha agonist does not antagonize the decrease in respiratory resistance (a ~2 response). Because Drug X abolishes only the reflex tachycardia, it must be the ganglion blocker hexame- thonium (choice A). Arterial con- traction due to the alpha agonist (choice E) is reversed by the alpha-blocker (choice C). Arteriolar relaxation and tachycardia due to epinephrine (choice B) is reversed by the beta-blocker (choice D). Figure 11-4-10: Classic example showing that denervated tissues do not respond to indirect- acting agonists. In this case, tyramine fails to cause mydriasis in the left eye, but this eye is more responsive than the right eye to epinephrine (denervation supersensitivity). Tachycardia due to Drug R is unaffected by any antagonist, indicative of a beta activator (choice D). Rate of depolarization depends on number of Na" channels open, which in turn depends on resting membrane potential of the cell. In some His-Purkinje cells, transient outward K+ currents and inward cr currents contribute to the "notch" and overshoot. Phase 3 • Repolarization phase in which the delayed rectifier K+ current rapidly increases as the Caz+ current dies out because of time-dependent channel inactivation. Note that during phases 0 through 3 a slow Na" current ("window current") occurs, which can help prolong the duration of the action potential. Conductance Rate of spread of an impulse, or conduction velocity-three major determinants: Rate of phase 0 depolarization-as Vmax decreases, conduction velocity decreases and vice versa. Fundamental Concepts No appreciable Na+ current during phase 0 in these cells because the Na channels are either absent or in an inactive form because of the existing voltage. During repolarization, the Ca2+ currents are opposed and overcome by the delayed rectifier K+ current. The relative magnitudes of these opposing currents determine the "shape" of the action potential. Automaticity The ability to depolarize spontaneously confers automaticity on a tissue. Refractoriness • The inability to respond to a stimulus-property of all cardiac cells. Inactivation of the h gate is slower; therefore, it stays open longer and the Na channel is active. Rate of recovery is slower in ischemic tissue because cells may be partly depolarized at rest. This reduces the number of channels able to participate in the next depolariza- tion, which leads to a decrease in conduction rate in ischemic tissue. Chapter Summary The sequences of ionic events in the action potential of cardiac cells are described. Responsivity, capacity of a cell for depolarization, depends on resting membrane potential; con- ductance is the rate of potential spread; refractoriness is the inability to respond to excitation. Three conformations exist-resting (ready), active (open), and inactive (refractory). Class I drugs are least active when Na" channels are in the resting state (state-dependent actions). This results in an increased threshold for excitation and less excitability of hypoxic heart muscle. The uses for lidocaine, mexiletine, and tocainide are discussed, as are the metabolism and adverse effects of lidocaine. However, homeostatic mechanisms may lead to compensatory increases in heart rate and/or salt and water retention. The metabolic characteristics, clinical uses, and potential adverse effects of sympathoplegic drugs, which decrease peripheral resistance by decreasing sympathetic tone, are discussed. Sympathoplegic drugs also may act directly as adrenergic neuron blockers, alpha blockers, or beta blockers.
Here or there at times discount 20mg apcalis sx with mastercard, though seldom generic 20mg apcalis sx overnight delivery, a single insufferably pleasant cheap 20mg apcalis sx visa, but unbearably itching vesicle, at its point sometimes filled with pus, and causing a burning sensation after rubbing, on a finger, on the wrist or in some other place. Suffering from several or from a greater number of these ailments (even at various times and frequently), a person will still consider himself as healthy, and is supposed to be so by others. He may also lead a quite endurable life in such a state, and without much hindrance, attend to his business as long as he is young or still in his vigorous years, and so long as he does not suffer any particular mishap from without, has a satisfactory income, does not live in vexation or grief, does not overexert himself; but especially if he is of quite a cheerful, equable, patient, contented, disposition. With such persons the psora (internal itch malady), which may be recognized by a connoisseur by means of a few or by more of the above symptoms, may slumber on for many years within, without causing any continuing chronic disease. This is mostly wont to happen in fall or winter, but often also by preference in springtime. But even where a person, whether a child or an adult, who has the psora slumbering within him, shows much semblance of health, but happens upon the opposite of the above-described favorable conditions of life, when his health and whole organism have been very much weakened and shaken by a prevalent epidemic fever or an infectious acute disease,* smallpox, measles, whooping cough, scarlet fever, purple rash, etc , or through an external severe lesion, a shock, a fall, a wound, a considerable burn, the breaking of an arm or a leg, a hard labor, the confinement due to a disease (usually helped on by the incorrect and weakening Allopathic treatment), confinement at a sedentary occupation in a gloomy, close room, weakening the vital force; the sad losses of beloved relatives bending down the soul with grief, or daily vexation and annoyance which embitter the life; deterioration of the food or an entire want of what is necessary and indispensable, exposure and inferior food beating down manÕs courage and strength; then the, psora, which has hitherto slumbered, awakes and shows itself in the heightened and augmented symptoms enumerated below, in its transition to the formation of severe maladies; one or another of the nameless (psoric) chronic diseases breaks out and most of all through weakening and exhausting improper treatment by allopathic physicians, they are aggravate from time to time without intermission, often to a fearful height, if external circumstances favorable for the patient do not interpose, and cause a moderation in the process of the malady. This the physicians explain as a new generation of itch in this individual body replete with bad humors (scilicet), since they know nothing of a psora in man which may be quiescent for a long period. But the itch-disease cannot now be generated or arise or be created anew of itself, just as no smallpox or cow-pox, no measles, no venereal chancre disease, etc. A passionate, peevish disposition gives an extraordinary predisposition to the development of the psora; so also previous exhaustion through frequent pregnancies, excessive nursing of infants, extraordinary hardships, exhausting erroneous medical treatment, debauchery, and a profligate mode of living. The internal itch-disease is, as before mentioned, of such a peculiar nature that it may remain, as it were, tied down and covered up for a long through external favorable surroundings, so that a man may seem to the superficial observer healthy for years, even for many years, until circumstances unfavorable to the body or the soul, or to both, may arise, and serve as a hostile impulse to awaken the disease slumbering within and thus develop its germs. His acquaintances and his physician, yea, the patient himself, can not then comprehend how his health could so suddenly fall into a decline. To bring some examples for explanation from my own experience: After a simple fracture of a limb attended with confinement to bed for five or six weeks, there may follow diseased conditions of another kind, the cause of which cannot be guessed, which diseased condition, even when measurably removed, nevertheless returns, and which even without any error in diet nevertheless at their return show aggravation. This is mostly the case in fall (winter) and spring and becomes a tedious ailment increasing from year to year, a lasting cure for which, without the substitution of a still worse disease for it by an allopathic cure, has been hitherto vainly sought for in the councils of former physicians and also in visits to mineral springs. There are in manÕs life innumerable stumbling-blocks or unfavorable occurrences of this kind which serve to awaken the psora (the internal itch- disease) which till then has been slumbering (perhaps for a long time previously) and which cause its germs to develop. They are often of such a nature that the grave evils which gradually follow on them are out of all proportion to them, so that no rational man can consider those occurrences as sufficient causes for the chronic diseases which follow and which are often of a fearful character. But such a man is compelled to acknowledge a deeper seated hostile cause of these appearances, which cause has only now developed itself. In a few weeks, however, her youthful constitution had pretty well recovered, and she might have been of a speedy return to lasting good health, when the announcement of the dangerous illness of a beloved sister, living at a distance, threw her back and augmented her former ailments, which had not yet been quite removed, by the addition of a multitude of nervous disorders and convulsions, thus turning them into a serious illness. But the sick young wife still remains sick, and even if she seems to recover for a week or two, her ailments nevertheless return without any apparent cause. Every succeeding confinement, even when quite easy, every hard winter, adds new ailments to the old, or the former disorders change into others still more troublesome, so that at last there ensues a serious chronic illness though no one can see why the full vigor of youth, attended by happy external surroundings, should not have soon wiped out the consequence of that one miscarriage; still less can it be explained why the unfortunate impression of those sad tidings should not have disappeared, on hearing of the recovery of her sister, or at least on the actual presence of her sister fully restored. In a similar manner, a robust merchant, apparently healthy, despite some traces of internal psoral perceptible only to the professional examiner, may in consequence of unlucky commercial conjunctures become involved in his finances, even so as to approach bankruptcy, and at the same time he will fall gradually into various ailments and finally into serious illness. The death of a rich kinsman, however, and the gaining of a great prize in a lottery, abundantly cover his commercial losses; he becomes a man of means - but his illness, nevertheless, not only continues but increases from year to year, despite all medical prescriptions, in spite of his visiting the most famous baths, or rather, perhaps, with the assistance of these two causes. A modest girl, who, excepting some signs of internal psora, was accounted quite healthy, was compelled into a marriage which made her unhappy of soul, and in the same degree her bodily health declined, without any trace of venereal infection. No allopathic medicine alleviates her sad ailments, which continually grow more threatening. But in the midst of this aggravation, after one yearÕs suffering, the cause of her unhappiness, her hated husband, is taken from her by death, and she seems to revive, in the conviction, that she is now delivered from every occasion of mental or bodily illness, and hopes for a speedy recovery; all her friends hope the same for her, as the exciting cause of her illness lies in the grave. She also improves speedily, but unexpectedly she still remained an invalid, despite the vigor of her youth; yea, her ailments but seldom leave her, and are renewed from time to time without any external cause, and they are even aggravated from year to year in the rough months. A person who had been unjustly suspected and become involved in a serious criminal suit, and who had before seemed healthy, with the exception of the marks of latent psora mentioned above, during these harassing months fell into various diseased states. But finally the innocence of the accused is acknowledged, and an honorable acquittal followed. We might suppose that such a happy, gratifying event would necessarily give new life to the accused and remove all bodily complaints. But this does not take place, the person still at times suffers from these ailments, and they are even renewed with longer or briefer intermissions, and are aggravated with the passing years, especially in the wintry seasons. If that disagreeable event had been the cause, the sufficient cause, of these ailments, ought not the effect; i. But these ailments do not cease, they are in time renewed and even gradually aggravated, and it becomes evident that those disagreeable events could not have been the sufficient cause of the present ailments and complaints - it is seen that they only served as an occasion and impetus toward the development, of a malady, which till then only slumbered within. The recognition of this old internal foe, which is so frequently present, and the science which is able to overcome it, make it manifest, that generally an indwelling itch (psora) was the ground of all these ailments, which can not be overcome even by the vigor of the best constitution, but only through art. When once, under the above-mentioned unfavorable outward surroundings, the transition of the psora from its slumbering and bound condition to its awakening and outbreak has taken place, and the patient leaves himself to the injurious activity of the usual allopathic physician, who deems it appropriate to his office and his income to mercilessly assault the organism of the patient (as we are sorry to witness every day) with the battering-rams of his violent, inappropriate remedies and weakening treatments; - in such a case, the external circumstances of the patient and his situation with respect to his surroundings may have changed ever so favorably, but the aggravation of the disease nevertheless proceeds under such hands without any escape. The awakening of the internal psora which has hitherto slumbered and been latent, and, as it were, kept bound by a good bodily constitution and favorable external circumstances, as well as its breaking out into more serious ailments and maladies, is announced by the increase of the symptoms given above as indicating the slumbering psora, and also by a numberless multitude of various other signs and complaints. These are varied according to the difference in the bodily constitution of a man, his hereditary disposition, the various errors in his education and habits, his manner of living and diet, his employments, his turn of mind, his morality, etc. Then when the itch-malady develops into a manifest secondary disease there appear the following symptoms, which I have derived and observed altogether from accounts of diseases which I myself have treated successfully and which confessedly originated from the contagion of itch, and were mixed neither with syphilis nor sycosis. I would only add further, that among the symptoms adduced there are also such as are entirely opposed to each other, the reason of which may be found in the varying bodily constitutions existing at the time - when the outbreak of the internal psora occurred. Yet the one variety of symptoms is found more rarely than the other and it offers no particular obstruction to a cure: Vertigo; reeling while walking. Vertigo; when closing the eyes, everything seems to turn around with him; he is at the same time seized with nausea. Vertigo, as if there was a jerk in the head, which causes a momentary loss of consciousness. Vertigo; she seems to herself now too large, now too small, or other objects have this appearance to her.
The work done on the body of the jumper by the force F during the jump is the product of the force F and the distance c over which this force acts (see Appendix A) generic 20mg apcalis sx with mastercard. At the full height of the jump H (before the jumper starts falling back to ground) generic apcalis sx 20mg mastercard, the velocity of the jumper is zero buy apcalis sx 20mg. At this point, the kinetic energy is fully converted to potential energy as the center of mass of the jumper is raised to a height (c + H). The gravitational constant of the moon, for example, is one-sixth that of the Earth; therefore, the weight of a given object on the moon is one- sixth its weight on the Earth. It is a common mistake to assume that the height to which a person can jump on the moon increases in direct proportion to the decrease in weight. That is, if a person can jump to a height of 60 cm on Earth, that same person can jump up 6. Note that the ratio H /H 11 is true only for a particular choice of F in the calculation (see Exercise 3-2). The additional height is attained by using part of the kinetic energy of the run to raise the center of gravity oﬀ the ground. Let us calculate the height attainable in a running jump if the 1 2 jumper could use all his/her initial kinetic energy ( mv ) to raise his/her body 2 oﬀ the ground. If this energy were completely converted to potential energy by raising the center of gravity to a height H, then 1 2 MgH mv (3. Then we must remember that the center of gravity of a person is already about 1 m above the ground. With little extra eﬀort, the jumper can alter the position of his body so that it is horizontal at its maximum height. Thus, our ﬁnal estimate for the maximum height of the running high jump is v2 H + 1. Obviously, it is not possible for a jumper to convert all the kinetic energy of a full-speed run into potential energy. In the unaided running high jump, only the force exerted by the feet is available to alter the direction of the running start. The situation is quite diﬀerent in pole vaulting, where, with the aid of the pole, the jumper can in fact use most of the kinetic energy to raise his/her center of gravity. These ﬁgures would agree even more closely had we included in our estimate the fact that the jumper must retain some forward velocity to carry him/her over the bar. A solution is required for the range R, the distance at which the projectile hits the Earth (see Fig. In other words a maximum range is obtained when the projectile is launched ata45◦ angle. In order to maximize the distance of the jump, the launching velocity and therefore also the resultant force should be directed at a 45◦ angle. We will assume as before that a jumper can generate with his feet a force equal to twice the body weight. The magnitude of the resultant force (Fr) and the angle θ at which the legs must apply the force to the body are obtained from the following considerations. W e will again assume that the force that launches the jumper is applied over a Section 3. The push-oﬀ force (2W) generated by the legs provides the vertical component of the launching velocity. The acceleration produced by the net force is 2W − W W a g m W/g If the push-oﬀ force acts on the jumper over a distance of 60 cm (the extent of the crouch) and if it is directed entirely in the vertical y direction, the vertical component of the velocity vy during the jump is given by 2 2 2 vy 2as 2 × g × 0. When an object moves through the air, the air molecules have to be pushed out of its way. The resulting reaction force pushes back on the body and retards its motion—this is the source of ﬂuid friction in air. We can deduce some of the properties of air friction by sticking our hand outside a moving car. Clearly, the greater the velocity with respect to the air, the larger is the resistive force. By rotating our hand, we observe that the force is greater when the palms face the direction of motion. We therefore conclude that the resistive force increases with the velocity and the surface area in the direction of motion. Because of air resistance, there are two forces acting on a falling body: the downward force of gravity W and the upward force of air resistance. From Newton’s second law (see Appendix A), we ﬁnd that the equation of motion in this case is W − Fa ma (3. If the body falls from a suﬃciently great height, the velocity reaches a magnitude such that the force due to air resistance is equal to the weight. Past this point, the body is no longer accelerated and continues to fall at a constant velocity, called the terminal velocity vt. At the terminal velocity, the downward force of gravity is canceled by the upward force of air resistance, and the net acceleration of the body is zero. The weight of an object is proportional to the volume, which is in turn proportional to the cube of the linear dimension L of the object, 3 W ∝ L The area is proportional to L2. With proper training, a person can jump from a height of about 10 m 42 Chapter 3 Translational Motion without sustaining serious injury. From this height, a person hits the ground at a speed of v 2gs 14 m/sec (46 ft/sec) Let us assume that this is the speed with which any animal can hit the ground without injury. At this speed, the force of air resistance on an animal the size of man is negligible compared to the weight. A simple calculation shows that a mouse can fall down a 100-m mine shaft without severe injury. Air friction has an important eﬀect on the speed of falling raindrops and hailstones.