With reference to a pulley system, the work equation is clearly discerned in its practical operation. In presenting the pulley, the writer uses a rectangular frame about two feet high and three feet wide. A number of hooks are screwed into the top cross piece of the frame. With such a device a number of different pulley combinations can be shown at one time

Begeman, L.

University of Northern Iowa

Science Bulletin Volume 2 Number 3 Article 7 11-1929 The Simple Machines L. Begeman Iowa State Teachers College Follow this and additional works at: https://scholarworks.uni.edu/science_bulletin  Part of the Health and Physical Education Commons, and the Science and Mathematics Education Commons Let us know how access to this document benefits you Copyright ©1929 by Iowa State Teachers College Recommended Citation Begeman, L. (1929) "The Simple Machines," Science Bulletin: Vol. 2: No. 3, Article 7. Available at: https://scholarworks.uni.edu/science_bulletin/vol2/iss3/7 This Contents is brought to you for free and open access by UNI ScholarWorks. It has been accepted for inclusion in Science Bulletin by an authorized editor of UNI ScholarWorks. For more information, please contact scholarworks@uni.edu. Offensive Materials Statement: Materials located in UNI ScholarWorks come from a broad range of sources and time periods. Some of these materials may contain offensive stereotypes, ideas, visuals, or language. • SCIENCE BULLETIN -know species, refusing only a few poisonous ones such as larkspur. The migratory locust may also equal or even exceed this record. On the other hand , many differ-ei1t insects feed upon the same kind of plant, the oaks, for example har-'boring seven or eight hundred dif-ferent species, while corn is at-tacked by at least two hundred kinds , twenty of which may be call-ed pests . Poison ivy is unique in being almost free from insect at--tack, though even this plant is eaten by two or three kinds of lar-vae vVhile practically ever_y kind of an imal is attacked by one or more insect pests, these parasitic forms are limited to only a few orders, the most savage of these being the Diptera represented by such com-mon forms as the stable-fly and the mosquito. The order Hemiptera, the "bug group", also contains some serious pests such as the bed-bug and the "cootie" or body louse. It is. common knowledge th at forms like butterflies and most ants and beetles never attack man. In fact, it may be said that most insects do not feed upon living animals. Like many other great groups, the insects contain num1erous spe-cies which prey upon their own kind or related spec ies. The dragon flies, or as they are often called, snake-doctors, spend most of their Jives catching mosquitoes and other small insects as prey. The robber-flies , large , powerful insects, are notorious as killers of their insects relatives, as also, are many kinds of ground beetles . The larvae of several species of lady-bird beetles are persistent killers of plant-lice. Certain ichneumon flies parasitize and destroy the eggs and larvae of many species of insects, and several kinds of wasps provision their nests entirely with caterpillars or grass-hoppers . What would happen to civilized man if the insects would cease their internecine strife and concentrate their destructive efforts solely upon him? Even if the insects ceased fight-ing among themselves , man would still have many powerful allies in his struggle for supremacy. First among these should be named the birds. It is difficult to conceive the prodigous quantities of insects de-stroyed by birds. The birds of Ne-braska alone, are credited with con-suming more than a hundred thous-and bushels of insects annually, and there is no reason why Iowa birds should not exceed this quantity. Such figures are not arrived at by mere guess. They are gained by patient watching of the food-habits of many kinds of nesting birds, and by examination of the crops of thousands of other specimens. Some birds are almost entirely insectivorous in food habit. Any one who has ever watched a turkey catching grasshoppers cannot fail to be impressed by the contribution of the birds to insect eradication. The common gardeµ toad i~ a great destroyer of insects ; so also are most garter-snakes, and nearly half of the food of the common striped-ground squirrel or spermo-phile consists of common insect pests of farm crops. A casual ex-amination of the dung around the burrow of the common skunk will quickly disclose the insectivorous habit of this creature; even foxes and raccoons feed upon them when other food is scarce. Roy L. Abbott. THE SIMPLE MACHINES Physics (Continued from October .) With reference to a. pulley system, the work equation is clearly discern-ed in its practical operation. In presenting the pulley, the writer uses a rectangular frame about two feet high and three feet wide. A number of hooks are screwed into the top cross piece of the frame. With such a device a riumber of different pulley combinations can be shown at one time. Let us consider the problem in the case where we set up a pulley system containing two pulleys, one fixed and the other movable. Let us also assume that the fixed pul-ley fastened to the frame above has three sheaves while the movable one suspended below it has only two. In setting up the pulleys, a very smooth flexible cord sl:}ould be used. The cord should be wound around the sheaves so that one of IOWA STATE TEACHERS COLLEGE 7 its ends is fastened to the top of ·the frame of the movable pulley. The other end is free for the ap-plication of the effort or force. A load of 100 gm, is attached to the lower movable pulley. If a pan with weights is attached to the loose end of the cord to draw up the 1oad, the class will readily see that to raise the load 10 cm. the spring balance must move down a distance of 50 cm. Furthermore . they will also note from the weights in the pan plus the weight of the pan itself that the force necessary to raise the load, where the motion is slow and uniform, is approxi-mately 2 0 gm. The work equation in the prob-lem would be as follows: · 20 gm. x 5o cm.=100 gm. x 10 cm. It will be noted in this equation that the ratio of the load, 100 gm. to the force applied, 20 gm., is ex-actly 5, which is just the number bf strands supporting the load . This -is the ca se in every pulley prob-lem, so that we frequently find the pulley equation written a s follows : F X n= R In this equation n stands for the number of strands supporting the load R . The following work equation holds good with reference to the screw: FXC=RXP In this C stands for the circum-ference of the circle in which the force acts and p stands for the 'pitch of the screw. The pitch of t he 'Screw is the distance between t wo of its consecutive threads. Appara-tus firms sell small jack s•:·r ews at a very small price. A shnrt lever arm thrust into one of the holes bored through the top of the jack screw enables one to give a visual demonstration of the work equa-tion as expressed above. In the discussion of simple ma-chines there are three concepts that should be mastered by the student. These concepts are cultural in na-ture as well as practical. They are commonly denoted by the terms, efficiency, mechanical advantage, and conservation of energy. A work equation applied to a fric-tionless machine is a specific ex-pression of the doctrine of the con-servation of energy. In a practical machine where there is fri ction the work equation would have to be modified to express the doctrine of conservation of energy. In the case of a pract ica l m achine , the work put into a machine is used up in two ways. One part of it does useful work and the rest is wasted in the heat of friction or other forms of energy. In practice, input equals the useful output of a ma-ch ine plus the energy wasted in the oper a tion of the machine. When every thing is considered, the doc-trine of conservation of energy al-so holds good in a practical 111a-chine. In the above disc ussion the term "input" means the total work a pplied to a machine and the term " output" means the work or service ta.ken out of it. The idea of efficiency ari ses from the fa.ct that the useful output of a machine in practice never equals the total input of work or energy applied to a machine. If th e input of a machine equals 100 foot pounds and its useful output is only 80 foot pounds then its effi-ciency is 80 per cent. Efficiency is evidently the ratio of the useful output to the total input expressed in per cent. A good practical problem iilus-trating the idea of efficiency can easily be carried out by means of an inclined plane and a small metal wagon, such as 'is commonly used with problems on the inclined plane. The inclined plane commonly sold by apparatus houses carries a small pulley fastened to the top end of the incline. A smooth cord is a.t-tached to the wagon and then dr.:twn over the pulley at the top of the incline. A pan for holding weight is fastened to the loose end of the cord, hanging down from the pulley. First weigh the pan. Then nttach the pan and place weights into it until the wagon moves with slow, uniform motion up the incline for. a given measured distance. Vvhen the wagon is empty, no useful work is done by the machine and the efficiency is zero. Now add a load of 50 gm. to the wagon which we will call the useful load. Then add weights to the pan until a slow uniform motion for the measured distance is obtained. Calculate the work done by the force applied,-that is obtain the product of the 8 SCIENCE BULLETIN weight of the pan plus the weights it contains times the distance through which it is raised. Divide the latter product by the former to get the efficiency. It will prohably not be a large per cent. Now in-crease the load successively five or six different times calculating the efficiency in each case. Finally plot the efficiencies against the use-ful work accomplished in each case. This problem will be found to be interesting to both student and teacher and will show how th e ef-fici ency of a machine can vary as the load is varied. The third idea. that the teacher shou ld emphasize in the d.udy of simple machines is that ol' mechan-ical advantage. This id ea like that of efficiency is expressed concrete-ly in term s of an arithmetical ra-tio but not in terms of per cent. It is denoted by the ratio of the resis-tance overcome in the machine to the force app.Jied . If i n a n operat-ing lever , for instance, 10 0 pounds of applied force overcomes a re-sistan ce of 500 pounds, the m e-chanical advantage is 5· or the ra-tio of 5 O O to 1 O O. Whenever this ratio turns out to be a whole num-ber as in the above problem, it in-dicates a m achine to do h eavy work at a slow speed. For a 100 pound for ce to overcome a force of 500 pounds in a machine, it would h ave to act through a distance of 5 f eet for every foot that the r esis tance is overcome. Such an action wouid be an extremely slow process in a machine wher e the m echanical ad-vantage runs into terms of hun-dreds of thousands as is frequently the ca.se in a h ydraulic machine . Sometimes t h e ratio denoting the m echanica l advantage of a m achine turns out to be a fractional num-ber . This is the case in the so-call-ed third class lever where the force is applied between the fulcrum and the resistance . In a n ap•plication of this kind, the resistance moves throu gh a la r ge distance while the applied force moves through a short distance . When the mechani-cal advantage is fractional , it · in-dicates a speed machine in which force is sacrificed to gain speed and save time . Such machines as the sewing machine and the bicycle are speed machines. Fina lly, it would be well as a matter of general information, to bring home to the student the va-rious advantages that man derives in the use of machines. First, there is the eco nomic advantage that saves labor. Natural forces, s uch as beasts of burden, steam, electric-ity, water power, are utilized by machines. Man directs a nd the forces of nature do the work. Sec-ond, a machine enables a force to be applied in a conve nient direction . A man might raise bricks and mor-tar to the top of a building by standing on the top of the build-ing and drawing up the material hand over hand by means of a rope. A more convenient way would be to fasten a pulley to the top of the bu ilding and then have some one standing on the ground below pull down on the rope to raise the ma-terial attached to the other end of the rop e drawn over the pull ey. Better still, he could fasten anoth-er pulley somewhere on the ground so that the rope could be drawn parallel to th e g round by means of a horse. Fina lly , he could improve this still more by using pulleys of three sheaves a bove and two sheaves below fastened to the load. In this case the horse would h ave to walk fiv e feet to raise the load one foot . However, the force re-quired to pull up the lo a d would be reduced acco rdin gly. In the last case distance is substituted to save force. It illustra t es the greatest advantage derived from a m achine, the possible mutual substitution of the two work elements, force and distan ce . Eq uation for the simple ma-chines . Lever ..... ...... ..... ... ... .... ... FXl=R X l' Wheel and axle .... ..... .. .. F x r=R X r' Inclined plane .. ..... ...... .. F X l = R X h Pulley ······ ··· ··· ···· ······ ·····"' X n= R Screw ..... .. .. ..... ... ..... .. .. ... F x c= RXP · A short drill in these equations will be found extremely profitable before taking up the numerical prob lems of the t ext. Below is given the prices of sim-nle m achines as listed by apparatus houses: Inclined pla n e with wagon .... $7.00 Wheel and axle ..... .. .... ........ ..... 3.25 Jack scr ew .... .. ................... .... . 1.10 Lever holders ···.···· ······ ······· , ··· ···· .2 5 Pulley .... .... ........... _ ........... .. ,...... .. .50 L . Begeman: 

The Simple Machines

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The Simple Machines

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