Principles of naval engineering - Historic Naval Ships Association

PRINCIPLES OF NAVAL ENGINEERINGenergy which is transferred by the action of aforce through a distance, orwhereE .FD^wk =F X D= work, in foot pounds= force, in pounds= distance (or displacement), in feetIn the case of work done against gravity, theforce is numerically the same as the weight ofthe object or body that is being displaced.It is important to note that no work is doneunless something is displaced from its previousposition. When we lift a 5-pound weight fromthe floor to a table that is 3 feet high, we havedone 15 foot-pounds of work. If we merely standand hold the 5-pound weight, we do not performany work in the technical sense of the term, eventhough we may feel like we are working. In thiscase, actually, all we are doing is exerting forcein order to support the weight against the actionof the force of gravity. The forces are balanced;there is no motion or displacement of the weight,so no work is done.If the force and the displacement are neitheracting in the same direction nor acting in totalopposition, work is done only by that componentof the force which is acting in the direction ofthe displacement of the body or object. A manpushing a lawnmower, for example, is exertingsome force that acts in the direction in whichthe lawnmower is moving; but he is also exertingsome force which acts downward, at rightangles to the direction of displacement. In thiscase, only the forward component of the exertedforce results in work— that is, in the forwardmotion of the lawnmower.Suppose that we move an object in such a waythat it returns to its original position. Have wedone work or haven't we? Let us consider againthe example of lifting a 5-pound weight to thetop of a 3-foot table. By this act ion we have performed15 foot-pounds of work. Now supposethat we let the weight fall back to the floor, sothat it ends up in the same position it had originally.Displacement is zero, so work must bezero. But what has happened to the 15 foot-poundsof work we put into the system when we liftedthe weight to the top of the table? By doing thiswork, we gave the system 15 foot-pounds ofmechanical potential energy. When the weightfell back to the floor, the mechanical potentialenergy was converted into mechanical kineticenergy. In one sense, therefore, we say thatour work was "undone" and that no net workhas been done.On the other hand, we may choose to regardthe two actions separately. In such a case, wesay that we have done 15 foot-pounds of work bylifting the weight and that the force of gravityacting upon the weight has done 15 foot-poundsof work to return the weight to its original positionon the floor. However, we must regard onework as positive and the other as negative. Thetwo cancel each other out, so there is again nonet work. But in this case we have recognizedthat 15 foot-pounds of work were performedtwice, in two separate operations, by two differentagencies.This example has been elaborated at somelength because we may draw several importantinferences from it. First, it may help to clarifythe concept of work as a form of energy thatmust be accounted for. Also, it may help toconvey the real meaning of the statement thatwork is mechanical energy in transition. Workis energy in transition because it occurs onlytemporarily, between other forms of energy, andbecause it must always begin and end as storedenergy. And finally, the example suggests theneed for arbitrary reference planes in connectionwith the measurement of potential energy,kinetic energy, and work. The quantitativeconsideration of any form of energy requires aframe of reference which defines the startingpoint and the stopping point of any particularoperation; the reference planes are practicallyalways relative rather than absolute.Note that mechanical potential energy, mechanicalkinetic energy, and work are allmeasured in the same unit, the foot-pound. Onefoot-pound of work is done when a force of 1pound acts through a distance of 1 foot. Onefoot-pound of mechanical kinetic energy or 1foot-pound of mechanical potential energy isthe amount of energy that would be required toaccomplish 1 foot-pound of work.The amount of work done has nothing to dowith the length of time required to do it. If aweight of 1 pound is lifted through a distanceof 1 foot, 1 foot-pound of work has been done,regardless of whether it was done in half asecond or half an hour. The rate at which workis done is called power. In the field of mechanicalengineering, the horsepower (hp) is thecommon unit of measurement for power. By160