PRINCIPLES OF NAVAL ENGINEERING 



energy which is transferred by the action of a 

 force through a distance, or 



where 



^wk 



= F X D 



E . = work, in foot pounds 



F = force, in pounds 



D = distance (or displacement), in feet 



In the case of work done against gravity, the 

 force is numerically the same as the weight of 

 the object or body that is being displaced. 



It is important to note that no work is done 

 unless something is displaced from its previous 

 position. When we lift a 5-pound weight from 

 the floor to a table that is 3 feet high, we have 

 done 15 foot-pounds of work. If we merely stand 

 and hold the 5-pound weight, we do not perform 

 any work in the technical sense of the term, even 

 though we may feel like we are working. In this 

 case, actually, all we are doing is exerting force 

 in order to support the weight against the action 

 of 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 neither 

 acting in the same direction nor acting in total 

 opposition, work is done only by that component 

 of the force which is acting in the direction of 

 the displacement of the body or object. A man 

 pushing a lawnmower, for example, is exerting 

 some force that acts in the direction in which 

 the lawnmower is moving; but he is also exert- 

 ing some force which acts downward, at right 

 angles to the direction of displacement. In this 

 case, only the forward component of the exerted 

 force results in work— that is, in the forward 

 motion of the lawnmower. 



Suppose that we move an object in such a way 

 that it returns to its original position. Have we 

 done work or haven't we? Let us consider again 

 the example of lifting a 5-pound weight to the 

 top of a 3-foot table. By this act ion we have per- 

 formed 15 foot-pounds of work. Now suppose 

 that we let the weight fall back to the floor, so 

 that it ends up in the same position it had origi- 

 nally. Displacement is zero, so work must be 

 zero. But what has happened to the 15 foot-pounds 

 of work we put into the system when we lifted 

 the weight to the top of the table? By doing this 

 work, we gave the system 15 foot-pounds of 

 mechanical potential energy. When the weight 



fell back to the floor, the mechanical potential 

 energy was converted into mechanical kinetic 

 energy. In one sense, therefore, we say that 

 our work was "undone" and that no net work 

 has been done. 



On the other hand, we may choose to regard 

 the two actions separately. In such a case, we 

 say that we have done 15 foot-pounds of work by 

 lifting the weight and that the force of gravity 

 acting upon the weight has done 15 foot-pounds 

 of work to return the weight to its original posi- 

 tion on the floor. However, we must regard one 

 work as positive and the other as negative. The 

 two cancel each other out, so there is again no 

 net work. But in this case we have recognized 

 that 15 foot-pounds of work were performed 

 twice, in two separate operations, by two dif- 

 ferent agencies. 



This example has been elaborated at some 

 length because we may draw several important 

 inferences from it. First, it may help to clarify 

 the concept of work as a form of energy that 

 must be accounted for. Also, it may help to 

 convey the real meaning of the statement that 

 work is mechanical energy in transition. Work 

 is energy in transition because it occurs only 

 temporarily, between other forms of energy, and 

 because it must always begin and end as stored 

 energy. And finally, the example suggests the 

 need for arbitrary reference planes in connec- 

 tion with the measurement of potential energy, 

 kinetic energy, and work. The quantitative 

 consideration of any form of energy requires a 

 frame of reference which defines the starting 

 point and the stopping point of any particular 

 operation; the reference planes are practically 

 always relative rather than absolute. 



Note that mechanical potential energy, me- 

 chanical kinetic energy, and work are all 

 measured in the same unit, the foot-pound. One 

 foot-pound of work is done when a force of 1 

 pound acts through a distance of 1 foot. One 

 foot-pound of mechanical kinetic energy or 1 

 foot-pound of mechanical potential energy is 

 the amount of energy that would be required to 

 accomplish 1 foot-pound of work. 



The amount of work done has nothing to do 

 with the length of time required to do it. If a 

 weight of 1 pound is lifted through a distance 

 of 1 foot, 1 foot-pound of work has been done, 

 regardless of whether it was done in half a 

 second or half an hour. The rate at which work 

 is done is called power. In the field of mechani- 

 cal engineering, the horsepower (hp) is the 

 common unit of measurement for power. By 



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