Elementary Text book of Theoretical Mechanics Kinematics And Statics

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For example, to represent the work done in raising a weight of 600 pounds to a height of 50 feet, let us assume a vertical scale of i inch - 200 pounds and a horizontal scale of i inch = 10 feet. From the origin O, Fig. 47, measure off on the F-axis the length OA = 3 inches (to represent the weight, 600 pounds), and on the Jf-axis measure off the distance OB = 5 inches (to represent the displacement of 50 feet). * Since OA represents a force and OB a Fig. 47- displacement caused by this force, ...it follows that the work done is represented in the diagram by the area of the rectangle OB A C, or what is the same thing OA X OB.
If the diagram is analyzed still further it will be seen that this conclusion is an entirely consistent one. Since the weight remains constant throughout the displacement, a perpendicular erected at B or at any point between O and B, and equal to OA, will represent the magnitude of the force for that particular point in the displacement. The locus of the extremities of such perpendiculars will be a line through point A parallel to OB.


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