By A. E. H. LOVE
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Extra resources for A TREATISE ON THE MATHEMATICAL THEORY OF ELASTICITY VOLUME-1
60. -The center of gravit~ as has just been explained is determined by the distribution of mass in a body or system of bodies. It has certain remarkable • , , • :;, Y MECHANICS 36 properties quite independent of weight, and is therefore also called the center oj mass or center of inertia of the body or system. For example, a freely rotating body like a spinning projectile will always rotate about an axis through its center of mass. FlO. 29. 61. -When a body is hung by a cord or balanced on a point the center of gravity must be in the vertical line passing through the point of support.
Me condusion is reached taking moments about some point such as C. 57. -If in the case just treated the upward force 4 is changed to 6, we have a case that calls for special consideration. The upward forces are exactly equal to the downward forces and yet the bar is not in equilibrium, for taking moments about P we find that the clockwise moment is 10 while the counterclockwise moment is 2 + 18 = 20. Here, then, there is a com- MECHANICS 34 binaUon 0/ forces that does not tend to produce translation, but simply rotation.
And having a 2-lb. weight on one end and a 7-lb. weight on the other. 7. Forces 2 and 4 actillg upward are applied 'to a horizontal bar at 2 ft. and 4 ft. from the left-hand end, respectively, also forces 3 and I acting downward are applied at 1 ft. and Sft. from the eameend. Find amount and point of application of a single force producing eqjJilibrium. 8. CUI downward at a point 3 ft. from the left-hand end of the bar. WORK AND ENERGY 39 9. A board 2 ft. square is acted on by five forees applied at the same point6 as shown in figure 22, but the forcel!