Mechanics An Elementary Text book Theoretical And Practical for Colleges

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Thus the forces are all determined. 32. Problems on Forces in one plane. The con- ditions of equilibrium can be put into different forms. Thus : 31-32] WORK. EQUILIBRIUM. 77 PROPOSITION 27. To prove that a system of forces is in equilibrium if the sum of the moments of the forces about each of three points not in the same straight line is zero. For let the sum of the moments about A be zero, then the system is either in equilibrium or has a resultant force through A. If the sum of the moments a...bout B is also zero, this result- ant must pass through B. Thus it must act in the line AB. But similarly since the sum of the moments about C is also zero the resultant acts along AC', and since A, B, C are not in a straight line this is impossible, hence the resultant is zero, and the system is in equilibrium. In the case in which the forces acting on the body reduce to three, the following proposition is useful. PROPOSITION 28. When three forces in one plane maintain a body in equilibrium their lines of action meet in a point or are parallel*.

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