ii6.J 



PARALLEL FORCES. 



6 7 



For continuous masses the same formulae hold, except that 

 the summations become integrations. 



The weight W of. a physical body of mass M is therefore a 

 vertical force passing through the centroid of its mass. 



116. Exercises. 



(1) A straight rod (lever} of length 2/= 5 ft. has suspended from its 

 ends masses of 12 and 27 pounds, respectively. Find the point (ful- 

 .crum) on which it balances in a horizontal position : (a) if its own 

 weight be neglected; (^) if it is homogeneous and weighs 2.2 pounds 

 per running foot. 



(2) A straight beam rests in a horizontal position on two supports 

 A, B. The distance between the supports (the span) is 27=24 ft- 

 The beam carries a weight of 14 tons at a distance of 8 ft. from A, and 

 .a weight of 10 tons at 16 ft. from A. Find the pressures on the sup- 

 ports (or the reactions of the supports): (a) when the proper weight of 

 the beam is neglected ; (b) when the beam weighs \ ton per running 

 foot ; (c) when the first third of the beam (from A) weighs -J- ton, the 

 second i ton, the third % ton per running foot. 



(3) A homogeneous circular plate weighing W pounds rests in a 

 horizontal position on three equidistant supports near its edge, (a) What 

 is the least weight P that will upset it when placed on the plate ? (b) If 

 there be four equidistant supports near the edge, what is the least weight 

 that will upset the plate ? 



(4) Construct the resultant of two parallel forces of opposite sense by 

 the graphical method of Arts. 104, 105. 



(5) Solve exercises (i) and (2) by the graphical method. 



84 



23560 



610 



33560 



23560 



13300 



Fig. 25. 



(6) Find the reactions of the supports of a bridge truss of 50 ft. span, 

 produced by a freight locomotive whose weight is distributed over the 

 three pairs of driving wheels and the front truck, as indicated in Fig. 25 : 

 (a) when it stands in the middle of the span ; (b) when its front truck 

 stands over one support. 



