86 STATICS OF SYSTEMS OF PARTICLES 



Putting x = ^ h, we find as the total increase in a span of 

 length h, caused by sagging, 



EXAMPLES 



1. The entire load of a suspension bridge is 320 tons, the span is 640 feet, 

 and the height is 60 feet. Find the tension at the points of support, and also 

 the tension at the lowest point. 



2. The weight of a freely suspended cable is 320 tons ; the distance between 

 the two points of support, which are in the same horizontal line, is 640 feet, 

 and the height of these points above the lowest point of the cable is 60 feet. 

 Find the tension at the points of support, and also the tension at the lowest point. 



3. The wire fora telegraph line cannot sustain a weight of more than a mile 

 of its own length without breaking. If the wire is stretched on poles at equal 

 intervals of 88 yards, what is the least sag permissible ? 



4. In the last question how much wire is required for a mile of the line ? 



5. A telegraph line has to be built of a certain kind of wire, stretched over 

 evenly spaced posts. Show that if the number of posts is very large, the line 

 will be built most economically as regards the cost of wire and posts, if the 

 cost of the posts equals twice that of the additional length of wire required by 

 "sagging." 



GENERAL EXAMPLES 



1. A block of stone weighing \ ton is raised by means of a rope 

 which passes over a pulley vertically above it and. is wound upon a wind- 

 lass one foot in diameter. The windlass is worked by two men who turn 

 cranks of length 2 feet. What force must each man exert perpendicular 

 to the cranks ? 



2. A man sitting in one scale of a balance presses with a force of 60 

 pounds against the beam in a vertical direction and at a point halfway 

 between the fulcrum and the end of the beam from which his scale is sup- 

 ported. If the beam is 5 feet long, find the additional weight which must 

 be put in the other scale to maintain equilibrium. 



3. The scales of a false balance hang at unequal distances a, b from 

 the fulcrum, but balance when empty. A weight appears to have weights 

 P, Q, respectively when weighed in the two scales. Find its true weight 

 and prove that 



