78 STATICS OF SYSTEMS OF PARTICLES 



2. A weight of 2 1 pounds stands on a rough table. A string tied to the 

 base of the weight hangs over the edge of the table and has attached to it 

 a second weight which hangs freely. If the coefficients of friction between 

 the weight and the table and the string and the table are ^ and respec- 

 tively, find how heavy the hanging weight must be to start the other weight 

 into motion. 



3. A weight of 2500 pounds is to be raised from the hold of a ship. A rope 

 attached to the weight makes 3^ turns round a steam windlass, its other end 

 being held by a seaman. With what force must he pull his end of the rope so 

 as to raise the weight when the windlass is in motion ? (/* = |.) 



4. In the last question, find what pull would have to be exerted on the rope 

 if the windlass were at rest. 



5. It is found that two men can hold a weight on a rope by taking three 

 turns about a post, and that one of them can do it alone by taking one half 

 turn extra. If each can pull with a force of 220 pounds weight, find the weight 

 sustained. 



6. In a tug of war the rope is observed to rub against a post at the critical 

 moment, in such a way that the two parts of the rope make an angle of 1 with 

 one another. If the coefficient of friction between the rope and the post is |, 

 show that this imposes a handicap on the winning side equal to about .0029 

 times its aggregate pull. 



Suspension Bridge 



56. An interesting problem is afforded by the kind of suspen- 

 sion bridge in which the weight of the bridge (supposed horizontal) 

 is taken by a suspension cable by means of vertical chains con- 

 necting the bridge with the cable. 

 Let us, for simplicity, agree to 

 neglect the weights of the chains 

 and cable, and suppose the weight 

 of the bridge to be distributed 

 evenly along its length. 



Let be the lowest point of 

 the cable, and let P be any other 

 point. Let o, p be the points of the bridge vertically below 0, P, 

 and let op = x. Let the tension at P be T, and let that at be H. 

 Let the direction of the cable at P make an angle 6 with the 

 horizontal. 



