SIMPLE STRUCTURES 



195 



282. In a Weston differential pulley the diameters of the sheaves in the upper 

 block are 8 in. and 9 in. Find the theoretical advantage. 



283. In the differential axle shown in Fig. 134 the rope is wound in oppos in- 

 directions around the two axles so that it unwinds from one and winds up on t| )( - 

 other at the same time. Find its mechanical advantage if the radius of tin- liu-,- 

 drum is #, of the small drum is r, and of the crank is c. 



284. A differential screw consists of two screws, one inside the other. Tin- 

 outer screw works through a fixed block, and is turned by means of a lever. This 

 screw is cored out and tapped for a smaller screw of less pitch which works through 

 another block, free to move along the axis of the screw, but prevented from rotat- 

 ing. Find the mechanical advantage of such a differential screw if the l-v-r 

 arm is 3 ft. long, the outer screw 



has 8 threads to the inch, and the 

 inner screw has 10 threads to the inch 



FIG. 135 



285. The bed of a straight river makes an angle a with the horizontal. Taking 

 a cross section perpendicular to the course of the river, the sides of the valley are 

 inclined at an angle /3 to the horizontal. Find the angle which the tributaries of 

 the river make with it. 



286. Find the least horizontal force necessary to pull a wheel 30 in. in diameter, 

 carrying a load of 500 lb., over an obstacle 4 in. high. 



287. A steelyard weighs 61b. and has its center of gravity in the short arm at 

 a distance of 1 in. from the fulcrum, and the center of suspension is 3 in. from the 

 fulcrum. The movable weight weighs 4 lb. Find the zero graduation, and the dis- 

 tance between successive pound graduations. 



288. A ladder 50ft. long, weighing 75 lb., rests with its upper end against a 

 smooth vertical wall and its lower end on rough horizontal ground. Find the 

 reactions of the supports when the ladder is inclined 20 to the vertical. 



289. A circular, three-legged table, 4 ft. in diameter, weighs 50 lb. and carries 

 a load of 100 lb. 10 inches from the center and in a line joining the center and one 

 leg. Find the pressure between each foot and the floor. Find also the smallest load 

 which when hung from the edge of the table will cause it to tip over. 



290. The average turning moment exerted on the handle of a screw driver is 

 120 in.-lb. The screw has a square slot, but the point of the screw driver is beveled 

 to an angle of 10 (Fig. 135). If the point of the screw driver is in. wide, find the 

 vertical force tending to raise the screw driver out of the slot. 



