66 STATICS OF SYSTEMS OF PARTICLES 



EXAMPLES 



1. Eight sailors, each pressing on the arm of a capstan with a horizontal force 

 of 100 Ibs., at a distance of 8 feet from its center, can just raise the anchor. 

 The radius of the axle of the capstan is 12 inches. Find the pull on the cable 

 which raises the anchor. 



2. In the apparatus of fig. 33 the weight Pis disconnected, and the free end 

 of the string is tied to the same point on Q as the other string. Show that in 

 equilibrium this point is vertically below the axis. 



3. A wheel is free to turn about a horizontal axis, and has fastened to it 

 two strings which are wound round its circumference in opposite directions. 

 The other ends are both tied to a small ring from which a weight is suspended. 

 Show that when the system is at rest the two strings will make equal angles 

 with the vertical. 



4. A man finds that he can just move a lock gate against the pressure of the 

 water, by pressing with a horizontal force of 150 Ibs. at a distance of 8 feet 

 from the pivot. What force must he exert if he presses at a distance of 9 feet 

 from the pivot ? 



5. A wheel capable of turning freely about a horizontal axis, has a weight 

 of 2 pounds fixed to the end of a spoke which makes an angle of 60 with the 

 horizontal. What weight must be attached to the end of a horizontal spoke to 

 prevent motion taking place ? 



6. A drawbridge is raised by a chain attached to the end farthest removed 

 from the hinges. When the bridge is at rest in a horizontal position, the chain 

 makes an angle of 60 with the bridge, and the pull on the chain necessary to 

 move the bridge is equal to the weight of three tons. Find what additional 

 pull is required in the chain when a weight of one ton is placed at the middle 

 point of the bridge. 



FOKCES IN ONE PLANE 



51. The simplest problems in statics are always those in which 

 all the forces have their lines of action in one plane. In such a 

 problem it is obviously most convenient to take moments about 

 a line perpendicular to the plane in which the forces act. Let any 

 such line intersect the plane in a point P. Each force is entirely 

 perpendicular to the line about which moments are taken, so that 

 the moment is equal to the product of the force and the shortest 

 distance of the line of action of the force from P. 



Taking moments about an axis which intersects the plane of 

 the forces at right angles in a point P is often spoken of as taking 



