

MISCELLANEOUS KXAMPLE& 



1 MICD of a cubical box. 



hinges at A : a given angle to toe 



by a d string connecting C with a point vertically 



over A : find the pressure on each hinge. 



2. Two equal forces act on a cube whose centre is fixed, 

 along diagonals which do not f two adjacent frees: 



ic couple whii-h u ill keep the cube at rest 



2fe**/f. Let P denote each force, a the edge of the . 

 the moment of the required couple is either J j- ac- 



cording to the directions of the two given 



ree equal heavy rods in the position of the three 

 edges of an inverted triangular pyramid are in equilibrium 

 under the following circumstances; their upper extremities 

 are connected by strings of equal lengths, and their lower 

 Miitics are attached to a hinge about which the rods 

 may move freely in all directions. lue tension of the 



4. A given number of uniform heavy rods, all of the 

 same weight, ha\ romities jointed together at a 



<>, about which they can turn freely; and being 

 .rough a circular hole in a honaontal plane 

 with their hinge end downwards, are spread out symmetri- 

 cally along the ence of the bole like the ribs of 

 a conical basket If a heavy sphere be now placed in the 

 or of the system of rods, so as to be supported by them, 

 nine the position of rest 



5. A with its base resting against a smooth 

 col plane is held up by a string fastened to it at a point 



... 



is A. Shew that A must be greater than &-*a tan* 



i!i;m 6, where 26 is the altitude of the cylinder, the radius 



<f the base, and B the angle which the string makes with the 



