EXAMPLES. 



4. A rectangular table stands on a rou-h inclined plain-, 

 and has two sides horizontal ; it' tin- codlicient of friction of 

 the lowest feet be /i and that of the others be //, iin<l the 

 iiu li nation of the plane when the table is on the point <>i 

 sliding. 



B, Two unequal wei-hts on a rough inclined j 

 connected by a string which passes through a fixed pully in 

 the plane : find the greatest inclination of the plane con.- 

 with the equilibrium of the weights. 



G. A heavy uniform rod whose length is 2a is supp< 

 by resting on a rough peg, a string of length J be in L: attached 

 to one end of the rod and fastened to a given point in the 

 same horizontal plane with the peg. If when the rod is on the 

 point of sliding the string is perpendicular to it the coefficient 



of friction is - . 

 a 



7. Two weights P t Q of similar material rest on a rough 

 double inclined plane, and are connected by a fine string 

 passing over the common vertex ; Q is on the point of motion 

 down the plane, shew that the weight which may be added to 

 P without producing motion is 



sin (-<) sin (a -<)' 



a, ft being the angles of inclination of the planes and tan </> 

 the coefficient of friction. 



8. A weight P is attached to a point in the circumference 

 of a rough circular ring whose weight is W-. shew that the 

 ring will hang on a horizontal rod in a plane perpendicnlai to 

 it with any point of the ring in contact with the rod, if the 

 coefficient of friction be not less than 



* jr 



, where n = -~ . 



0. Two equal heavy rings are moveable on a horizontal 

 rough rod; a string of given length which passes through 



