EXAMPLES. 



from the two ends; if <-a.-li Land wh-n un^n-tehed 

 just pass round one rod, and a weight .f 1 11 . w.mld just 

 stretcn it to twice its natural length, shew that it would 

 re a force of 9lbs. to extract tie- middle rod, the co- 

 efficient of friction being equal to JTT. 



In. Two elastic strings are just long enough to fit on a 

 sphere without stretching ; they are placed in two planes at 

 right angles to each other, and the sphere is suspended at 

 their point of intersection. If 20 be the angle subtended at 

 the ivntre by the arc which is unwrapped, shew that 



3?r 11' 

 = -1 X ' 

 being supposed small. 



11. In the common catenary, if the string be slightly 

 sible, shew that its whole <u will }>c jroporti.>nal 



to the product of its length and the height of tre ol 



gravity above the directi i 



12. A uniform rough cylinder is supported with its 

 horizontal by an clastic string without weight; the - 



in the plane which is perpendicular to the axis <>i . nder, 



and passes through its centre of gravity ; the ends of the 

 string are attached to points which are in the same horizontal 

 plane above the cylinder and at a distance equal to the dia- 

 meter of the cylinder. Find how much the string is Btret 



Result. Let 2 W be the weight of the cylinder. n tin- 

 radius of the cylinder, b' the natural length of each vertical 

 portion of the string ; then the extension is 



2//ir 2a. 



A heavy string very slightly elastic is suspended 

 from two points in the same horizontal plane.; shew that it 

 c, I be the lengths of unstretched string whose weights are 

 respectively equal to the tension at the lowest point and tin- 

 modulus of elasticity, the equation to the catenary will be 

 approximately 



