ROT 



,*. 2g X Ps Pra 4. Wrs X 1 



t v - - 



-~ " ~ 



2* 

 Or by substituting ~ for v ; s or may be found. 



Ex. 6. Let a weight P, fastened to a string going over a wheel, by its 

 descent cause two weights W, W' to be wound up on two axles. Re-' 

 quired the velocity of P after it has descended t" ; the radii of the wheel 

 and of the two axles being r, , $'. 



Here 



( Ps W X H W X -} = P r* + W* x i-frW* c 8 X ?!? 



\ v/X T 



IX -- - (Pra -f W f 4- W ^ 



P V<i - 



y = gt X 



P ra W r g \\ r/ / g 



p /-a _j_ \y 2 +. W '* ' 

 Here the weight of the wheel and axles are not taken into the account. 



Ex. 7. The force which accelerates the centre of gravity of a sphere, 

 while it rolls down an inclined plane, is to the force by which it would 

 be accelerated, were the sphere to slide, in the ratio of 5 to 7. 



Let W = weight of the sphere, s space descended along the plane, 

 v velocity generated in time t when the sphere rolls, v' ~ do. \vhen it 



slides, then since the distance of the centre of gyration r / 

 have, when the sphere rolls, 



2gXWXsX^ = W t 2 4- W X r 2 X ?- 



H 7 , 

 or gi v X y -v- *. 



When the ephere slide?, 



/.?: v :: 5 : -j. 



