45-] 



RECTILINEAR MOTION. 



45. If the two particles of Art. 43 move on inclined planes 

 intersecting in the horizontal axis of the pulley (Fig. 6), it is 

 only necessary to resolve the weights m^g and m^g into two 

 components, one parallel, the other perpendicular, to the inclined 



Fig. 6. 



plane. If the planes be smooth, the system formed by the 

 two particles is made free by introducing the normal reactions 

 of the planes which counterbalance the perpendicular com- 

 ponents of the weights. The effective force is therefore the 

 difference of the parallel components, and the acceleration is 



m-i sin 01 m sin 



7 L 1 A 



J 



(8) 



where V 2 are the angles of inclination of the planes to the 

 horizon. 



The tension T of the connecting cord is again determined by 

 equating this value of j to the one obtained by considering 

 either of the two particles separately. Thus, m^ taken by itself, 

 becomes free if we introduce not only the normal reaction of 

 the plane, but also the tension of the string. This gives 



(9) 



(10) 



With l = z = TT/2 the formulae (8) to (11) reduce, of course, 

 to the formulae (4) to (7). 



'Similarly, we have for 

 i - 



Hence, 





