22 



KINETICS OF A PARTICLE. [44. 



Hence, we have for the acceleration 



the pulley) is 

 j of the system, 



This acceleration is constant, and the relations between space, 

 time, and velocity are found just as for a single particle falling 

 freely, except that the acceleration of gravity g 

 is replaced by the fraction (m l m 2 )/(m 1 -\-m 2 ) 

 of g. It follows that if the masses m lt m 2 be 

 selected nearly equal, the acceleration will be 

 small, and the motion can be observed more 

 conveniently than that of a freely falling body. 



W 2 



Fig. 5. 



44. The tension T of the cord is, of course, 

 the same at every point of the cord if, as is 

 here assumed, the weight of the cord and the 

 axle-friction of the pulley be neglected. To 

 determine this tension, we have only to consider either particle 

 separately. 



If the cord be cut just above m lt and the tension T 

 be introduced, the particle m 1 will move like a free particle , 

 under the action of the resultant force W l T=m l gT./ 

 Hence, as the sense of the acceleration/ of m l agrees with that 



m lg -T 

 m 1 



Similarly, we have for the acceleration of 

 opposite to that of g y 



m^g-T 



(6) 



Eliminating / between any two of the equations (4), (5), (6), 

 we find the tension 



(7) 



