43-] RECTILINEAR MOTION. 2I 



This equation shows that the tension is equal to the weight of 

 the stone, not only when it is hanging at rest, but also when- 

 ever it is raised or lowered with constant velocity ; and that the 

 tension is zero if the stone is lowered with an acceleration equal 

 to that of gravity, as is otherwise evident. 



42. The above formula will give the tension T in poundals 

 (or dynes), if the mass m be expressed in pounds (or grammes), 

 and the accelerations in feet (or centimetres) per second per 

 second. 



In engineering practice, gravitation measure is commonly 

 used for weights as well as for the forces that replace con- 

 straints (tensions, pressures, friction, etc.). The engineer would, 

 therefore, divide by g the numerical value of T just found, so as 

 to reduce it to pounds. 



It should be noticed that the general equations of theoretical 

 mechanics are of course independent of the system of units 

 adopted, and that in applying them to numerical examples it 

 is only necessary to use one and the same system of ~ units con- 

 sistently throughout. As modern physics has settled upon 

 mass as a fundamental unit (see Part II., Art. 68), regarding the 

 unit of force as derived from and based upon the unit of mass, 

 this absolute system will always be adopted in this book, unless 

 the contrary be specified. In other words, it will always be 

 assumed that mass is expressed in pounds (or grammes), and 

 consequently force in potmdals (or dynes). 



43. Let us next consider two particles, m lt m v connected 

 by a cord hung over a vertical fixed pulley, as in the apparatus 

 known as Atwood's machine (Fig. 5). If m^ > m%, m-^ will 

 descend while m^ ascends. The effective force of the system 

 formed by the two particles is evidently the difference of the 

 weights of the particles, viz. W 1 W 2 = (m l m^g> while the 

 whole mass moved (neglecting the mass of the cord and of 



