20 



KINETICS OF A PARTICLE. 



[39- 



39. As long as a single free particle only is considered, there 

 is generally no advantage in introducing the idea of force ; the 

 equation of motion can be divided by m, and this reduces it to 

 a purely kinematical form. 



Thus, for a particle of mass m falling in vacuo, the dynamical 

 equation of motion is 



where W=-mg is the weight of the particle; i.e. the force of 

 attraction exerted by the earth on the particle (in poundals or 

 dynes, if m be expressed in pounds or grammes, see Part II., 

 Art. 115). Dividing by m, we find the kinematical equation 



which has been treated in Part I., Arts. 107-114. 



The following articles give examples in which it is more con- 

 venient to retain the idea of force. 



40. Let us consider a mass m that is being raised or lowered 

 by means of a rope or chain (Fig. 4), such as a building stone 

 suspended from a derrick. The rope acts as a 

 constraint) conditioning the motion of the stone. 

 To make the stone free we may imagine the 

 rope cut just above the stone and the tension 

 of the rope, T, introduced as a substitute. The 

 stone then moves under the action of two forces, 

 viz. its weight W=mg and the tension T of 

 the rope. Taking the downward sense as posi- 

 tive, we have the equation of motion, 



Fig. 4. 



(2) 



41. Writing/ for the acceleration d*s/dt z with which the stone 

 is being lowered or raised, we find for the tension T of the rope 



T=m(g-j). (3) 



