34 INTRODUCTION TO DYNAMICS. [55. 



II. Momentum; Farce; Energy. 



55. Let us consider a point moving with constant accelera- 

 tion from rest in a straight line. We know from Kinematics 

 (Art. in) that its motion is determined by the equations 



v=jt, s = yfl, J *=;>, (I) 



where s is the distance passed over in the time /, v the velocity, 

 and j the acceleration at the time t. 



If, now, for the single point we substitute an Mr-tuple point, 

 i.e. if we endow our point with the mass m, and thus make it a 

 particle (see Art. 6), the equations (i) must be multiplied by m> 

 and we obtain 



(2) 



The quantities mv, mj y \rniP occurring in these equations 

 have received special names because they correspond to certain 

 physical conceptions of great importance. 



56. The product mv of the mass m. of a particle into its 

 velocity v is called the momentum, or the quantity of motion, of 

 the particle. 



57. In observing the behaviour of a physical body in motion, we 

 notice that the effect it produces for instance, when impinging on 

 another body, or more generally, whenever its. velocity is changed 

 depends not only on its velocity, but also on its mass. Familiar exam- 

 ples are the following : a loaded railroad car is not so easily stopped as- 

 an empty one ; the destructive effect of a cannon-ball depends both on 

 its velocity and on its mass ; the larger a fly-wheel, the more difficult is 

 it to give it a certain velocity ; etc. 



It is from experiences of this kind that the physical idea of mass is 

 derived. 



The fact that any change of motion in a physical body is affected by 

 its mass is sometimes ascribed to the so-called "inertia" or "force of 

 inertia," of matter, which means, however, nothing else but the property 

 of possessing mass. ^ V 



