36 INTRODUCTION TO DYNAMICS. [60. 



60. The product mj of the mass m of a particle into its 

 acceleration j is called force. Denoting it by F, we may write 

 our equations (2) in the form 



p 

 mvFt, s=\ fi, ^mv*=Fs. (3) 



As long as the velocity of a particle of constant mass remains 

 constant, its momentum remains unchanged. If the velocity 

 changes uniformly from the value v at the time t to v' at the 

 time t', the corresponding change of momentum is 



mv' mv mjt ! mjt = F (/'/); (4) 



hence . , p-*"^. " (?) 



Here the acceleration, and hence the force, was assumed con- 

 stant. If F be variable, we have in the limit when t' t 



becomes dt t 



j? d(mv) dv //cx 



... F= * =m -* ' (6) 



Instead of defining force as the product of mass and accelera- 

 tion, we may therefore define it as the rate of change of momen- 

 tum with the time. 



61. Integrating equation (6), we find 



Fdt = mv 1 mv. (7) 



The product F(t' t) of a constant force into the time t' t during 



which it acts, and in the case of a variable force, the time- 



Jt r 

 Fdt, is called the impulse of the force during this time. 



It appears from the equations (4) and (7) that the impulse 

 of a force during a given time is equal to the change of momen- 

 tum during that time. 



62. The idea of force is no doubt primarily derived from the sensa- 

 tion produced in a person by the exertion of his " muscular, force." 



