

v MATTER IN RELATION TO MOTION 59 



what force is. All we can know are the effects produced by 

 a something we call force. 



Unit of Force. A change of momentum is produced by force ; 

 the rate at which the momentum changes may therefore be 

 used as a measure of force. The unit of force can be defined 

 in several ways. 



A 'unit of force acting for the unit of time is able to produce a 

 unit of velocity in a unit of mass. 



Or, a unit of force produces a unit of acceleration in a unit of 

 mass. But since the product of a mass and its velocity is 

 spoken of as the momentum of the body, we can measure force 

 by the momentum it generates, the unit force giving rise to the 

 unit 'of moment nm in the unit of time. Equal forces are, 

 therefore, those which produce equal momenta in equal 

 times. 



The momentum generated by a force of two units is twice as 

 great as that produced by one unit ; and, further, a force of one 

 unit acting for two seconds will produce twice the momentum 

 which it would do if it only acted for one second. This is why 

 it is necessary in defining the unit of force to introduce the 

 words ''acting for the unit of time." 



Acceleration produced by a Force. The momentum of any 

 particular body is determined by the body's mass and velocity. 

 As the mass of the body may be regarded as constant, change of 

 momentum can only be produced by changing the velocity. But 

 rate of change of velocity is acceleration, hence when the 

 acceleration of a body is altered, the momentum is altered, and 

 an alteration of momentum signifies, as has been explained, that 

 the body is being acted upon by a force. If the acceleration is 

 uniform, the body must be acted upon by a uniform force. 



Hence we come to the very important fact that the number 

 of units of force in any force is equal to the product of the 

 number of units of mass in any body on which it may 

 act and the number of units of acceleration produced in 

 that mass by the force in question. 



The relation between force, mass, and acceleration may be 

 expressed algebraically as follows : Let F represents the 

 number of units of force in a given force, m the number of 

 units of mass on which it acts producing a units of acceleration, 

 then our definition can be written, 



= m x : a, 



