CHAPTEE X 

 MOTION OF A PARTICLE UNDER A VARIABLE FORCE 



203. In almost all the cases of motion of a particle which 

 have so far been considered, the forces acting on the particle 

 have remained constant throughout the whole of the path, so 

 that the acceleration of the particle has been constant. We pro- 

 ceed now to consider the motion of a particle which is acted 

 upon by forces which vary from point to point of the path of 

 the particle. 



These problems fall into two classes, according to whether the 

 path described by the particle is or is not given as one of the data 

 of the problem. The former class is the simplest and is considered 

 first. It includes such cases as the motion of a pendulum, in which 

 the " bob " of the pendulum is constrained to describe a circle by 

 the mechanism of suspension of the pendulum, as also that of the 

 motion of a bead on a wire, in which the bead is compelled to 

 describe the path marked out for it by the wire. 



EQUATIONS OF MOTION 



204. Let s denote the distance described by the particle along 

 its path at any instant t, this distance being measured from any 



fixed point on the path. The velocity along 



ds 

 the path is then Calling this v, the accelera- 



u/t 



. dv d?s 

 tion is or 



We can also obtain a value for the accelera- 

 tion from a knowledge of the forces acting. To find the acceler- 

 ation, we must resolve all the forces which act on the particle in 

 the direction of the path. If S is the component of force in this 



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