460 . Dr. R. C. Tolman on the 



Relation between the Components of Force Parallel 

 and Perpendicular to the Acceleration. 



Fig. 1. 



X 



Consider a body (fig. 1) moving with the velocity 



Let it be accelerated in the Y direction by the action of the 

 component forces ¥ y and F z . 

 From equation (2) we have 



m 



*V 



du x d 

 2~di It 



?n ( 



y/i-i* V'- 



F*= 



V" 



_ tf dt 



c 2 



du„ d 

 + dt 



m 



u 2 

 - ?J 



t Uy 



(3) 



w 



Introducing the condition that there is no acceleration in 

 the X direction, which makes du x \dt = 0, further noting that 

 u2 = ul + u* by the division of equation (3) by (4) we obtain 



F M 



1l T Uy 



F x = 



U x Vy 



F 

 2 x y 



(5) 



Hence in order to accelerate a body in a given direction, 

 we may apply any force F y in the desired direction, but must 

 at the same time apply at right angles another force F^ whose 

 magnitude is given by equation (5). 



From a qualitative consideration, it is also possible to see 

 the necessity of a component of force, perpendicular to the 



