DYNAMICS OF A POINT. 



II. Central Forces. 



1386. Prove that the parabola y 9 = 4o# can be described 

 under a constant force parallel to the axis of y, and a force 

 ]>r'i><>rti>nal to y parallel to the axis of x. Also under two 

 forces 4/x. (c + x), //.y, parallel to the axes of x and y. 



1387. A cardioid is described with constant angular velocity 

 about the cusp under a constant force to the cusp and another 

 constant force ; prove that the magnitude of the latter is twice 

 that of the former, and that its direction always touches an epi- 

 cycloid generated by a circle of radius a rolling on one of radius 

 *2a j Sa being the length of the axis. 



1388. The force to the pole, tinder which the hyperbc la 



r cos 20 = a cos 



cos* 20 



can be described, will vary as r-^ . 



cos*0 



1389. SY is the perpendicular from the pole S of a 1< in- 

 to upon the tangent at P, ;u d tl.r 1. cus of Y is d.M-ribed by 

 tide under a force to S : prove that this force ocSI J ~ l \ 



1390. The force to the pole under which the pedal of a 

 given curve r=f(p) can be described will vary as 



r dr 



'(/' ' 

 If the given curve be 



tli; inm; will be const: 



1391. A ] i 



of curvature at the vertex ; prove tl at any 



w. 1U 



