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DYNAMICS OF A POINT. 



I. Rectilinear Motion, Kinematics. 



1355. A heavy particle is attached by an elastic string to a 

 fixed point, from which the particle is allowed to fall freely; when 

 the particle is in its lowest position the length of the string is 

 twice its natural length ; prove that the coefficient of elasticity is 

 four times the weight of the particle, and find the time during 

 which the string is extended beyond its natural length. 



1356. A particle at B is attached by an elastic string at its 

 natural length to a point A, and attracted by a force varying as 

 the distance to a point C in BA produced, BG being equal to 4J5J, 

 and the particle just reaches the centre of force; prove that the 

 velocity of the particle will be greatest at a point which divides 

 CA in the ratio 8 : 7. 



1357. A particle is attracted to a fixed point by a force 

 = p (dist.)~*, and repelled from the point by a constant force f\ 

 the particle is placed at a distance a from the centre, at which 

 point the attractive force is four times as great as the repulsive, 

 and projected directly from the centre with velocity vj prove 

 that, (1) the particle will move to infinity or not according as 



(2) if x, x -t- c be the distances from the centre of force of two 

 positions of the particle, the time of describing the given dis- 

 tance c between them will be greatest when x (x + c) = 4a 2 . If 

 v= J(2af) or 3 *J(2f), determine the time of describing any 

 distance. 



