XXXV111 INTRODUCTION. 



i.e., the distances are as the square of the times. Hence, from (1) and (2) it follows (by 

 eliminating that 



V-V^ (3)- 



The velocities are as the square roots of the distances traversed 



Therefore ^=s (4). 



The freely falling body, and in fact every freely moving body, possesses kinetic 

 energy, and is in a certain sense a magazine of energy. The kinetic energy of any- 

 moving body is always equal to the product of its weight (estimated by the balance), 

 and the height to which it would rise from the earth, if it were thrown from the 

 earth w r ith its own velocity. 



Let W represent the kinetic energy of the moving body, and P its weight, then AV = P.s, so 

 that from (4) it follows that 



w = p ^ < 5 >- 



Hence, the kinetic energy of a body is proportional to the square of its velocity. 



Work. If a force (pressure, strain, tension) be so applied to a body as to move 

 it, a certain amount of work is performed. The amount of work is equal to the 

 product of the amount of the pressure or strain which moves the body, and of the 

 distance through which it is moved. 



Let K represent the force acting on the body, and S the distance, then the work W = KS. 

 The attraction between the earth and any body raised above it is a source of work. 



It is usual to express the value of K in kilogrammes, and S in metres, so that 

 the " unit of work " is the kilogramme-metre, i.e., the force which is required to 

 raise 1 kilo, to the height of 1 metre. 



2. Potential Energy. The transformation of Potential into Kinetic Energy, and 

 conversely: Besides kinetic energy, there is also "potential energy," or energy of 

 position. By this term are meant various forms of energy, which are suspended in 

 their action, and which, although they may cause motion, are not in themselves 

 motion. A coiled watch-spring kept in this position, a stone resting upon a tower, 

 are instances of bodies possessing potential energy, or the energy of position. It 

 requires merely a push to develop kinetic from the potential energy, or to transform 

 potential into kinetic energy. 



Work, u\ w r as performed in raising the stone to rest upon the tower. 



w=p, s, where p = the weight and s = the height, 

 p*=m.g, is = the product of the mass (m), and the force of gravity (g), so that v)*=mgs. 



This is at the same time the expression for the potential energy of the stone. 

 This potential energy may readily be transformed into kinetic energy by merely 

 pushing the stone so that it falls from the tower. The kinetic energy of the stone 

 is equal to the final velocity with which it impinges upon the earth. 



V \J2g s (see above (3) ). 

 V 2 = 2gs. 

 7ttV 2 =- 2mgr*. 



-V-= mgs. 

 m g 8 was the expression for the potential energy of the stone while it was still 



