XXIV INTRODUCTION. 



Work, w, was performed in raising the stone to rest upon the 

 tower. 



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



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

 w = m g s. 



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 = V~2?7 (see above (3). 

 V 2 = 2gs. 

 = 2m gs. 



-,-rn 



2 V ~ 



m g s was the expression for the potential energy of the stone while 

 it was still resting on the height; - V 2 is the kinetic energy corre- 



sponding to this potential energy (Briicke). 



Potential energy may be transformed into mechanical energy under 

 the most varied conditions; it may also be transferred from one body 

 to another. 



The movement of a pendulum is a striking example of the former. When the 

 pendulum is at the highest point of its excursion, it must be regarded as absolutely 

 at rest for an instant, and as endowed with potential energy, thus corresponding 

 with the raised stone in the previous instance. During the swing of the pendulum, 

 this potential energy is changed into kinetic energy, which is greatest when the 

 pendulum is moving most rapidly towards the vertical. As it rises again from 

 the vertical position, it moves more slowly, and the kinetic energy is changed 

 into potential energy, which once more reaches its maximum, when the pen- 

 dulum comes to rest at the utmost limit of its excursion. Were it not for the 

 resistances continually opposed to its movements, such as the resistance of the 

 air, and friction, the movement of the pendulum, due to the alternating change of 

 kinetic into potential energy and vice versd, would continue uninterruptedly, as 

 with a mathematical pendulum. Suppose the swinging ball of the pendulum, 

 when exactly in a vertical position, impinged upon a resting but movable sphere, 

 the potential energy of the ball of the pendulum would be transferred directly to 

 the sphere, provided that the elasticity of the ball of the pendulum and the sphere 

 were complete; the pendulum would come to rest, while the sphere would move 

 onward with an equal amount of kinetic energy, provided there were no resistance 

 to its movement. This is an example of the transference of kinetic energy from 

 one body to another. Lastly, suppose that a stretched watch-spring on uncoiling 

 causes another spring to become coiled; and we have another example of the 

 transference of kinetic energy from one body to another. 



The following general statement is deducible from the foregoing 

 examples: If, in a system, the individual moving masses approach the 

 final position of equilibrium, then in this system the sum of the kinetic 



