FORCES. 21 



themselves being movement. The wound clock-spring prevented from 

 unwinding by a catch, the stone resting upon the cornice of a tower, are 

 illustrations of bodies possessing potential energy. Only an impulse is 

 required to evolve actual from potential energy or to convert the poten- 

 tial into kinetic energy. The stone resting upon the cornice of the tower 

 was raised to that place by means of work (A). 



A = p, s, p representing the weight and s the height, p = m, g, thus the 

 equivalent of the product of the mass (m) and the force of gravity (g) ; therefore 

 A = m, g, s. 



This is at the same time the expression for the potential energy 

 residing within the stone. This elastic energy may readily be converted 

 into kinetic energy by causing the stone to fall from the edge of the 

 tower by means of a slight push. The actual energy of the stone is 

 equal to the terminal velocity with which it reaches the ground. 



= \/2~gs (see 3). 



v* = 2 gs 



mv 3 = 2ings 

 m , 



v a = mgs 



m, g, s represents the potential energy residing within the stone at 

 rest in its elevated position; v 2 is thus the kinetic energy correspond- 

 ing to this potential energy. 



Actual energy and mechanical potential energy can be transformed 

 into each other under most varied conditions; they can also be con- 

 veyed from one body to another. 



Of the first statement the movement of a pendulum furnishes a striking 

 illustration. The pendulum-bob, located at the highest point of the excursion, 

 and which must be considered to be in a state of absolute rest at this point for 

 a moment, is, exactly as the resting stone in the previous illustration, provided 

 with potential energy. In the free movement that now takes place this potential 

 energy is, converted into kinetic energy, which is greatest when the bob with 

 greatest movement is in the vertical plane. Rising again from this point, the 

 kinetic energy, with diminution in the free movement, is transformed into poten- 

 tial energy, which again attains its maximum at the resting-point at the height 

 of the excursion. In the absence of constantly operating resistances (resistance 

 of the air, friction) this play of the alternate transformation of kinetic energy into 

 potential energy and the reverse taking place in the pendulum would continue 

 uninterruptedly (as in a mathematical pendulum). If it be conceived that the 

 swinging pendulum-bob encounters exactly in the vertical plane a movable body 

 resting at this point, such as a sphere, then (assuming perfect elasticity on the 

 part of the pendulum-bob and the sphere) the kinetic energy of the pendulum-bob 

 would be transmitted directly to the sphere: The pendulum would come to rest, 

 while the sphere would continue in movement with equal kinetic energy (again 

 providing there is no resistance). This is an instance of the transmission of 

 kinetic energy from one body to another. Finally it may be conceived that a 

 coiled clock-spring in unwinding causes another to become coiled. This would be 

 an instance of the transmission of potential energy from one body to another. 



From the illustrations given the general proposition may be deduced : 

 If in a system the individual moving masses approach a final condition 

 of equilibrium, the sum of the kinetic energies in the system will be 

 increased; and if the particles are removed from the final condition of 

 equilibrium, then the sum of the potential energies is increased at the 

 expense of the kinetic energies; that is, the kinetic energies diminish. 



