ENERGY 109 



we shall define " force" quantitatively in terms of the 

 change in energy. 



When we move a body from a point of lower to one 

 of higher gravitational potential we must supply a 

 force and we do work. Potential energy is thus 

 stored in the system. But when a body is allowed to 

 pass from a point of higher to one of lower potential, 

 e.g. to fall, what becomes of the potential energy 

 which it possessed? We know that the body moves 

 faster and faster as it falls. An acceleration is the result 

 when its potential energy is allowed to decrease. We 

 shall postpone the quantitative definition of accelera- 

 tion to the chapter on " Rates" and be content at this 

 point with the qualitative definition implied above. 

 The very fact that the body falls, that is, is set into 

 motion, means that it is given kinetic energy. The 

 farther it falls the more potential energy the system 

 has expended. But the farther it falls the greater is its 

 speed, the larger its kinetic energy, and the smaller its 

 potential energy. 



Suppose we consider a numerical case of a body of 

 one pound lifted 20 feet above sea level. It has a 

 potential energy of 20 ft. Ibs. Of course, if the body 

 was two pounds it would have twice as much energy. 

 In fact the potential of the point to which it is lifted 

 is the potential energy possessed by each pound of 

 the body, or as we say the potential of this point is 

 the energy per pound of a body placed there. Allow 

 the body to fall. When it is at a point 19 feet above 

 the zero of potential it has 19 ft. Ibs. of potential per 

 pound. How much kinetic energy has it? If none 

 of the energy of the system has been given up to other 



