ENERGY. 79 



157. Ail Easier Method. If we can obtain the 

 same result without the trouble of finding how high the 

 given velocity could raise it, it is generally desirable to do 

 so. Be it remembered that the two elements of our meas- 

 ure are units of weight and units of height. The first of 

 these is given ; for the second we may substitute its equiv- 

 alent in terms of the velocity which also is given. The 

 determination of this equivalent is our present problem. 

 We must use our knowledge of the laws of falling bodies. 

 Our vertical height is the whole space passed over by an 

 ascending body ( 132). We have given v to find 8. 



gt = v. (Formula 1, Falling Bodies.) 



9 



S = %gP. (Formula 3, Falling Bodies.) 

 Substituting the above value of f, we have, 



Energy = ivS (the weight into the height). Substitut- 

 ing our new value for 8 9 we have the following important 



formula : wv z 



Kinetic Energy = - ti . 

 0g 



158. Two Types of Energy. There are two types 

 of energy which may be designated as energy of motion 

 and energy of position. With the first of these we are 

 familiar. A falling weight or running stream, possesses 

 energy of motion ; it is able to overcome resistance by 

 reason of its weight and velocity. On the other hand, be- 

 fore the weight began to fall, while, as yet, it had no 



