FALLING BODIES. OO 



. Unimpeded Fall. By transferring matter 

 from K' to K, the velocity with which the weights move 

 will be increased. When all of K' has been transferred to 

 K, the weights will fall, in this latitude, 16.08 ft. 

 or J^.9 m. during the first second. 



If the plane be given a greater inclination, the ball will, 

 of course, roll more rapidly and our unit of space will in- 

 crease from one foot, as supposed thus far, to two, three, 

 four or five feet, and so on, but the number of such spaces 

 will remain as indicated in the table above. By disre- 

 garding the resistance of the air, we may say that when 

 the plane becomes vertical, the body becomes a freely 

 falling body. Our unit of space has now become 16.08 ft. 

 or 4.9 m. It will fall this distance during the first second, 

 three times this distance during the next second, five times 

 this distance during the third second, and so on. 



127. Increment of Velocity. During the first 

 second the freely falling body will gain a velocity 

 of 32.16 feet. It will make a like gain of velocity 

 during each subsequent second of its fall. This distance 

 is therefore called the increment of velocity due to gravity, 

 and is generally represented by g = 32.16 ft. or 9.8 m. 



Note This value must not be forgotten. 



128. Formulas for Falling Bodies. If now we 



represent our space by \g, the velocity at the end of any 

 second by v, the number of seconds by t, the spaces fallen 

 each second by s, and the total space fallen through by S, 

 we shall have the following formulas for freely falling 

 bodies : 



(1.) v=gt or \g x 2. 



(2.) a = te(2*_l). 

 (3.) S = %gt\ 



