190 



MOTION UNDER CONSTANT FORCES 



time 



is ft. After falling a distance h its velocity is, by equation (48), 

 equal to ^J'lgh. This is frequently spoken of as the "velocity 



due to a height h" 



We notice that the distance 

 fallen varies as the square of the 

 time during which the body has 

 been falling. In fig. 103 the 

 time is measured horizontally, 

 while the distance fallen is 

 measured vertically. The thick 

 curve gives a graphical repre- 

 sentation of the distance fallen. 

 Denoting the horizontal dis- 

 tance by x and the vertical by 

 y, we have x = t,y = ^gt*, so that 



distance 

 fallen 



FIG. 103 



156. This is the equation of a parabola, so that the curve is a 

 parabola. The graph can be obtained experimentally by a method 

 known as Morin's method. A weight 

 P is free to fall vertically in a slot 

 formed in a rod AB, and is arranged 

 so that, as it falls, a pencil attached to 

 it makes a mark on a drum CD which 

 is covered with paper. The drum is 

 made to rotate uniformly. On unroll- 

 ing the paper from the drum we obtain 

 the graph of fig. 103, for the hori- 

 zontal distance is proportional to the 

 time, while the vertical is the distance 

 fallen through. The fact that the curve 

 obtained in this way is accurately a 

 parabola gives experimental confirma- 

 tion of the fact that motion under gravity is motion with uni- 

 form acceleration. 



D 



FIG. 104 



