CHAPTER XVII 
EFFORT, ACCELERATION, AND VELOCITY 
DIAGRAMS 
244. Effort.—If a force P, acting on a body A (Fig. 444) which 
moves or may move in a definite direction BC, 
be resolved into two components, one Q 
parallel to BC, and the other R at right angles 
to BC, the component Q is called the effort of 
P on the body A. 
245. Unbalanced Effort.—If the motion of 
the body A (Fig. 444) is opposed by a force 
S, whose components parallel and perpendicular 
to BC are T and U respectively, then Q-—T Fia. 444. 
is the wnbalanced effort on A, and this unbalanced effort will accelerate 
the speed of A, the work done by it appearing as an increase in the 
kinetic energy of A. If Q-T is negative, then the acceleration of the 
speed of A will also be negative, and the kinetic energy of A will de- 
re by an amount equal to that required to overcome the resistance 
246. Effort-Space Diagram.—In the well-known diagram repre- 
senting the work done by a force or an effort acting through a given 
distance, the base represents the distance or space, and the ordinates 
represent the effort. Such a diagram is shown in Fig. 445, where 
lengths on the base OX represent - 
distances or spaces through which a ® Pp 
body A is moved by an effort P, whose 
magnitude for any position N of the 
body is represented by the ordinate F 
Np of the curve BpDE. The same ps, 
figure also shows that the motion of A ®™ N M > 
is opposed by a resistance R, whose Fra. 445 
magnitude for any position N of the pry 
body is represented by the ordinate Nr of the curve FrDH. From O to N 
the work done by Pis represented by the area of the figure OBpN, and the 
work done on R is represented by the area of the figureOFrN. The differ- 
ence between these two areas, namely, the area of the figure F Bpr, represents 
the excess work which goes to increase the kinetic energy, and therefore also 
to increase the speed of A. Let W=weight of A, »=speed of A when 
at O, v=speed of A when at N, and K=work represented by the area 
FBpr, then x v2)=K, and v= are : 
The speed will increase so long as P is greater than R, and the speed 
283 
