Page:Model steam turbines; how to design and build them (IA modelsteamturbin00harrrich).pdf/12

8 the end of the second of time, the figure 40 represents the acceleration or increase of velocity in the body.

It is evident that the unknown force, which we will call F, is greater than 8 lbs. (the force of gravity) as the acceleration 40 exceeds 32⋅2, and we can therefore find the value of F by rule of three thus: F : 8 : : 40 : 32⋅2; and

This may be stated in words as follows:--

To find the force acting to generate motion in a body, multiply the weight of the body (in pounds) by the acceleration produced (feet per second) and divide the product by the acceleration due to gravity (32⋅2=g). Calling the weight W, and the acceleration attained a, the above can be represented symbolically by


 * F = $8×40/32⋅2$ . .  .  .  .  .  .  . (1)

By definition, unit mass is that quantity of matter contained in a body weighing 32⋅2 lbs. ; therefore the mass of 1 lb. is $Wa/g$; of 8 lbs. $1/32⋅2$, and of W pounds $8/32⋅2$; consequently in (1)$W/32⋅2$ represents the mass of the body in question, and calling this quantity M, (1) can be written


 * F=Ma .  .  .  .  .  .  (2)

that is, Force=Mass×Acceleration; pounds, feet, and second being understood.