Decembeb 24, 1909] 



SCIENCE 



921 



eration 4 in a body whose weight is W, then 

 the force in pounds is numerically equal to 

 the weight in pounds divided by 32.2 and 

 multiplied by the acceleration in feet per sec- 

 ond per second. 



Work, Energy, Effect of Force Acting 

 through Space. — If a weight W is lifted 

 against gravity through the height H, the 

 product WR is called work, in foot-pounds. 

 It is equal to the force exerted through dis- 

 tance, or FS = WH = WS. If the body falls 

 through the space S, it acquires a velocity 

 \/2gS. If it is moved a distance S by a 

 constant force F, other than the force of 

 gravity, with an acceleration A, then the 

 acquired velocity V = \/2AS, from which 

 5^1^/2^^. Taking this equation together 

 with equation (10) F^\V/g'y(^A, we find 



(11a) 



l'H=lil\- 



Fs = iw/9X y- 



ni) 



Work is defined as the sustained exertion of 

 force through space, and its quantity, meas- 

 ured in foot-pounds, is the product of the 

 force by the space, F X S- If the force is 

 exerted to lift a weight W through the height 

 E, and the weight is stored at the top of the 

 lift, it is evident that it is capable of being 

 used to do work (illustrate). This capacity 

 of a body at rest for doing work is called 

 potential energy. If the body falls through 

 the height E, it acquires a velocity ■\/2gE, 

 and it is capable of doing work by reason of 

 that velocity, on any body which may offer 

 resistance to its motion. This capacity is 

 known as kinetic energy, or energy of motion, 

 and its quantity is expressed by the second 

 term of equation (11), viz., i{.W/g)V and is 

 stated in foot-pounds. Let us collect together 

 some of these equations for review: 



(5) Acceleration in terms of weight and force, 



A = Fg-^W, 



( 10) Force in terms of weight and acceleration, 



F='W/g X A, 



(11) Energy in terms of weight and velocity, 



F8 = iW/gy.\^. 



If we replace the expression W-^g by the 

 letter M, the equations take a simpler form : 

 (5a) A = F^iI, 



(10a) F — ilA, 



Mass. — It is convenient to call the quantity 

 M = W/g by a name, and the name " mass " 

 has been given to it, although this name is 

 perhaps unfortunate, since the word mass is 

 also used in other senses. Thus it is com- 

 monly used to mean an indefinite quantity of 

 matter, as a lump or portion. It is also used 

 by many text-book writers in the sense in 

 which we have used the word weight, for a 

 definite quantity of matter stated in pounds, 

 and these writers try to restrict the word 

 weight to mean only the force with which the 

 earth attracts matter. (Do not tell the stu- 

 dent that " the engineer's unit of mass is 32.2 

 pounds." The engineer has no such unit. 

 When he weighs a quantity of matter he 

 records the result as a weight, and his unit is 

 a pound.) 



Giving the word mass to the quantity W/g, 

 the above equations may be read thus: 



(5a) Acceleration equals force divided by mass, 

 (10a) Force equals mass X acceleration, 

 (11a) Force into spacer} the product of the mass 

 by the square of the velocity. 



Momentum. — ^From equation (Y) A = V/T; 

 substituting this value of A in equation (10a) 

 F = MA, we obtain F = MV/T, whence 



FT = MV. (12) 



This may be explained to mean that a force 

 F acting constantly on a mass M (= W/g) 

 which is free to move, will in the time, T, 

 give it a velocity V. The quantity FT is 

 sometimes called impulse, and the quantity 

 MV momentum, and the equation is said to 

 show the equality of impulse and momentum, 

 dn some books momentum is called quantity 

 of motion, but this is an error; it is merely the 

 product of mass and velocity.) 



The following equations should be mem- 

 orized, as they are constantly needed in 

 solving problems in mechanics: 



y = \/2gff, velocity of falling bodieB, 

 F^MA^=iIV/T, force equals mass X accelera- 

 tion, 

 FS = iMV', force into space equals energy, 

 FT^ilV, force into time equals momentum. 



By these four equations and their algebraic 



