Apkil 30j 1915] 



SCIENCE 



645 



gested that perhaps some readers might be in- 

 terested in a method of approach to the accu- 

 rate physical conceptions of force and mass 

 which I have been using recently with appar- 

 ent success, and which differs, I believe, from 

 that found in any text-book. I have come to 

 believe that except for the very unusual stu- 

 dent the disciplinary value of a dogmatic, 

 mathematical presentation of mechanics is 

 small, and that it is better to arouse and main- 

 tain interest by progressing from matters of 

 every-day experience by as easy steps as pos- 

 sible, following largely the development of 

 ideas which history has shown to be the nat- 

 ural one. 



For the sake of brevity, I shall have to give 

 the steps merely in outline. In fairness, then, 

 the reader should remember that the work is 

 supposed to extend over a period of several 

 weeks, giving ample opportunity for the illus- 

 tration of the various conclusions by numerous 

 examples and problems, only a few of which 

 can be suggested here. 



Physics is largely a study of forces, and of 

 the motions and strains due to forces. We will 

 begin, then, with a study of common forces. 



A. Force 



1. Introduction. — Common experience. Mus- 

 cular sensations. Common effects of muscular 

 exertion: 



(1) Gravitational force overcome — weight 



raised; 



(2) Elastic force overcome — spring compressed 



or stretched; 



(3) Frictional force overcome — sled dragged; 



(4) Speed changed — ^ball thrown or caught; 



(5) Direction of speed changed — stone whirled 



in circle. 

 To study these it is necessary to be able to 

 compare or measure forces. 



2. Measurement of Force. — It is simplest to 

 use the first effect, for preliminary work. It is 

 natural to assume, in agreement with common 

 experience, that the effort or force required to 

 lift a number of equal blocks of iron is pro- 

 portional to the number of blocks, or, more 

 generally, to the volume of iron lifted. For 



present purposes we will define the following 

 as our units of force : 



A kilogram weight (kg. wt.) is the force re- 

 quired to lift 128 c.c. of iron; 

 A pound weight (lb. wt.) is the force re- 

 quired to lift 3.55 cu. in. of iron. 

 We are now able to measure the forces required 

 to produce the various effects mentioned above. 



3. Elastic Forces — Spring Balance. — Stretch 

 proportional to force. Hooke's Law. Calibra- 

 tion of spring balances for use where actual 

 weights are inconvenient. Bending of a beam, 

 stretching of a wire, twisting of a rod. 



4. Forces in Equilihrium. — Two or more 

 forces acting on a ring. Force table. Parallel 

 forces acting on a beam. Non parallel forces 

 acting on a derrick, etc. Definition of vector, 

 vector sum, mom,ent of force, lever arm. 

 Experimental laws: 



(1) The vector sum of all forces acting must 

 be zero. 



(2) The algebraic sum of the moments of 

 force about any axis must be zero. 



Ghem,ical balance. — Use to compare weights. 

 Calibration of a set of brass and iron weights 

 for use as standard forces. 



5. Frictional Forces. — Friction is evidently 

 equivalent to a resisting force equal and oppo- 

 site to the force necessary to move the sled or 

 other body uniformly along a horizontal plane. 

 Study friction of wood on iron and wood on 

 wood. 



Experimental laws: 



(1) Frictional force depends only slightly 

 on the speed of relative motion. Kinetic and 

 static friction. 



(2) Frictional force is directly proportional 

 to the force pressing the two surfaces together. 

 F=^fxP. Define coefiicient of friction. 



(3) Frictional force is independent of the 

 area of contact. 



(4) Frictional force varies with the nature 

 of the surfaces involved. 



(5) A body started with a certain initial 

 speed s„, is brought to rest in a distance which 

 is inversely proportional to the coefficient of 

 friction. This suggests that on a perfectly 

 smooth horizontal surface (/^^O), a body 

 would keep moving with constant speed. 



