340 



SCIENCE 



[N. S. Vol. XLVI. No. 1L88 



appointed lecturer in anatomy at the Johns 

 Hopkins University. 



DISCUSSION AND CORRESPONDENCE 



WHEN IS A FORCE NOT A FORCE? 



In his communication to Science for March 

 16, 1917, Mr. A. H. Patterson very pertinently 

 calls attention to the vagueness, lack of pre- 

 cision and error in the treatment of the force 

 concept by current physics text-books. Much 

 of Mr. Patterson's criticism deals with New- 

 ton's third law of motion and appears to be 

 based on a misinterpretation of that law. To 

 this I wish to call attention. 



Force is always exerted by one portion of 

 matter, Aj upon a second portion of matter B. 

 These may be distinct bodies or parts of the 

 same body. If A exerts a force on B then, 

 the third law tells us, B exerts an equal force 

 in the opposite direction on A. If the force 

 of 4 on 5 is called the action, the force of 

 jB on 4 is called the reaction. The action and 

 reaction do not act on the same body or body- 

 part. Failure to fully appreciate this seems 

 to be responsible for the present as well as 

 many other misinterpretations of the third 

 law. 



Mr. Patterson asks: "What is a student to 

 think when he is told that to every action 

 there is always an equal and contrary action, 

 and is then informed that (only) an unbal- 

 anced force acting on a mass produces ac- 

 celeration ? " The two statements are mutu- 

 ally consistent and true. In order to safe- 

 guard the student against some of the pit- 

 falls which are dangerous even to his teachers 

 it is only necessary to make the information 

 more complete. 



Mr. Patterson's problems may weU serve this 

 purpose. The ball at the end of a rubber 

 band is the first of these. Let us ignore the 

 effect of gravity. When the ball is whirled 

 about in a circular path at uniform speed the 

 pull exerted by the rubber band on the hall 

 is called the centripetal force. 'No other 

 balanced force and gives rise to an acceler- 

 ation which manifests itself in the change 

 in direction of the velocity. The equal and 

 contrary action is the outward pull of the 



ball on the string, known as the centrifugal 

 force. The string is not accelerated because 

 the pull of the support at the fixed end is 

 equal and opposite to the centrifugal pull at 

 the free end. The forces on the string are 

 balanced. 



A porter pushes a truck at uniform speed 

 over level ground. Then the force which he 

 exerts forward on the truck is equal to the 

 backward frictional force. If this frictional 

 resistance were suddenly to vanish, the for- 

 ward force exerted on the truck by the porter 

 would be the only horizontal force, hence un- 

 balanced and a forward acceleration would re- 

 sult. Both with and without friction the 

 truck pushes backward on the porter with an 

 equal force. In addition to pushing forward 

 on the truck the porter is pushing backward 

 on the ground with his feet, and consequently 

 the ground is pushing him forward. If the 

 forward push of the ground and the backward 

 push of the truck are equal the forces on the 

 porter are balanced and he moves without 

 acceleration. Everywhere the forces act in 

 pairs, because there must be an exerter of the 

 force and a body on which it is exerted. 

 ISfewton's law has a meaning only when both 

 bodies are considered. 



N'ewton's third law requires no distinction 

 between inertia-reactions and other forces. 

 To introduce them serves to complicate rather 

 than to simplify. The following problem 

 utilizes Mr. Patterson's method, quoting 

 freely from the closing paragraphs of his 

 communication. 



A mass M rests on a perfectly smooth 

 horizontal surface. To M we apply a hori- 

 zontal force F. Being the only horizontal 

 force it is unbalanced. It is opposed by an 

 inertia reaction which can in a sense halance 

 it, hut can not hold it in equilihrium hecause 

 a force opposed only by inertia reaction always 

 produces acceleration. 



It is difficult to see the need of this devital- 

 ized form of the third law, either from the 

 point of view of principle or of practice. 

 Forces do always exist in pairs, yet the 

 forces on either or both of two bodies between 

 which force-action exists may be unbalanced. 



