Honal Institution of (Brrat ^Britain. 



WEEKLY EVENING MEETING, 



Friday, January 26, 1912. 



The RiPrHT Hon. Loed Rayleigh, O.M. D.C.L. 

 LL.D. D.Sc. F.R.S., in the Chair. 



Professor Bertram Hopkinson, M.A. F.R.S. M.Inst.C.E. 

 The Pressure of a Blow. 



The scientific analysis of a blow requires first the determination of 

 the actual pressures or forces set up between the colliding bodies, and 

 second an investigation of the distribution of these pressures and of 

 their physical effects. The pressure produced by a blow does not 

 differ in kind from that produced by any other agency, such as an 

 hydraulic press, but it differs in degree because of its great intensity 

 and of its extremely short duration, and these characteristics, as we 

 shall see, have a marked influence on the effects which it produces. 



The first part of the problem, that is the calculation of the pres- 

 sure in tons or pounds, is based on the familiar principles of mechanics 

 which were first precisely stated in Newton's laws of motion. The cause 

 of the pressure is the rapid change of motion of the colliding bodies 

 which occurs when they come into contact, and, according to Newton's 

 second law, the force is simply proportional to the rate at Avhich this 

 change is effected. The rate of change may be measured in terms of 

 energy and distance, or in terms of momentum and time. Thus, a 

 hammer head, moving at a rate of 16 feet per second, and weighing 

 1 lb., possesses 4 foot-lbs. of energy, because its velocity could have 

 been acquired by falling freely through 4 feet. If it strikes a nail 

 and drives it one-eighth of an inch, the energy which was generated 

 by the weight of 1 lb. acting through 4 feet is destroyed in ^i^ part 

 of that distance, and the force necessary to effect this change of 

 motion is 400 times as great, say 400 lbs. The same effect would be 

 produced by a 4-lb. hammer striking with the velocity which would 

 be acquired by falHng tlirough 1 foot, namely 8 feet per second. 

 Regarding the same instance from the point of view of momentrma, 

 the 1-lb. hammer would take half a second to fall 4 feet, and the 

 quantity of motion or " momentum," reckoned as the product of the 

 force acting into the time required to generate it, would be one-half 

 of a pound-second unit. While driving the nail in, the hammer 

 covers a distance of ^ inch with a velocity which starts at IG feet per 

 second and drops to zero. To cover the distance of | inch with the 

 average velocity of 8 feet per second takes g^„ of a second, which is 

 Vol. XX. (No. 106) u 



