34 SOME PHYSICAL FORCES EXEMPLIFIED IN MAN 



Elasticity is the property by virtue of which a body resists and recovers 

 from deformation produced by a force. If the elongation, s, is produced by a 

 weight of mass, m, in a sample with cross-sectional area, A, and length, /, 

 the modulus (Young's) for stretching is given by 



stress mg /s mgl 

 strain A/ I As 



which has dimensions of a pressure, m is high for materials difficult to 

 stretch. 



The smallest value of the stress which produces a permanent alteration is 

 called the elastic limit. Concussions, fractures, torn ligaments, and even 

 bruises are examples of tissues having been forced beyond their elastic limit, 

 usually during impact. 



Impact resistance, or hardness, can only be measured relatively. It usually 

 is done by dropping a hard steel sphere, or pointed instrument, on the ma- 

 terial, then reading either the diameter of the deformation caused by the 

 sphere, or the depth of penetration of the pointed instrument. Bone, teeth, 

 and nail have yielded useful values for impact resistance. 



Impulse is the product of pressure (stress) and time of application (con- 

 sideration of the second law will show that impulse is also equal to momen- 

 tum transferred per unit area). This is the physical description of the im- 

 pact. Impulse measurements during impact applied directly to the brains of 

 animals show that impulses composed of pressures of 30 to 90 psi acting for 

 1 millisecond (1 msec) or more cause physiological concussion (defined here 

 as an immediate posttraumatic unconsciousness). Further, the impulse 

 necessary to cause such damage increases rapidly with decreasing stress or 

 pressure. There is a minimum time of application, of course, below which 

 no damage is done. 



Analysis of stress-strain patterns in the human being has been going on 

 for many years, especially studies on bones in relation to how bones are 

 formed, grow, and are broken; and on lumbar intervertebral discs. Strain in 

 a bone is most accurately measured by an electric wire strain gauge; the 

 electrical resistance of the wire changes with stress. By transverse loading 

 of a femur, for instance, with stresses of ~1 ton/in. 2 , strains of the order 

 of only 0.0001 in. /in. are found. The bone is remarkably rigid. On the other 

 hand, the discs are relatively easily strained, as they must be if they are to 

 do their job during spinal maneuvers. Strains per disc are of the order of 

 0.02 in. 



On Hydro- (or Hemo-) Statics 



It was indicated on page 30 that the gravitational force of attraction of a 

 body to the earth is given by m g, where m is the mass in grams, and g is 

 the acceleration (cm/sec 2 ) or the force by which 1 gram mass is attracted to 



