MECHANICAL FORCES 29 



factor of heat energy. The accompanying capacitive factor in effect sums up 

 the energies which can go into all the vibrations, rotations, and translations 

 of each molecule. This capacitive factor is called entropy, S. Heat energy is 

 therefore given as the product TS, and 5* must have the units calories per 

 degree, since the product must be simply calories. 



Heat energy was chosen over electrical, mechanical, or other forms for no 

 other reason than that it is so common. All forms of energy can be factored 

 into two parts, a potential part and a capacitative part: thus in addition to 

 heat energy, we have force times distance for mechanical energy; voltage 

 times charge for electrical energy; pressure times volume for the mechanical 

 energy contained by a compressed gas; chemical potential times number of 

 moles for chemical energy. Energy and its factors will be considered more 

 fully in Chapter 7. 



Kinetic energy of mass in motion is given by force x distance, which has 

 the dimensions (g cm/sec 2 ) cm, or g cm 2 /sec 2 . Kinetic energy of motion is 

 also given by the familiar 1/2 mv 2 , with the same dimensions. Another 

 familiar property of mass in motion is the momentum, M, defined as mv. 

 Hence KE = 1/2 Mv. 



Some of these quantities can be illustrated by the example of a 200-lb** 

 football player running at full speed with the ball. His potential energy in 

 the form of food has been reprocessed into glycogen, etc., and stored as po- 

 tential energy. That part ready for rapid conversion is available in the form 

 of the mobile chemical adenosine triphosphate (ATP), whose role as a mo- 

 bile power supply is wondrously general throughout the living system. Dur- 

 ing the motion this chemical energy is being transformed, at least in part, to 

 the mechanical kinetic energy of motion. His KE amounts (speed 100 yds in 

 12 sec; 1 lb = 454 g) to about 26,000,000,000 (or 26 x 10") ergs, or 2600 

 jou, about 550 small calories. If he is stopped completely within 1 sec by 

 collision, he will have transferred energy at an average rate during that 

 second of 2600 jou per sec, 2600 w, or just over 3 hp. If that energy all went 

 into heat, it could vaporize about 1 g of water. On the other hand this 

 energy could have been transformed into electricity, and the power delivered 

 could have lighted twenty-four 100-w light bulbs to full brilliance for a sec- 

 ond! A further insight into the power expended in such collisions can be 

 gained if it is remembered that the bulk of the energy is transferred in 

 about 1/10 sec of contact, during which time the power is about 30 hp! It is 

 obvious that, in spite of the delights attached to such athletic pursuits, from 

 the point of view of pure physics alone, they are sheer waste of energy and 

 power which could be used more efficiently to do other tasks. In fact even 



** Weight, a force. Since F = ma: 1 lb force = 1 lb mass x 32 ft/ sec 2 , and 980 dynes 

 force = 1 g force = 1 g mass x 980 cm/ sec 2 . (1 lb force is the force of attraction between 

 the earth and 454 g mass.) 



