ON COLLISION. 61 



mentum as would have been obtained by the immediate action of an equal 

 force on the body to be moved. 



An elastic ball of 2 ounces weight, moving with a velocity of 3 feet in a 

 second, possesses an energy, as we have already seen, which may be ex- 

 pressed by 18. If it strike a ball of 1 ounce which is at rest, its velocity 

 will be reduced to 1 foot in a second, and the smaller ball will receive a 

 velocity of 4 feet : the energy of the first ball will then be expressed by 2, 

 and that of the second by 16, making together 18, as before. The mo- 

 mentum of the larger ball after collision is 2, that of the smaller 4, and the 

 sum of these is equal to the original momentum of the first ball. 



Supposing the magnitude of an elastic body which is at rest to be 

 infinite, it will receive twice the momentum of a small body that strikes 

 it ; but its velocity, and consequently its energy, will be inconsiderable, 

 since the energy is expressed by the product of the momentum into the 

 velocity. And if the larger body be of a finite magnitude, but still much 

 greater than the smaller, its energy will be very small ; that of the smaller, 

 which rebounds with a velocity not much less than its original velocity, 

 being but little diminished. It is for this reason that a man, having a 

 heavy anvil placed on his chest, can bear, without much inconvenience, the 

 blow of a large hammer striking on the anvil, while a much slighter blow 

 of the hammer, acting immediately on his body would have fractured his 

 ribs, and destroyed his life. The anvil receives a momentum nearly twice 

 as great as that of the hammer ; but its tendency to overcome the strength 

 of the bones and to crush the man, is only proportional to its energy, which 

 is nearly as much less than that of the hammer, as four times the weight of 

 the hammer is less than the weight of the anvil. Thus, if the weight of 

 the hammer were 5 pounds, and that of the anvil 100, the energy of the 

 anvil would be less than [only] one fifth as great as that of the hammer, 

 besides some further diminution, on account of the want of perfect elas- 

 ticity, and from the effect of the larger surface of the anvil in dividing the 

 pressure occasioned by the blow, so as to enable a greater portion of the 

 chest to cooperate in resisting it. 



When a body strikes another in a direction which does not pass through 

 its centre of gravity, the effect produced involves the consideration of 

 rotatory motion, since, in this case, the body is made to revolve on an axis. 

 But this can never happen when the body is spherical, and its surface 

 perfectly polished ; since every impulse must then be perpendicular to the 

 surface, and must consequently be directed to the centre of the body. If 

 the motion of a ball which strikes another is not directed to its centre, the 

 surface of contact must be oblique with respect to its motion, and the 

 second ball will only receive an impulse in a direction perpendicular to 

 this surface, while the first receives, from its reaction, an equal impulse in 

 a contrary direction, which is combined with its primitive mption. The 

 magnitude of this impulse may be determined by resolving the motion of 

 the first ball into two parts, the one parallel to the surface of contact, and 

 the other perpendicular ; the first part remaining always unaltered, the 

 second being modified by the collision. If, for example, the balls were 

 equal, this second part of the motion would be destroyed, and the remain- 



