I4 KINETICS OF A PARTICLE. [29. 



As the right-hand member of this equation is essentially 

 negative, it appears that while in impact the total momentum 

 remains unchanged, the total kinetic energy is in general dim- 

 inished; only in the limiting case of perfectly elastic bodies 

 (e=i) does the kinetic energy remain the same after as before 

 impact. The "lost" kinetic energy (16) mainly represents 

 the amount of energy spent in producing the permanent defor- 

 mation of the impinging bodies. 



29. Exercises, 



(1) A hammer weighing 1.5 Ibs. strikes a nail weighing ^ oz. with 

 a velocity of 20 ft. per second, and drives it J in. Find the mean 

 resistance of the wood, and determine the useful and wasteful work. 



(2) In Art. 20, Ex. (3), find the loss of kinetic energy due to the 

 impact. 



(3) A train of 120 tons runs, with a speed of 15 miles an hour, into a 

 train of 80 tons at rest. Neglecting elasticity, determine the destructive 

 work of the collision, and the velocity along the track after impact. 



(4) A pile weighing m' Ibs. is driven into the ground by a ram of m 

 Ibs., falling from a height of h ft. If the pile sinks s in. into the ground 

 after n falls of the ram, show that the resistance of the ground (assumed 



as uniform) is = l?-^[ * , , ) m'h pounds. 

 s \i + m'/mj 



(5) If, in Ex. (4), the elasticity of ram and pile be neglected, ram 

 and pile will have equal velocities after impact, and move together. 

 Hence, the factor m' should be replaced by m + m 1 , and the resistance is 



- U1L J m h pounds. 



s i + m'/m 



(6) TO blows of a ram of 500 Ibs., falling from a height of 5 ft., sink 

 a pile of 400 Ibs. 4 in'. If the permanent load of a pile be taken as 

 one-fifth of the resistance, what permanent load can the pile bear ? 



(7) A steam-hammer of 3 tons is used in forging. It has a fall of 

 5 ft. If the weight of the anvil be 20 tons, what is the useful and what 

 the wasteful work? 



30. Recoil. The explosion of the powder in a gun produces 

 an impulsive pressure both on the shot and on the body of the 



