EXAMPLES 251 



5. A uniform chain 6 feet long, having a mass of 2 pounds per foot, is 

 laid in a straight line along a rough horizontal table, for which the coeffi- 

 cient of friction is |, a portion hanging over the edge of the table so that 

 slipping is just about to occur. If a slight disturbance sets the chain slip- 

 ping, find the tension at the edge of the table when x feet have slipped off. 



6. Two equal balls A, B, each of mass m, are at a distance a apart. 

 An impulse / acts on A in the direction AB, and a constant force F acts 

 on B in the same direction. Show that A will not overtake B if 



7 2 < 2 aFm. 



7. A bullet weighing one ounce is fired with a velocity of 1200 feet per 

 second at an elevation of 1 degree so as to hit a bird weighing 2\ pounds 

 when the bullet is at the highest point of its path. Supposing the bird to 

 have been at rest when hit and afterwards to fall with the bullet embedded 

 in it, find how far from the point of firing the bird will fall. 



8. If a bullet weighing w pounds is fired with velocity v at a body 

 weighing W pounds, advancing with velocity F, prove that the body will 

 retain the velocity 



WV-wv Tr w , 



___, or ! -_(-), 



according as the bullet is embedded, or perforates and retains a velocity u. 

 Calculate the energy liberated, and thence infer the average resistance of 

 the body from the length perforated by the bullet. 



9. A pile is being driven in by repeated impacts of a falling weight. 

 How does the extent to which the pile is driven in by each blow depend 

 (a) on the magnitude of the weight, and (&) on the height to which it is 

 raised before being released ? 



If the weight be 1 ton, and the height from which it falls be 10 feet, 

 and the pile be driven in a tenth of an inch, find the resistance in tons. 



10. An inelastic pile, of mass m pounds, is driven vertically into the 

 ground a distance of a feet at each blow of a hammer of mass M pounds, 

 which falls vertically through h feet. Show that the weight which would 

 have to be placed on the top of the pile to clrive it slowly into the ground 

 would be 



i/r M ll A 



M H -- pounds. 

 (M + m)a* 



11. A hammer head of W pounds, moving with a velocity of v feet a 

 second, strikes an inelastic nail of w pounds fixed in a block of M pounds 

 which is free to move. Prove that if the mean resistance of the block to 

 penetration by the nail is a force of R pounds, then the nail will penetrate 

 each blow a distance, in feet, 



MW* v* 



(M + W + w)(W + w) 2gR 



