238 MOTION OF SYSTEMS OF PARTICLES 



5. The string of an Atwood's machine has masses mi, m 2 attached to its 

 ends, m-i being the heavier. After it has been in motion for 1 second mi strikes 

 the floor. Find (a) for how long w 2 will continue to ascend, (6) with what 

 velocity mi will start into motion again when the string becomes tight. 

 v 6. On a certain day one inch of rain fell in 10 hours, the drops falling with 

 a velocity of 20 feet per second. Find the average pressure per square foot on 

 the canvas roof of a tent, supposed horizontal, produced by the impact of the 

 raindrops. (One cubic foot of water weighs 62 1 pounds.) 



7. The earth, moving in its orbit with velocity "P", runs into a swarm of small 

 meteorites, of density one kilogramme to the cubic mile, moving with a velocity 

 v in a direction exactly opposite to that of the earth. Find the rate of decrease 

 of the earth's speed in consequence of its bombardment by the meteorites, 

 and find also the increase in the height of the barometer at different points on 

 the earth's surface, it being assumed that all the meteorites are dissipated into 

 dust before they reach the ground. (The earth's mass is 6 x 10 27 grammes, its 

 diameter is 7927 miles.) 



w 8. A uniform chain is coiled in a heap on a horizontal plane, and a man 

 takes hold of one end and raises it uniformly with a velocity v. Show that 

 when his hand is at a height x from the plane, the pressure on his hand is equal 



v 2 

 to the weight of a length x -\ of the chain. 



ELASTICITY 



193. It is a matter of common experience that if we drop a 

 ball of steel on to a hard floor it rebounds to a considerable height, 

 while a ball of wood will rebound to a much smaller height, and a 

 ball of wool, paper, or putty will hardly rebound at all. 



When the contact between the surfaces of two bodies is of such 

 a nature that they do not rebound at all after impact, it is said to 

 be perfectly inelastic, while if the bodies rebound, the contact is 

 said to be elastic. Obviously there are varying degrees of elasticity. 



Moment of Greatest Compression 



194. Probably the collision of two billiard balls supplies the 

 most familiar instance of an impact with a high degree of elasticity. 

 We shall discuss this impact best by referring the motion of the 

 second ball to a frame of reference moving with the first. Before 

 impact the center of the second ball is approaching that of the first, 



