216 MOTION UNDEK CONSTANT FORCES 



2. A balloon is moving upwards with a speed which is increasing at the 

 rate of 4 feet per second in each second. Find how much the weight of a 

 body of 10 pounds, as tested by a spring balance on it, would differ from 

 its weight under ordinary circumstances. 



<^3. An Atwood's machine is placed, with the string clamped, on one 

 scale of a weighing machine. Show that as soon as the string is undamped 

 the apparent weight of the machine is diminished by 



where m, mf are the suspended weights. 



4. A uniform chain of length / and weight W passes over a smooth 

 peg, hanging vertically on each side. If the chain be running freely, prove 

 that when the length on one side is x, the pressure on the peg is 





5. A jet of water falls vertically from a hose to the ground, starting with 

 a velocity which is negligible. Show that the center of gravity of the 

 water which is in the air at any instant is two thirds of the way up from 

 the ground to the hose. 



6. A heavy uniform chain of weight w is tied to a string which is pulled 

 up with tension T. Find the tension in the chain at any point. 



7. Prove that the shortest time from rest to rest, in which a chain, 

 which can bear a steady load of P tons, can lift or lower a weight of W 

 tons through a vertical distance of h feet is 



seconds. 



8. In a system of pulleys with one fixed and one movable block, in 

 which the cord is attached to the axis of the movable block, then passes 

 over the fixed one, then under the movable one, and then over the fixed 

 one, find the weight P which, when attached to the cord, will support a 

 given weight W hung from the movable block. (The blocks are so small 

 that all the straight portions of the cord may be considered parallel.) 



Show that, if the weights do not balance, the downward acceleration of 

 W-, when let go, will be w ^ P 



W + 9P 9 ' 



the weight of the cord being neglected, and that of the movable block 

 being included in W. 



9. A pulley carrying a total load W is hung in a loop of a cord which 

 passes over two fixed pulleys, and has weights P and Q freely suspended 

 from its ends, each segment of the cord being vertical; show that, when 



