174 WORK 



5. A bicycle and rider weigh 200 pounds, and, when riding along a level 

 road at 26 miles an hour, the rider suddenly applies a brake which presses 

 on the tire with a force equal to the weight of 60 pounds. If the coefficient of 

 friction between the brake and the tire is |, find how far the machine will go 

 before coming to rest. 



6. In the last question, how far will the machine go if, instead of the road 

 being level, it is down an incline of 1 in 20 ? 



7. A bullet fired with a velocity of 1000 feet per second penetrates a block 

 of wood to a depth of twelve inches. Prove that if it were fired through a board 

 of the same wood, two inches thick, its velocity on emergence would be about 

 913 feet per second. (Assume the resistance of the wood to the bullet to be 

 constant.) 



8. Two equal weights P and P are supported by a string passing over two 



small smooth pulleys A and B in the same horizontal line, and a weight 



o 

 W = P is attached to the middle point of the string between A and B. 



V3 



Prove that W will continue to descend until WAB forms an equilateral triangle, 

 and examine what will happen after this. 



9. A string of natural length I and modulus X is suspended between two 

 points A, B in the same horizontal line and at a distance h apart, and has a 

 weight W attached to its middle point. The weight W is held at rest midway 

 between the points J., 5, and is suddenly set free. Find how far it will fall 

 before being brought to rest by the strings. 



10. A heavy particle hangs by a string of natural length Z, which it stretches 

 to a length l\ the other end of the string being fixed. The particle is pulled 

 down to a length 2 1' below the point of support, and is then set free. How high 

 will it rise V 



11. Determine the horse hower which could be obtained from the kinetic 

 energy of a river at a place where the width is 100 feet, the mean depth 20 feet, 

 and the mean velocity 4 miles per hour. (A cubic foot of water weighs 62.6 

 pounds.) 



12. The river of the last question ends in a waterfall of which the bottom 

 is 60 feet below the river bed. Find the horse power which could be obtained 

 from the water. 



13. A locomotive burns l\ pounds of coal per horse-power-hour. How much 

 coal must be burned, beyond that consumed in overcoming gravity, friction, etc. , 

 in giving to a train of 300 tons a velocity of 65 miles an hour ? 



STABLE AND UNSTABLE EQUILIBRIUM 



147. Let us consider a system at rest in a position of equilibrium, 

 and capable of moving from this position by only one path, over 

 which it may, of course, move in either direction. As an illustra- 

 tion of a system of this kind we may take a locomotive standing 



