148 WORK 



8. If 200 horse power is required to drive a steamer 150 feet long at a speed 

 of 9 knots, prove that 25,600 horse power will be required to drive a similar 

 steamer, 600 feet long, similarly immersed, at 18 knots, assuming that the 

 resistance is proportional to the wetted surface and the square of the velocity 

 through the water. Prove also that the cost of coal per ton of cargo will be 

 the same in the two steamers. 



9. Fifty horse power is transmitted from one shaft to another by means of 

 a belt moving over two wheels on the shafts with a linear velocity of 250 feet 

 per minute. Find the difference of tensions on the two sides of the belt. 



10. A locomotive consumes 1 pounds of coal per horse-power-hour. How 

 much coal is required to haul a train of total weight 1000 tons over 50 miles of 

 level road on which the resistance to friction is 12 pounds weight per ton ? 



11. A liner of 22,000 horse power makes a run of 3300 miles in six days. 

 Find the resistance to the ship's motion. 



WORK DONE AGAINST A VARIABLE FORCE 



112. If a body is moved in opposition to a force which is not 

 of constant intensity but varies from point to point on the path 

 of the moving body, we can no longer use the formula JFs for the 

 amount of work performed. 



To calculate the amount of work done, we divide up the whole 

 range over which motion takes place into an infinite number of 

 infinitesimally small ranges, each of these ranges being so small 

 that the force opposing the motion may be regarded as of constant 

 magnitude during the motion through any one of them. 



If ds is any small range at a distance s from the starting point, 

 and if F is the intensity of the force opposing the motion while 

 the body moves through the small range ds, then the work done in 

 moving through this range is Fds. The total work done, the sum 

 of the amounts of work done in all the ranges, is, accordingly, 



I 



Fds. 

 WORK DONE IN STRETCHING AN ELASTIC STRING 



113. As an example of the use of this formula, let us find th< 

 work done in stretching an elastic string. Let the natural lengtl 

 of the string be /, and let X denote its modulus of elasticity. 



