36 KINETICS OF A PARTICLE. [66. 



machine (such as animal force, the expansive force of steam, 

 the pressure of the wind, etc.) ; W Q the so-called lost or wasteful 

 work spent in overcoming friction and other passive resistances 

 of the machine ; and W^ the useful work done by the machine. 



While W and W l allow of precise determination, it is in 

 general difficult to determine W Q accurately ; but it is found 

 that the more exactly in any given machine W is determined, 

 the more nearly will the equation W= W Q + W l be fulfilled. 



As explained in Part II., Art. 255, the ratio W^l W of 

 the useful work to the total work is called the efficiency of the 

 machine. The term modulus is used sometimes for efficiency. 



66. Exercises. 



(1) In electrical engineering a watt\s defined as the power of doing 

 one joule, i.e. io 7 ergs, per second. Find the relation between the watt 

 and the horse-power. 



(2) In countries using the metric system of weights and measures 

 the horse-power is defined as 75 kilogramme-metres per second. Find 

 its relation to the watt and to the British horse-power. 



(3) Find the horse-power of the engine in Art. 62, Ex. (i), if it 

 make i stroke per second. 



(4) The cylinder of a steam engine has a diameter of 15 in. ; the 

 stroke is 3 ft. ; the number of strokes per minute is 77 ; the mean press- 

 ure of the steam is 40 Ibs. per square inch. What is the horse-power 

 of the engine ? 



(5) Find the horse-power required of the locomotive to haul a train 

 of 100 tons at the rate of 30 miles an hour, the resistances amounting 

 to 8 Ibs. per ton : (a) on a level road ; (b) up a i % grade ; (c) up a 

 2% grade. 



(6) How much water can an engine furnishing 50 H.P. raise per 

 minute from the bottom of a mine 1000 ft. deep? 



(7) The diameter of the cylinder of a steam engine is 30 in.; the 

 stroke 4 ft. ; the mean pressure 15 Ibs. per square inch ; the number of 

 revolutions 24 per minute. If the efficiency of the engine be f , what 

 is the amount of water raised per hour from a depth of 250 ft.? 



