236.] THE PRINCIPLE OF VIRTUAL WORK. 145 



In the gravitation system where the pound, or the kilo- 

 gramme, is taken as unit of force, the British unit of work is 

 the foot-pound, while in the metric system it is customary to 

 use the kilogramme-metre as unit. 



235. The numerical relations between these units are obtained 

 as follows. Let x be the number of ergs in the foot-poundal, 

 then (comp. Art. 66), 



gm. cm. 2 _ Ib. ft. 2 

 x - - I - > 

 sec. 2 sec. 2 



hence * = ^'(^) =453 ' 59>< 3O-4797 2 =4-2i39X io 5 ; 



i.e. i foot-poundal = 4. 2139 x i o 5 ergs, and I erg=2.3/2i x IO" 6 

 = 0.000002 372 i foot-poundal. 



Again, let x be the number of kilogramme-metres in I foot- 

 pound, then 



. m. = i ft. Ib., 



hence ^=-^-=0.45359x0.3048=0.13825, 

 kg. m. 



i.e. i foot-pound =0.13825 kilogramme-metres. 



Finally, i foot-pound =g foot-poundals (Art. 69) ; hence i foot- 

 pound = 1.3 56 x io 7 ergs, and i erg = 7. 3737 x io~ 8 foot-pounds, 

 if ^=32.2. 



236. Exercises. 



(1) A joule being defined as io 7 ergs, show that i foot-pound = 1.356 

 joules, and that i joule is about 3/4 foot-pound. 



(2) Show that a kilogramme-metre is nearly io 8 ergs. 



(3) What is the work done against gravity in raising 300 Ibs. through 

 a height of 25 ft. : (a) in foot-pounds, (b) in ergs? 



(4) Find the work done against friction in moving a car weighing 3 

 tons through a distance of fifty yards on a level road, the coefficient of 

 friction being 0.02. 



PART II 10 



