4 o INTRODUCTION TO DYNAMICS. [70. 



I kilogramme (force) = 1000^- dynes, 

 I pound (force) =g poundals, 



where g is about 981 in metric units, and about 32.2 in British 

 units. In most cases the more convenient values 980 and 32 

 may be used. 



70. Exercises. 



(1) What is the exact meaning of "a force of 10 tons"? Express 

 this force in poundals and in dynes. 



(2) Reduce 2000000 dynes to British gravitation measure. 



(3) Express a pressure of 2 Ibs. per square inch in kilogrammes per 

 square centimetre. 



(4) Prove that a poundal is very nearly half an ounce, and a dyne a 

 little over a milligramme, in gravitation measure. 



(5) The numerical value of a force being TOO in (absolute) F.P.S. 

 units, find its value for the yard as unit of length, the ton as unit of 

 mass, and the minute as unit of time (see Art. 66). 



71. The quantity Jmv 2 , i.e. half the product of the mass of a 

 particle into the square of its velocity, is called the kinetic energy 

 of the particle. 



Let us consider again a particle of constant mass m moving 

 with a constant acceleration, and hence with a constant force ; 

 let v be the velocity, s the space described at the time /; v', s' 

 the corresponding values at the time t 1 . Then the last of the 

 three fundamental equations (see Arts. 55 and 60) gives 



F(s f -s)', (8) 



hence " F= \mv*-\m* ^ > fe) 



If F be variable, we have in the limit 



n^i = mv <iv. 

 ds ds 



