155-3 



ACCELERATION. 



(3) Show that for a connecting rod of infinite length the two loops 

 of the curve of Ex. i reduce to two equal circles. 



(4) The driving wheels of a locomotive are 6 ft. in diameter; find 

 the number of revolutions per minute and the angular velocity, when 

 running at 50 miles per hour. If the stroke be 2 ft., find the speed of 

 the piston. 



(5) The pitch of a screw is 24 ft., and the number of revolutions 70 

 per minute. Find the speed in knots. If the stroke is 4 ft., find the 

 speed of piston in feet per minute. 



(6) The stroke of a piston is 4 ft., and the connecting rod is 9 ft. 

 long. Find the position of the crank, when the piston has completed 

 the first quarter of the forward and backward strokes respectively. Also 

 find the position of the piston when the crank is upright. 



(7) The valve gear is so arranged in the last question as to cut off 

 the steam when the crank is 45 from the dead-points both in the for- 

 ward and backward strokes. Find the point at which steam will be cut 

 off in the two strokes. Also when the obliquity of the connecting rod 

 is neglected. 



3- ACCELERATION IN CURVILINEAR MOTION. 



155. Let the velocity of a moving point be represented by 

 the vector v = PTat the time /, 

 and by the vector v t = P'T 1 at 

 the time /+ A^ (Fig. 37). Then, 

 drawing from any point O OV 

 and OV respectively equal and 

 parallel to FT and P'T f , the 

 vector W represents the geo- 

 metrical difference between v r 

 and v ; in other words, VV 1 is 

 the velocity which, geometrically 

 added to v, produces v'. The 

 vector VV approaches the limit 

 o at the same time with A/ and 



Fig. 37. 



PP'. This limit of VV for an infinitely small time dt may be 

 called the geometrical differential or vector differential, of v. 



