62.] RECTILINEAR MOTION. 33 



It should be noticed that these equations hold only as long as the 

 string is actually stretched, i.e. as long as s > / ; the motion that ensues 

 when s becomes less than / is, however, easily determined from the 

 velocity for s = I. 



62. Exercises. 



(1) In a steam engine, let/= 15 Ibs. per square inch be the mean 

 piston pressure during one stroke, s = 4 ft. the length of the stroke, and 

 .d= 1.5 ft. the diameter of the cylinder, (a) What is the work per 

 stroke? (b) To what height could a mass of 500 Ibs. be raised by this 

 work? 



(2) A train of 80 tons starting from rest acquires a velocity of 30 

 miles an hour on a level road at the end of the first mile. Determine 

 the average tractive force of the engine : (a) if the frictional resistances 

 te neglected ; (b) if these resistances be estimated at 8 Ibs. per ton. 

 (c) What tractive force is required to haul the same train over a level 

 road at a constant speed? 



(3) A train of 60 tons runs one mile with constant speed ; if the 

 resistances be 8 Ibs. per ton, find the work done by the engine : (a) on 

 a level track ; (b) on an average grade of i % . (t) On a i % grade, 

 what is the ratio of the work done against gravity to that done against 

 the resistances ? 



(4) Determine the work expended in raising from the ground the 

 materials for a brick wall 30 ft. high, 40 ft. long, and 2 ft. thick, the 

 weight of a cubic foot of brickwork being 112 Ibs. 



(5) Knowing that on the surface of the earth the attraction per unit 

 of mass is g= 32, find what it would be on the sun if the density of the 

 sun be \ of that of the earth, and its diameter 108 times that of the 

 earth. 



(6) Show that the velocity acquired by a body in- falling to the sur- 

 face of the earth from an infinite distance, under the action of the 

 earth's attraction alone, would be v = ^/2gR, or about 7 miles per 

 second (with R = 4000 miles). 



( 7) A homogeneous straight rod, AB = /, of constant density p, 

 attracts a particle P of mass i according to the law of the inverse 

 square of the distance. The initial position P of P is on AB produced 

 beyond B, at the distance BP^ = S Q , and the initial velocity is zero. 



PART III 3 



