MOTION AND FORCE 23 
e 
“" plane, are such that AB=3 feet, BC=2 feet, and AC=2'6 feet. At 
_ @ certain instant it is known that the point A has a velocity of 4 feet per second 
in the direction from A to C, and that the point B is moving in the direction 
_ from Cto B. Show how the velocity of any other point on the body may be 
obtained, "parang / or otherwise, and determine the values for the velocities 
4 point midway between A and B. 
acting on a body weighing 250 lbs. for 10 seconds changes 
body from 8 to 24 feet per second. Find the magnitude 
2%. Two men, each exerting a constant force of 50 lbs., set a waggon weighin 
5 tons in motion. The frictional resistances amount to 10 lbs. per ton. F 
the distance through which the waggon is moved from rest in 1 minute. 
25. A locomotive draws a train of 100 tons with a uniform acceleration such 
that a speed of 60 miles per hour is attained in 4 minutes on the level. If the 
frictional resistances are 10 lbs. per ton and the resistance of the air, which 
varies as eet erage ene ae unas, Der, beer, Fad the pal 
exerted by otive at 30 and at 60 miles per hour. [Inst.C.E.} 
ce See Socata Uae Oppeenaom OF 9 Sse 
equal to one-fortieth of its gross weight, and be braked with a force equal to 
one-tenth of its gross weight, find the least time in which it may run from one 
to another of two stopping stations 5000 feet apart. What is the 
ra tee {Inst.C.E.] 
27. In an electric railway the average distance between stations is 4 mile, 
the ronning time from start to stop 1} minutes, and the constant between 
the end of acceleration and beginning of retardation 25 miles an hour. If the 
acceleration and retardation be taken as uniform and numerically equal, find 
their values; and, if the weight of the train be 150 tons and the frictional 
resistance 11 Ibs. per ton, find the tractive force necessary to start on the level. 
{Inst.C.E.} 
28. A projectile weighing 100 lbs. is fired from a gun weighing 5 tons with 
a velocity of 1000 feet per second. What is the velocity of free recoil of the 
- gun? 
E66 -A we of 10 Ibs. is s ded from a balloon by a cord. What is the 
tension in the cord when the is ascending with an acceleration of 3 feet 
per second per second? 
30. t of 5 lbs. hangs from the hook of a spring balance nded 
a er of a balloon. is the vertical acceleration of the 
the spring balance indicates 5°5 lbs. ? 
31. A cage weighing 1000 lbs. is being lowered down a mine by a cable. 
e cable (1) when the speed is increasing at the rate of 5 
2) when the speed is uniform, (3) when the speed is 
ig at the rate of 5 feet per second per second. The weight of the 
may be neglected. [Inst.C.E.] 
32. gp comply Jeo A W and w Ibs. respectively are connected by a fine 
pulley, as shown in Fig. 20. 
Show that the tension in the string is -”™ 1bs., and that the 
E 
F 
Wiw 
33. A locomotive weighing 60 tons rune on a horizontal track 
1000 feet radius at a speed of 15 miles per hour. What is 
horizontal thrust exerted on the outer rail? 
FS 
34. Referring to Fig. 20, W and w are weights of 1000 lbs. 
and 800 lbs, io ely. The pulley over which the rope pe | we | 
passes which co and w is 2 feet in diameter, measured 
to the centre of the rope, its weight is 80 Ibs., and its radiasof —-—*F1G. 2). 
gyration is 10 inches. Assuming that the rope is flexible, and 
neglecting friction, find the torque which must be applied to the pulley to raise 
4 
B 
¥ 
wer w with an acceleration of 5 feet per second per second. 
