= 
P 
FRICTION AND LUBRICATION 281 
Find the magnitude of the force Q, (a) neglecting friction, (+) allowing for 
friction at the journals A, B, and © and also at the guide DE, neglecting the 
ag og of the moving parts. Take «=0°05. 
A horizontal pump, stroke 4 inches, is driven by means of an eccentric, 
11} inches diameter, keyed to a shaft 4 inches diameter. The shaft is driven by 
a vertical belt on a 14 inch diameter pulley. The belt embraces an arc of 180°, 
and the coefficient of friction between belt and pulley is 0°25. If the tension on 
the tight side of the belt is 350 lbs., find the maximum horizontal force that can 
be delivered to the pump when the radius of the eccentric is at 60° to the inner 
dead centre. Assume the eccentric rod to be very long. Coefficient of friction 
between eccentric sheave and strap and between shaft and bearing is 0°1. [U.L.] 
26. A pulley weighing 1000 lbs. is supported on a5 inch shaft midway between 
two bearings. The mass centre of the pulley is }? inch from the axis of the 
shaft. Neglecting the effect of the deflection of the axis of the shaft from the 
axis of revolution, calculate the horse-power required to overcome the friction of 
the bearings in consequence of the error of balance in the pulley when the shaft 
makes 200 revolutions per minute. Assume the coefficient of friction between 
the bearing surfaces to be 0°05. [U.L.] 
26. The journals of a shaft are 6 inches in diameter. The shaft carries a 
load of 8 tons, and makes 75 revolutions per minute, If the coefficient of friction 
between the journals and bearings is 0°05, at what rate, in B.Th.U. per minute, 
is heat being generated at the bearings ? 
27. The radius of gyration of a tly-wheel and crank shaft is 10 feet. The 
shaft journals are 12 inches in diameter. The turning effort on the shaft is with- 
drawn when the speed is 65 revolutions Nad minute. There being no resistance 
except the friction at the journals, find how many revolutions the wheel and 
shaft will make before coming to rest after the effort is withdrawn. Take 
u=0°065. 
28. A shaft 8 inches in diameter carries a vertical load of 6 tons and a 
horizontal load of 8 tons. Taking «=0-05, find the horse-power lost in friction 
at Soe journals when the shaft is driven by a pure torque at 100 revolutions per 
minute. 
29. A wheel under a torque of 2000 inch-lbs. is mounted on a shaft along 
which it has to slide. The rotary motion of the wheel is transmitted to the 
shaft through two accurately fitting sliding keys which are opposite to one 
another, as shown in Fig. 420, p. 275. The resultant force on each key is at a 
distance of 1} inches from the axis of the shaft. If the coefficient of friction is 
0°08, what force acting on the boss of the wheel, parallel to the axis of the shaft, 
will be necessary to slide the wheel along the shaft ? 
30. Referring to Fig. 421, p. 276, the rotating guides are horizontal, and are 
each 0°3 inch in diameter. The weight of the sliding piece is 0°5 lb. Taking 
the coefficient of friction as 0-05, find the tractive force T when the guides rotate 
at 600 revolutions per minute, and the sliding piece travels 5 inches in 20 seconds, 
and express it as a fraction of the tractive force when the guides are at rest. Find 
also the ratio of the work done when the guides are rotating at the above speed 
to the work done when the guides are at rest. Neglect the friction of the thrust 
bearings of the guides. 
$1. A solid cast-iron disc, 40 inches in diameter, and 8 inches thick, is 
rotating at a uniform speed of 240 revolutions per minute. If the air frictional 
resistance is assumed to be equal to KV? lbs. per square foot, where V is the 
linear velocity of any point, obtain an expression for the horse-power required to 
keep the disc in rotation. [B.E. 
32. A flat band laps half round a fixed pulley. From one end of the ban 
there hangs a weight W of 100 lbs., while the other is pulled by a force P. If 
#=0°3, what is the smallest value of P which will raise W, and what is the value 
of P which will lower W with a uniform velocity ? 
33. Find the answers to the preceding question if the band is round and lies 
in a V-groove on the pulley, the angle of the V being 45°. 
34. If a cord hanging in a vertical plane over a fixed horizontal cylinder with 
20 lbs. at one end and 10 lbs. at the other be on the point of slipping, what is the 
coefficient of friction between the cord and the cylinder ? 
35. How many times must a hemp rope 1} inches in diameter be 
round a post if a force of 5 lbs. at the slack end is just to hold it when it is 
