342 APPLIED MECHANICS 
of the ascent from the lowest position is equal to the speed at the beginning of 
the descent from the highest position? Also, what is the range of speed for this 
governor under these conditions ? , 
9. Referring to the preceding exercise, if the friction is 4 Ibs. at the sleeve, 
what must be the lift if the maximum descending speed is equal to the minimum 
ascending speed ? : 
10. In a Porter governor the arms and links are each 10 inches long, and 
the axes of the top and ‘bottom joints intersect the main axis. Each ball weighs 
5 lbs., and the central load is 50 lbs. R, the force of friction at the sleeve, is 5 lbs. 
The inclination of the arms to the vertical is 30° and 45° in the lowest and 
highest positions respectively. Calculate the following: (1) The travel of the 
sleeve,in inches. (2) The speeds at the bottom, middle, and top of the travel of 
the sleeve, neglecting friction. (3) The speeds at the bottom, middle, and top 
of the upward travel of the sleeve, allowing for friction. (4) The speeds at the 
top, middle, and bottom of the downward travel of the sleeve, allowing for 
friction. 
Speeds to be in revolutions per minute. Plot the results as in Fig. 527, p. 335. 
11. The arms and links of a Porter governor are all 9 inches long, and the 
axes of the top and bottom joints are at a distance of 1 inch from the main axis. 
The balls weigh 5 lbs. each, and the central load is 55 Ibs. The friction is 
equivalent to a force of 4 lbs. at the sleeve. The sleeve is in its lowest position 
when the arms are inclined at 30° to the vertical. Find the lift of the sleeve, in 
inches, when the speed at the beginning of the ascent from the lowest position is 
equal to the speed at the beginning of the descent from the highest position. 
12. Referring to the governor of the preceding exercise, if r is the radius of 
the circle described by the centres of the balls as they revolve, what are the 
extreme speeds in revolutions per minute corresponding to »=5 inches, and what 
is the range of speed between r=5 inches and r=6 inches? 
13. The balls of a Porter governor weigh 4 lbs. each, the load on the governor 
is 40 lbs., and the arms intersect on the axis. What height will this governor 
run at if it revolves at the rate of 240 revolutions per minute ? 
If the speed of the balls suddenly increases 2} per cent., what 
pull will be exerted on the gearing attached to the governor? 
If the friction of the regulating apparatus is equal to a dead 
load on the governor of 5 lbs., by how much will the speed 
increase before the balls rise ? [U.L.] 
14. A spring-controlled governor is as shown in the sketch 
(Fig. 531), the fixed fulcrum of the arm being at F, and the 
weight of each ball being 5 lbs. There is no tension in the 
spring when the balls are at a radius of 3 inches. Neglecting 
the controlling effect of the balls and arms, draw the curve 
of controlling force. Find the speed at which the governor Fia. 531. 
runs when the balls are at 5 inches radius, and find also the 
force on the sleeve if when the balls are in that position the speed is 10 per cent. 
higher. The spring extends 1 inch for 30 lbs. Show on your curve, roughly, the 
controlling effect exercised by the balls. [U.L.] 
15. A spring-loaded governor is placed horizontally, as shown in Fig. 532. 
Let W be the weight of each of the balls in lbs, ; 7 the radius of the path of the 
balls; Z the length of each of the four arms; 
w the angular velocity in radians per second. 
When the radius is zero, the tension in the spring 
is T lbs., and the force required to elongate the 
spring unit length is Q Ibs. Show that 
T+2Q(0- JP—7) 
ee oes be) Fig. 532. 
w 
If the rate of change of w with respect to r is to be 80 when w is 26 radians 
per second, r is 0°25 foot, and J is 1 foot, and the weight of each ball is 3 lbs., 
find the values of T and Q. [U.L.]J 
16. A Wilson-Hartnell spring loaded governor is shown in Fig. 533. The 
maximum and minimum distances of the centres of the balls from the axis of 
the governor are 7 and 3°5 inches respectively. 7, and 79, the lengths of the arms 
of the bell crank levers, are 4°5 and 3°5 inches respectively. Each ball weighs 
