ie. 
— ee 
°357? Assume the law 
WORK AND ENERGY 29 
7. A weight of 1 lb., hanging at rest on the hook of a spring-balance, has 
tched the spring one-tenth of an inch. How many foot-pounds of work must 
be done in stretching the spring 14 inches farther? 
8. A weight of 50 lbs. is lifted 30 inches. ‘The force which does this work 
acts through a s -balance, which at the beginning registers zero and at the 
end 50 lbs. ‘The stiffness of the spring is such that a weight of 20 lbs. gradually 
applied stretches the spring 1 inch. Determine the work done by the lifting 
9. Find the horse-power of a steam-pump which can raise 1100 gallons of 
water to a height of 90 feet in 5 minutes. 
10. What weight will an engine of 8 horse-power raise to a height of 90 feet 
in ? minute? 
11. Coal is raised from a mine 660 yards deep. The cage and its load weigh 
5 tons, and the rope weighs 24 lbs. per fathom. Find the horse-power of the 
winding-engine if the load is raised from the bottom to the surface in 55 seconds. 
12. How many gallons of water may be raised per hour from a depth of 
140 feet by an engine of 200 indicated horse-power, the efficiency of the engine 
and pump being 80 per cent. ? 
13. An electrically driven overhead crane raises a weight of 5 tons at the rate 
of 90 feet per minute. What is the horse-power? Convert this into watts. The 
motor drives the lifting machinery, whose efficiency is 70 per cent. How many 
ampéres of current must be supplied to the motor if the voltage is 220 and the 
efficiency of the motor is 87 per cent.? If the current is supplied by a company 
which c es at the rate of 24d. per Board of Trade unit for power purposes, 
what is the cost of lifting in pence per foot-ton ? tee 
14. Electric current is supplied to a certain motor plant at 220 volts, an 
150 ampéres are taken. What H.P. does this represent? How much would it 
cost if used for an average of 6-5 hours per day for a whole year of 313 days? 
The power is supplied at 2-24d. per H.P. hour (i.e. 3d. per B.T.U.). [B.E. 
15. A machine is concealed from sight, except that there are two verti 
ropes; when one of these is pulled downwards the other rises. If the falling of 
a weight A on one causes a weight B on the other to be steadily lifted, first 
when A is 12 lbs. and B 700 Ibs., second when A is 7°6 lbs. and B is 300 lbs., 
what is A likely to be when B is 520 lbs.? If B rises 1 inch when A falls 
70 inches, what is the efficiency of this lifting machine in each of the three 
cases ? [B.E.] 
16. In a lifting machine an effort of 26-6 lbs. just raised a load of 2260 lbs. ; 
what is the mechanical advantage? If the efficiency is 0°755, what is the 
velocity ratio? If on this same machine an effort of 11°8 lbs. raised a load 
of 580 Ibs., what is now the efficiency? What is probably the effort required 
to raise a load of 1000 lbs., and what would the efficiency be? Explain why, 
when the efficiency is somewhat less than ,0°5, a lifting machine does not 
' overhaul. [B.E.] 
17. The law of a machine is P=0-03W+1, and its velocity ratio is 210. 
What is the mechanical advantage, and what is the efficiency when W = 300 lbs. ? 
What is the maximum mechanical advantage, and what is the maximum 
efficiency? Denoting that part of the effort which is used in overcoming the 
friction of the machine by F, find F when W=300 lbs., and determine the 
relation between F and W for any value of W. Plot the effort, friction, and 
efficiency, on the resistance as a base, from W=0 to W=300 lbs. Scales.—Effort 
and friction, 1 inch to 2 lbs.; resistance, 1 inch to 50 lbs. ; efficiency, 1 inch to 
4 per cent. 
18. Referring to the machine of the preceding exercise, if Q is the effort to 
reverse the machine, or lower the load W, find the relation between Q and W. 
19. If B be the B.H.P. of a certain gas-engine and I the re 
I.H.P., and the results of two tests gave B=57 corresponding to I=73, an 
B=117 corresponding to I=139, what would the B.H.P. be if the I.H.P. were 
B=al+y,wherez and Ww 28 56 84 112 | 140 | 168 | 196 
[Inst.C.E-].} p | 73 | 123 | 16 | 21 | 255 | 30g | 343 
Weston differential pulley tackle having a velocity ratio of 16, and the results 
