Machinery's Handbook, 31st Edition
194 Work and Power a Note: The metric SI unit of work is the joule (one joule = 1 newton-meter), and the unit of power is the watt (one watt = 1 joule per second = 1 N·m/s). The term horsepower is not used. Thus, those formulas above that involve horsepower and the factor 550 are not applicable when working in SI units. The remaining formulas can be used, and the units are: S = distance in meters; V = constant or average velocity in meters per second; t = time in seconds; F = force in newtons; P = power in watts; K = work in joules. Example: A casting weighing 300 pounds is to be lifted by means of an overhead crane. The casting is lifted 10 feet in 12 seconds. What is the horsepower developed? Solution: Here F = 300 lbs, S = 10 ft, and t = 12 sec. . t F S 550 550 12 300 10 045 hp # # # = = A similar example using metric SI units is as follows: A casting of mass 150 kg is lifted 4 meters in 15 seconds by means of a crane. What is the power? Here F = 150 g N, S = 4 m, and t = 15 s. Thus: . . t FS g kW 15 150 4 15 150 9 81 4 392 0 392 Power watts or # # # = = = = Centrifugal Force = When a body rotates about an axis other than the one at its center of mass, the inertia of its rotating body exerts an apparent outward force, drawing it away from that center. This is called centrifugal force . F = centrifugal force in pounds W = weight of revolving body in pounds v = velocity at radius R on body in feet/second n = number of revolutions per minute g = acceleration due to gravity = 32.16 feet/second 2 R = perpendicular distance in feet from axis of rotation to center of mass, or for practical use, to center of gravity of revolving body Note: If a body rotates about its own center of mass, R equals zero and v equals zero. This means that the resultant of the centrifugal forces of all the elements of the body is equal to zero or, in other words, no centrifugal force is exerted on the axis of rotation. The centrifu gal force of any part or element of such a body is found by the equations given below, where R is the radius to the center of gravity of the part or element. In a flywheel rim, R is the mean radius of the rim because it is the radius to the center of gravity of a thin radial section.
g WR n WRn 60 60 4 2 2 # π =
F gR Wv = W v R Fg Wv =
. 3216 Wv 2 Rn 2933 2 Wn 2933 2
2
2
.
WRn
2
=
=
=
2933 0 000341
R
FRg = =
W FRg
F
v
=
2
WR F 2933 =
F
2
n
=
(If n is the number of revolutions per second instead of per minute, then F = 1227 WRn 2 .) If metric SI units are used in the foregoing formulas, W / g is replaced by M , which is the mass in kilograms; F = centrifugal force in newtons; v = velocity in meters per second; n = number of revolutions per minute; and R = the radius in meters. Thus:
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