162
WORK AND POWER
reverse its direction of rotation. For what length of time must this constant torque act to stop the flywheel and bring it up to a reverse speed of 5 radians per second? Applying Formula (c), To t = JM ( ωf – ωo ) 20t = 25 ( 10 – [ – 5 ] ) = 250 + 125 t = 375 ÷ 20 = 18.8 seconds A similar example using metric SI units is as follows: A flywheel with a moment of inertia of 20 kilogram-meters2 is revolving with an angular velocity of 10 radians per second when a constant torque of 30 newton-meters is applied to reverse its direction of rotation. For what length of time must this constant torque act to stop the flywheel and bring it up to a reverse speed of 5 radians per second? Applying Formula (c), the calculation is: T o t = J M ( ω f – ω o ), 30t = 20 ( 10 – [ – 5 ] ). 20 × 15 Thus, t = ------------------ = 10 seconds 30 Formulas for Work and Power.—The formulas in the accompanying table may be used to determine work and power in terms of the applied force and the velocity at the point of application of the force. Formulas for Work and Power To Find S
V
t
F
Known
Formula
To Find
Known
Formula
P, t, F
S=P×t÷F
K, F
S=K÷F
t, F, hp
S = 550 × t × hp ÷ F
P, F
V=P÷F
hp
P = 550 × hp
K, F, t
V = K ÷ (F × t)
F, S
K=F×S
F, hp
V = 550 × hp ÷ F
P, t
K=P×t
F, S, P
t=F×S÷P
F, V, t
K=F×V×t
K, F, V
t = K ÷ (F × V)
t, hp
K = 550 × t × hp
F, S, hp
t = F × S ÷ (550 × hp)
F, S, t
hp = F × S ÷ (550 × t)
P, V
F=P÷V
P
hp = P ÷ 550
K, S
F=K÷S
F, V
hp = F × V ÷ 550
K, V, t
F = K ÷ (V × t)
K, t
hp = K ÷ (550 × t)
V, hp
F = 550 × hp ÷ V
P
K
hp
F, V
P=F×V
F, S, t
P=F×S÷t
K, t
P=K÷t
Meanings of Symbols: S = distance in feet; V = constant or average velocity in feet per second; t = time in seconds; F = constant or average force in pounds; P = power in foot-pounds per second; K = work in foot-pounds; and hp = horsepower. 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