Page 69 - Electric Machinery Fundamentals

INTRODUCTION TO MACHINERY PRINCIPLES 45

When the machine reaches steady state, Find = 0 and i = O. Therefore,
VB = eind = vssBl
VB
Vss = Bt
120V
(0.1 T)(10 m) ~ 120 mls
(b) Refer to Figure 1-27b. If a 30-N force to the right is applied to the bar, the final
steady state will occur when the induced force F ind is equal and opposite to the
applied force F app' so that the net force on the bar is zero:
Fapp = Find = itB
Therefore,
. Find 30 N
l~ - ~
IE (10 m)(O. l T)
( = 30 A flowing up through the bar
The induced voltage eind on the bar must be

~ 120 V + (30A)(0.3 11) ~ 129 V
and the final steady-state speed must be

129 V
(0.1 T)(1O m) ~ 129 mls
The bar is producing P = (129 V)(30 A) = 3870 W of power, and the battery is
consLlming P = (120 V)(30 A) = 3600 W. The difference between these two num-
bers is the 270 W of losses in the resistor. This machine is acting as a generator.
(c) Refer to Figure 1-2Sc. This time, the force is applied to the left, and the induced
force is to the right. At steady state,
Fapp = Find = fIB
• Find 30N
I ~ ill ~ (10 m)(O.l T)
= 30 A flowing down through the bar
The induced voltage e ind on the bar must be

~ 120 V - (30 A)(0.3 11) ~ 111 V
and the final speed must be
(
11IV
(0.1 T)(10 m) ~ 111 mls
This machine is now acting as a motor, converting electric energy from the bat-
tery into mechanical energy of motion on the bar.