Answer:
(a) 7 m
(b) 1 m
Explanation:
Given:
The magnitude of displacement vector 'a' is 3 m
The magnitude of displacement vector 'b' is 4 m.
The vector 'c' is the vector sum of vectors 'a' and 'b'.
(a)
Now, when the angle between the vectors is 0°, it means that the vectors are in the same direction. When vectors are in the same direction, then their resultant magnitude is simply the sum of their magnitudes.
So, magnitude of 'c' when 'a' and 'b' are in same direction is given as:
Therefore, the magnitude of vector 'c' is 7 m when angle between 'a' and 'b' is 0°.
(b)
When the angle between the vectors is 180°, it means that the vectors are exactly in the opposite direction. When the vectors are in opposite direction, then their resultant magnitude is the subtraction of their magnitudes.
So, magnitude of 'c' when 'a' and 'b' are in opposite direction is:
Therefore, the magnitude of vector 'c' is 1 m when angle between 'a' and 'b' is 180°.
INDUCTION MOTOR:-
Speed:-Less speed range than PMAC motors • Speed range is a function of the drive being used — to 1,000:1 with an encoder, 120:1 under field-oriented control
Reliability:-Waste heat is capable of degrading insulation essential to motor operation • Years of service common with proper operation
Power density:-Induction produced by squirrel cage rotor inherently limits power density
Accuracy:-Flux vector and field-oriented control allows for some of accuracy of servos
Cost:-Relatively modest initial cost; higher operating costs
PERMANENT MAGNET MORTOR:-
speed:-VFD-driven PMAC motors can be used in nearly all induction-motor and some servo applications • Typical servomotor application speed — to 10,000 rpm — is out of PMAC motor range
Reliability:-Lower operating temperatures reduces wear and tear, maintenance • Extends bearing and insulation life • Robust construction for years of trouble-free operation in harsh environments.
power density:-Rare-earth permanent magnets produce more flux (and resultant torque) for their physical size than induction types.
Accuracy:-Without feedback, can be difficult to locate and position to the pinpoint accuracy of servomotors
<span>Cost:-Exhibit higher efficiency, so their energy use is smaller and full return on their initial purchase cost is realized more quickly</span>
