Final answer:
To calculate the number of poles for the induction motor, the synchronous speed formula Ns = 120f/P is used. Assuming the no-load speed is close to the synchronous speed, the motor running at 715 r/min with a 60 Hz power supply has approximately 10 poles.
Step-by-step explanation:
Induction Motor Pole Calculation
A three-phase 60−Hz induction motor runs at 715r/min at no load and at 670 r/min at full load. To determine how many poles the motor has, we can use the formula for the synchronous speed of an AC motor, which depends on the frequency of the electric supply and the number of poles. The formula is: Ns = 120f/P, where Ns is the synchronous speed in revolutions per minute (rpm), f is the frequency of the power supply in hertz (Hz), and P is the number of poles.
Firstly, let's find the synchronous speed (Ns) using the supplied frequency, f = 60 Hz. The no-load speed is just below the synchronous speed. The closer to the synchronous speed, the fewer poles the motor has. As the motor speed at no load is 715 r/min, let's assume this value is close to the synchronous speed. Now, let's solve for P:
120 * 60/P = 715.
Therefore:
P = 120 * 60/715 ≈ 10 poles, which matches the information provided that this machine has 10 poles.