Calculating Slip and Number of Poles in Induction Motor

[prat]

an 8 pole 3 phase alternator is coupled to a prime mover running at 750 rpm.it supplies an induction motor which has a full load of 960rpm find the number of poles of the motor and the slip

i think the induction motor would work as a generator we can find slip by usin

s=(ns-nm)/ns

where ns=stator synchronous speed and nm is rotor speed or frequency

i know that no of poles can be found by

f=nsP/120 where P is the no of poles
f here is the frequency

but how to sum these formulas and use them to get appropriate result

 

[collinsmark]

an 8 pole 3 phase alternator is coupled to a prime mover running at 750 rpm.it supplies an induction motor which has a full load of 960rpm find the number of poles of the motor and the slip

i think the induction motor would work as a generator we can find slip by usin

s=(ns-nm)/ns

where ns=stator synchronous speed and nm is rotor speed or frequency

I don't think you're interpreting the problem correctly. There are two machines involved, the alternator (a synchronous machine that has no slip), and the induction motor (that has slip).

The prime mover (mechanical) is attached to the alternator mechanically. The alternator is working as a (synchronous) generator. It produces electricity.

The induction motor is connected electrically (not mechanically) and acts a motor. We can come back to the induction motor later.

First, one must calculate the frequency of the induced voltage produced by the alternator.

i know that no of poles can be found by

f=nsP/120 where P is the no of poles
f here is the frequency

but how to sum these formulas and use them to get appropriate result

First we must calculate the frequency of the induced voltage produced by the alternator (before we even consider the induction motor). Use
$$f = \frac{NP}{120 [\mathrm{s/min}]}$$
where
$f$: frequency of induced voltage, in units of Hz.
$N$: rotational speed of alternator's rotor, in units of RPM.
$P$: number of poles in Alternator.

With that, you should be able to calculate the frequency of the induced voltage.

Your next step is to calculate the stator synchronous speed. There is a formula for that and it is a function of the frequency of induced voltage, and the number of poles in the induction motor. (You haven't listed the equation, but there is one.) Once you find the equation, pick a value for the number of poles that makes sense.

After that, you can calculate the slip.

Good luck!