A C172 INSTRUCTOR SAFETY RETURNED TO LAND WHEN A PROP BLADE SEPARATED AND THE ENG FAILED DURING A STUDENT'S PRACTICE MISSED APCH.

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ON IFR TRAINING FLT ACFT SUFFERED AN INFLT ENG FAILURE DUE TO FAILURE OF THE PROP. THE ACFT HAD JUST FLOWN A VOR APCH TO ON AN IFR FLT PLAN IN VFR CONDITIONS. WE EXECUTED A MISSED APCH APPROX .5 NM BEFORE THE MISSED APCH POINT DUE TO TFC LNDG OPPOSITE DIRECTION ON RWY 5. PASSING THROUGH 1700 FT ON THE MISSED APCH CLBOUT TO 2000 FT A LOUD POP WAS HEARD AND THE ACFT BEGAN TO SHAKE VIOLENTLY. THE FLT INSTRUCTOR IMMEDIATELY TOOK THE CTLS AND SHUT DOWN THE ENG TO PREVENT FURTHER DAMAGE TO THE ACFT. THE INSTRUCTOR THEN MADE A L TURN AND PROCEEDED TO GLIDE BACK TO THE ARPT PLANNING A PWR OFF APCH AND LNDG. DURING THE DSCNT A MAYDAY CALL WAS ISSUED ON 121.5 WHERE THE INSTRUCTOR ANNOUNCED AN ENG FAILURE INFLT AND INTENTIONS TO LAND. UPON TOUCHDOWN; THE INSTRUCTOR CONTACTED GND CTL AND TOLD THEM THAT THE ONLY FURTHER ASSISTANCE NEEDED WAS A TOW OFF THE RWY. DURING THE EVENT; THE STUDENT; AN INST RATED COMMERCIAL PLT WORKING ON INST PROFICIENCY CHK; WAS IN SHOCK AND WHEN ASKED BY THE INSTRUCTOR TO TUNE THE RADIO TO THE TWR FREQ HE WAS UNABLE TO PERFORM THIS TASK. DURING THE PREFLT INSPECTION OF THE ACFT THE STUDENT AND INSTRUCTOR HAD BOTH VISUALLY INSPECTED THE CONDITION OF THE PROP INCLUDING RUNNING A HAND DOWN THE LEADING AND TRAILING EDGES OF THE BLADES AND NO ABNORMALITY WAS NOTICED. DURING THE POSTFLT WALKAROUND THE INSTRUCTOR AND STUDENT REALIZED THAT A 2 1/2 FT LONG SECTION OF THE PROP HAD SEPARATED SEVERAL INCHES FROM THE HUB. THE VIBRATIONS CAUSED BY THE LOSS OF HALF OF THE PROP CAUSED THE HUB TO CONTACT THE COWLING; WHICH WAS KNOCKED LOOSE. THE ALTERNATOR THAT IS MOUNTED TO THE FRONT OF THE ENG WAS ALSO TORN FROM ITS MOUNTS AND WAS RESTING ON THE BOTTOM OF THE COWLING. THE EXHAUST THAT NORMALLY EXTENDS 4 INCHES BELOW THE COWLING WAS EXPOSED UP TO THE MANIFOLD. VISIBLE THROUGH THE GAP BTWN THE COWLING AND THE FUSELAGE; THE TOP R HAND MOTOR MOUNT WAS ALSO DAMAGED.