On May 21, 2003, about 1900 Pacific daylight time, a Bellanca 7GCBC, N68567, landed hard following a loss of engine power during takeoff from the Reno/Stead Airport, Reno, Nevada. The pilot was operating the airplane under the provisions of 14 CFR Part 91 on a local instructional flight. The certified flight instructor (CFI) pilot and the private pilot undergoing instruction (PUI) were not injured; the airplane sustained substantial damage. Visual meteorological conditions prevailed, and a flight plan had not been filed. In a written statement, the CFI reported that after adding 10 gallons of fuel to the airplane, the CFI and PUI taxied to the hold short line and completed an uneventful run-up for runway 26. The airplane rotated at 60 miles per hour (mph) indicated airspeed (IAS), and the CFI told the PUI to pitch for the best rate of climb speed (Vy). Approximately 500 feet above ground level (agl), as the PUI was turning crosswind, the engine "coughed." The CFI instructed the PUI to apply full throttle and mixture; the tachometer read 2,100 rpm. The engine "coughed" again and the rpm decreased to 1,500 rpm. Then, the engine completely lost power. The CFI made a radio call advising that they had an engine failure and were intending to return to the runway. Although he knew the difficulties associated with turning back to the runway after an engine failure, the CFI stated that other landing spots were unavailable due to buildings, vehicles, and/or other obstructions. The airplane was in a right turn at 500 feet agl. As the airplane approached runway 8, the airspeed was 61 mph IAS. The airplane touched down on the runway, still in the turn. The left main landing gear sheared off, and the CFI instructed the PUI to pull the mixture control to the "OFF" position. The airplane slid, and came to rest in the gravel on the south side of the runway. Post accident examination of the engine revealed that the mixture control arm could not reach the "FULL RICH" position. However, there were no marks on the carburetor. No other discrepancies were noted with the engine.