On August 11, 2007, at 1530 eastern daylight time, a Cessna 172M, N13586, sustained substantial damage during a forced landing to runway 22 (3,100 feet by 60 feet, asphalt) at the Marine City Airport (76G), Marine City, Michigan, when it over ran the runway and nosed over. The certified flight instructor (CFI) and student pilot were not injured. The 14 Code of Federal Regulations Part 91 instructional flight departed 76G at 1445 on a local instructional flight. Visual meteorological conditions prevailed at the time of the accident. No flight plan was filed. The CFI reported that he was providing flight instruction on takeoffs and landings to the student pilot, and that the student pilot was having difficulty holding runway centerline and using proper descent technique during normal approaches to landing. He reported that during the accident approach, the airplane was at a height of 20 feet over the displaced threshold with power at idle and the airspeed at 65 knots. He reported that he determined that a go-around was necessary when the airplane was about halfway down the runway. The CFI took control of the airplane, applied power, and pushed the carburetor heat in simultaneously. He reported that the engine sputtered so he executed a forced landing to the runway. The airplane departed the runway and nosed over in the soft terrain. The student pilot reported that on the last landing, "The power was pushed in and the plane did not respond as expected. So we had to land and roll off of the runway." She reported that the airplane struck some soft soil and subsequently nosed over. A witness reported that he observed the airplane make several approaches and landings. He reported that each approach crossed the threshold at an elevation higher and much faster than typical. He observed that the airplane was about 75 feet above the displaced threshold with the power pulled back to idle during the accident approach. He reported that the airplane was about 25 feet above ground level (agl) when it was about halfway down the runway, and then it settled to the runway. He saw a "puff of blue/white smoke" that he assumed came from the airplane's tires. The engine was removed from the airframe and an engine run was conducted under Federal Aviation Administration (FAA) oversight. The engine started and operated within its RPM ranges.