On September 8, 2001, approximately 1400 mountain daylight time, a Cessna 177RG, N52043, was substantially damaged when it collided with terrain and nosed over during landing roll at St. George, Utah. The flight instructor and the private pilot receveing instruction were not injured. Visual meteorological conditions prevailed, and no flight plan had been filed for the instructional flight being conducted under Title 14 CFR Part 91. The flight departed St. George at 1330. According to the flight instructor's accident report, the landing was normal until the private pilot applied brakes to decelerate. He told the instructor that he was having a problem, and the instructor took control of the airplane. When the instructor applied pressure to the toe brakes, only the right brake operated; the left brake pedal "went to the floor with no braking." He then began pumping the brakes in an attempt to restore brake system pressure. The airplane went off the side of the runway, but the instructor was able to return it to the runway. It went off the side of the runway again, slid on gravel, struck a rock, and nosed over. According to an FAA inspector, two sets of skid marks were noted, one set was located just past the point where the airplane touched down, and the other where the airplane departed the runway. A mechanic was asked to examine the airplane's brake system. The airplane was up righted and placed on its landing gear. The right brake assembly was bent and the brake line was damaged, precluding a definitive assessment. Brake fluid had leaked out, and the reservoir was empty.