According to the student pilot, he was attempting a second touch and go landing to runway 6 at a cross country airport. As he turned the airplane on to final approach, another airplane was crossing the runway threshold for a full stop landing. The student pilot continued the approach, but slowed the airplane due to "excess" airspeed during the first landing, and to give the other airplane time to clear the runway. After crossing the runway threshold, the student pilot reduced the power to idle and began a flare. The main landing gear touched down harder than he anticipated, and the airplane "must have bounced." When the nose landing gear touched down, it broke away from the airplane and the propeller struck the runway. According to a Federal Aviation Administration inspector, the airplane incurred substantial damage to the engine firewall. The student pilot did not report any preexisting mechanical anomalies with the airplane, and winds recorded at the airport 9 minutes earlier were from 120 degrees true at 4 knots.