The student pilot of the special light sport airplane reported that he was practicing touch-and-go landings and had completed six, when the air traffic controller requested that he perform a short approach. The student pilot was aligned with the arrival runway numbers when he turned base leg. According to the student pilot, he forced the airplane down and made a hard landing. The airplane then bounced at least once and when it struck the ground the final time, the nose gear collapsed. A postaccident examination of the airplane by a Federal Aviation Administration inspector revealed substantial damage to the firewall and engine mounts. The student pilot reported no preimpact mechanical malfunctions or failures that would have precluded normal operations.