The pilot reported that he performed a go-around on the first landing attempt. On the second landing attempt the airplane ballooned during the flare and subsequently impacted the runway with the propeller and the nose landing gear; the nose gear collapsed and separated from the airplane. A postaccident damage assessment revealed that the airplane's engine mount had sustained substantial damage as a result of the hard landing. The pilot reported no mechanical malfunctions or failures with the airplane that would have precluded normal operation.