The instructor pilot (IP) and a student were practicing stop-and-go landings in a Cessna 152, N89585, at an uncontrolled airport. The IP reported that they were monitoring the UNICOM frequency and had announced their intentions before each stop-and-go. The IP observed another aircraft, Piper PA-28, N8836N, in the pattern. After making several touch-and-go landings, the pilot of the Piper PA-28 (a student pilot) departed the pattern for a short time. The IP in the Cessna 152 saw the Piper PA-28 reenter the traffic pattern and advised the Piper that his rotating beacon was not working. After again announcing their intentions, the Cessna aircrew stopped about 1200 to 1300 ft from the approach end of the runway. While the Cessna was being reconfigured for takeoff, it was struck from behind by the Piper. The student in the Piper reported he did not realize the Cessna would stop on the runway. He did not see it stopped on the runway until after touchdown. The Piper's right wing hit the Cessna's tail.