During an instructional flight, the instructor (CFI) positioned the fuel selector from both to the left tank, then reduced the throttle to idle, simulating engine failure. The student performed the emergency procedures to simulate restarting the engine, to include positioning the fuel selector to both. The student maneuvered the aircraft to the selected landing area. At about 300 ft AGL, the CFI was assured that the student could have landed in the selected area, so he took control of the aircraft and raised the flaps to 20 degrees. During the climb out at about 400 ft, the engine quit running. The emergency checklist was followed, but the engine would not restart. During a forced landing in a field, the aircraft nosed over after touchdown. An exam of the engine revealed no evidence of a preimpact part failure or malfunction. When checked after the accident, the engine operated normally to about 1500 RPM, but was not operated to a higher RPM due to damage to the propeller. The fuel selector handle was rotated and found to be worn, making the detent difficult to locate.