PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Commercial
Flight Crew Last 90 Days 50; Flight Crew Total 310; Flight Crew Type 140
Time Pressure; Troubleshooting
Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Loss Of Aircraft Control
Flight Crew Overcame Equipment Problem; Flight Crew Returned To Departure Airport; Flight Crew Landed As Precaution; General Maintenance Action; General Flight Cancelled / Delayed
Aircraft
While conducting 'pattern work' at ZZZ; during a touch and go landing; the aircraft began an initial climb. The out of currency private pilot stated 'Did you mess with the trim.' I; the instructor; replied 'No. What's wrong?' The pilot stated 'I can't get the nose to come down; the yoke is stuck.' I took control of the airplane; applied forward force on the yoke and it was stuck. With no usable runway remaining; I decided to leave power in and continue the takeoff. The aircraft was climbing at 65mph; above Vs1 and below Vx. I used elevator trim to attempt to get the nose down and stabilize the climb at a safe airspeed. The aircraft pitch decreased; airspeed increased. Shortly after; the controls suddenly popped; the aircraft pitched down due to the excess nose down trim; and control was returned to the yoke. I adjusted the trim and continued the climbout at Vy; we landed immediately and terminated the flight without further event. Upon inspection of the aircraft; all control cables appeared to be free and unmolested. Upon a post flight walk around; it was observed that a tail section screw had backed out and lodged itself between the stabilator; causing the control surfaces to be restricted. A preflight inspection of the aircraft was conducted by myself and the student; however neither of us noticed this issue.
PA-28-140 Flight Instructor reported an uneventful precautionary landing  after experiencing a temporary loss of normal pitch control.