A 3400 kg plane flying at a constant speed of 170 m/s is to do a vertical loop. What is the radius of the loop if the pilot feels three times his normal weight when he is at the top of the loop?
1. First draw a free-body diagram of the airplane at the top of the loop.
2. The only forces acting on the plane is gravity (mg) and the force on the wing. Neglect the thrust and friction in this case. Or if you include them they will cancel.
3. The acceleration of the plane is due only to circular motion, v^2/r, and acts in the nadir (earthward or down) direction.
4. Apply Newtons second law, F=ma. The left side is -mg-3g, the 3g comes from the requirement of the sensation of 3 times his normal weight.
5. Te right side of the equation is -m*v^2/r.
6. Solve the equation for r