Physics - Vertical Loops - Max Weight a pilot can withstand?

The maximum force a pilot can stand is about seven times his weight. What is the minimum radius of curvature that a jet plane's pilot, pulling out of a vertical dive can tolerate at a speed of 250 m/s?

Physics - Vertical Loops - Max Weight a pilot can withstand?
Think about the pilot in the cockpit at the bottom of a vertical loop.





Newton's Second Law for this situation is:





ΣForces = Normal Force-Weight = mass x accel





the Normal force is the force the pilot feels; and is the force of the seat pushing on him/her





the weight acts down





the acceleration produced by the combination of these forces is the centripetal accel, which acts toward the center of the circle of motion, or in this case, acts up (since at the bottom of a vertical loop, the center is up)





this gives us Newton's Law as:





ΣForces=N-mg=mv^/r


N=m(g+v^2/r)





remember, it is N that the pilot feels, so if N cannot exceed 7 times the pilot's weight, we have:





N=7mg=mg+mv^2/r or


v^2/r=6g or r=v^2/6g=1063m
Reply:F=mV²/r


F=7W


F=7mg


7mg=mV²/r


7(9.8)=(250)²/r


r=911.0787172 m
Reply:7g = v^2/r


7g = 250^2/r


r = 250^2/7g



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