I need help in these problems with the final result 1-The maximum force a pilot

Question

I need help in these problems with the final result 1-The maximum force a pilot can withstand is about 8.3 timeshis weight. What is the minimum radius of curvature that a jetplane's pilot, pulling out of a vertical dive, can tolerate at aspeed of 210 m/s?
radius? Unit? 2-A frictionless curve of radius 100 m, banked at an angle of36;, may be safely negotiated at a speed of
safe speed on frictionless inclined curve in m/s? 3-The gravitational attractive force between two masses is F.If the masses are moved to half of their initial distance, what isthe gravitational attractive force? which one is the answer? A) 2F
B) F/2
C) 4F
D) F/4  
I need help in these problems with the final result 1-The maximum force a pilot can withstand is about 8.3 timeshis weight. What is the minimum radius of curvature that a jetplane's pilot, pulling out of a vertical dive, can tolerate at aspeed of 210 m/s?
radius? Unit? 2-A frictionless curve of radius 100 m, banked at an angle of36;, may be safely negotiated at a speed of
safe speed on frictionless inclined curve in m/s? 3-The gravitational attractive force between two masses is F.If the masses are moved to half of their initial distance, what isthe gravitational attractive force? which one is the answer? A) 2F
B) F/2
C) 4F
D) F/4  
3-The gravitational attractive force between two masses is F.If the masses are moved to half of their initial distance, what isthe gravitational attractive force? which one is the answer? A) 2F
B) F/2
C) 4F
D) F/4  

Explanation / Answer

the minimum radius of curvature that a jet plane'spilot, pulling out of a vertical dive, can tolerate at a speed of210 m/s F=m*v2/r =8.3*mg ; v=220 m/s => r=542.17 m (2)the component of object gives the centripetalacceleration it is safe when mg*sin36=m*cos36*v2/r ; r=100m => v{max}=26.7 m/s   (3)we have: F between two masses : F=G*m*M/r2 r --> r/2 => F--> 4F => answerC r --> r/2 => F--> 4F => answerC

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