Complete Question
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 250m/s?
Answer:
The value is [tex]r = \frac{250^2 }{6 * 9.8 }[/tex]
Explanation:
From the question we are told that
The weight of the pilot is [tex]W = mg[/tex]
The maximum force a pilot can withstand is [tex]F_{max} = 7 W = 7 (mg)[/tex]
The speed is [tex]v = 250 \ m/s[/tex]
Generally the centripetal force acting on the pilot is equal to the net force acting on the pilot i.e
[tex]F_c = F_{max} - mg[/tex]
Here N is the normal force acting on the pilot
Now
[tex]F_c = \frac{m v^2 }{r}[/tex]
So
[tex]\frac{m v^2 }{r} = 7(mg) - mg[/tex]
=> [tex]r = \frac{v^2 }{6g}[/tex]
=> [tex]r = \frac{250^2 }{6 * 9.8 }[/tex]
=> [tex]r = 1063 \ m[/tex]
