Answer:
1.47 km
Explanation:
When the pilot hangs freely in the seat and does not push against the seat belt, his centripetal acceleration would counter balance gravitational acceleration g = 9.81m/s2 = a
We can calculate the radius of the loop using velocity v = 120m/s and a
[tex]a = \frac{v^2}{r}[/tex]
[tex]r = \frac{v^2}{a} = \frac{120^2}{9.81} = 1467.89 m[/tex] or 1.46 km
The radius of the plane's loop is 1.47 km.
According to the question, the pilot does not push against the seat belt, which means the apparent weight of the pilot is zero. this can happen when the outward centrifugal force is equal to the weight of the pilot.
The centrifugal force on the pilot is given by:
[tex]F=\frac{mv^2}{R}[/tex]
where m is the mass of the pilot = 75kg
v is the velocity of the plane = 120 m/s
and R is the radius of the loop,
the weight of the pilot = mg
So,
[tex]\frac{mv^2}{R} = mg\\\\R=\frac{v^2}{g} \\\\R=\frac{120\times120}{9.8}\\\\R=1470 \;m[/tex]
therefore, the radius of the loop is 1.47 km.
Learn more about centrifugal force:
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