Really intense AP physics question?

Question

A 50kg pilot comes out of a vertical dive in a circular arc such that at the bottom of the arc her upward acceleration is 8.5g.

What is the magnitude of the force exerted by the airplane seat on the pilot at the bottom of the arc?

If the speed of the plane is 345 km/h, what is the radius of the circular arc?

You don't have to do all the math, I just have no idea where to even begin!

If you could help me out, it would be greatly appreciated!

Thanks!

Answer 1

What is the magnitude of the force exerted by the airplane seat on the pilot at the bottom of the arc?

F=ma, a=8.5g

If the speed of the plane is 345 km/h, what is the radius of the circular arc?

v^2/r = a = 8.5 g - 1g (gravity)

*Note the plane may pull 8.5 g, but at the bottom, 1 of the gs is used to offset gravity. Therefore only 7.5 g are used for the determining the arc of the circle

:-)

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Madhukar Daftary (answerer below) is a bright guy. He does good work. But here he misses American venacular in that the term 'gs' is used to describe the forces on a military combat plane. Gs are multiples of the acceleration of gravity. They are comparable to mach numbers for sound.

Answer 2

How can unit of acceleration be g? I assume you mean 8 m/s^s.

At the bottom of the arc, two forces act on her.
1) Her wt., mg, downwards and
2) Reaction from the car seat, R, upwards.

The net force in the upward direction is the centripetal force.
Balanceing forces,
R - mg = ma
=> R = m(g + a) = 50(9.8 + 8.5) = 915 N.

Use mv^2 / r = 8 to find radius r of the circular arc.