Calculating Load on Pilot in Horizontal Curve Flight

[Miri]

Homework Statement

An airplane flies through a horizontal curve at a speed of 250km/h (69.44m/s). Radius=0.7km or 700m
Find the load of the pilot on the seat if her mass is 67kg.

Homework Equations

centripetal acceleration=v^2/r
and then the solution times the mass of the pilot, but this gives me the wrong result. The result should be 0.80kN

 

[Dick]

You've got the horizontal component of the force the captain exerts on the seat because of the rotation. There is also a vertical component of force due to the captains weight. I think you are supposed to add those two vectors and find the total magnitude of the force.

 

[Miri]

I don't get what you mean...Can you tell me the formulas which I have to use? What do you mean by the two components? The first one is the mass and the second one the radius or what? Thanks

 

[rl.bhat]

When the car takes a turn you are thrown in the outward direction due to centrifugal force. Its magnitude is mv^2/r. Similarly the pilot experiences the centrifugal force which is horizontal and away from the center of the curved path. The weight of the pilot mg acts in the downward direction. The resultant of these two forces will be total load of the pilot on the seat.

 

[Miri]

so you mean that mv^2/r + mg=0.80kN ? But that's wrong...i'm sorry, but I just don't get it...

 

[rl.bhat]

so you mean that mv^2/r + mg=0.80kN ? But that's wrong...i'm sorry, but I just don't get it...

mv^2/r and mg are perpendicular to each other. Therefore resultant force = sqrt[ (mv^2/r)^2 + (mg)^2]^1/2