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zakh508
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Homework Statement
A pilot of mass m flies a jet plane on a "loop-the-loop" course by flying in a vertical circle of radius R at a constant speed v. The force that the cockpit seat exerts on the pilot at the top of the loop is
(A) [itex]mg[/itex].
(B) [itex]mg\left(\frac{v^{2}}{R+1}\right)[/itex].
(C) [itex]\frac{mv^{2}}{R(g+1)}[/itex].
(D) [itex]m\left(\frac{v^{2}}{R-g}\right)[/itex].
(E) [itex]\frac{mv^{2}}{R}[/itex].
Homework Equations
[itex]a_{c}=\frac{v^{2}}{R}[/itex]
The Attempt at a Solution
I determined that because the centripetal acceleration is pressing the pilot into the seat while gravity is pulling him away from the seat that [itex]F_{N}=\frac{v^{2}}{R}-mg[/itex]. I simplified this to [itex]F_{N}=m\left(\frac{v^{2}-g}{R}\right)[/itex]. (Just realized this is wrong, should be [itex]F_{N}=m\left(\frac{v^{2}}{R}-g\right)[/itex]) The only answer in the book close to that is D but I have no idea how g ended up in the denominator. Could the textbook be wrong or am I missing something?
EDIT: The book's explanation is that the normal force plus force of gravity have to equal mass times centripetal acceleration, therefore [itex]F_{N}+mg=\frac{mv^{2}}{R}[/itex] which they simplified to D. So their explanation makes more sense now but I still think it's wrong.
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