a plane

[Alem2000]

My question is as follows..."An airplane flies in a loop(a circular path in a

vertical plane) of radius 150m. The pilot's head always points

toward the center of the loop. The speed of the airplane is not constant, the

aiplane goes slowest at the top of the loop and fastest at the bottom. a) At

the top of the loop, the pilot feels weightless. What is the speed of the

airplane at this point?"

Since the speed is not constant I would use the formula\sum{\vec{F}}

=m\vec{a}. I then drew a free body diagram, and there were no

horizontal forces and the only vertical force was the weight. So I did this

\sum{F_x}=ma_x=0 and for the y component \sum{F_y}

=ma_y since I chose from 0 and up to be posative on my y

axis i made weight =negative -mg=m\frac{v^2}{R} then I

multiplied both sides by \frac{R}{m} the \frac{-mgR}{m}

=v^2 and then m cancels out and -v=\sqrt{gR}

I think I choose a bad axis system...my answer is the correct

magnitude but...theres that negative sign lurking about... :bugeye: Is it bad

algebra or a bad cordinate system?

[Parth Dave]

Which way does the centripetal force point?

[Alem2000]

twords the -x axis