# Homework Help: A plane

1. Oct 16, 2004

### 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

algebra or a bad cordinate system?

2. Oct 16, 2004

### Parth Dave

Which way does the centripetal force point?

3. Oct 16, 2004

### Alem2000

twords the $$-x$$ axis