Airplane pilot in a dive, net force, minimum speed, and normal force.

[timnswede]

Homework Statement

A 65 kg airplane pilot pulls out of a dive by following at constant speed, the arc of a circle whose radius is 300 m. At the bottom of the circle her speed is 180 km/h.
a.) Calculate net force on pilot at bottom or circle.
b.) Calculate force exerted on pilot by seat at top and bottom of circle.
c.)Calculate minimum speed required so pilot doesn't fall out at top of circle if she's not wearing a seatbelt.

Homework Equations

Newton's second law, a=v^2/r

The Attempt at a Solution

For part a) the only two forces I could think of are the normal and weight down. So net force would be zero since they cancel each other out?

For part b) at top: n+mg=(v^2/r)m, plugging in numbers I get -95.3 N.
For the bottom n-mg=(v^2/r)m, and I got 1179 N.

For part c.) n would = 0, so mg=(v^2/r)m, and plugging in numbers I get 54.22 m/s^2.

I'm not sure if I did part a) right, but I feel pretty confident about the other parts, did I go about doing those parts correctly?

 

[haruspex]

For part a) the only two forces I could think of are the normal and weight down. So net force would be zero since they cancel each other out?

If the net force is zero then there's no acceleration. Does an object moving in an arc at constant speed accelerate?

 

[timnswede]

Oh, I should've thought of that, it does have acceleration since the direction is constantly changing. Would it be the answer I got for part b) then, 1179 N minus mg, 637? So 1179-637=542 N?

 

[haruspex]

Oh, I should've thought of that, it does have acceleration since the direction is constantly changing. Would it be the answer I got for part b) then, 1179 N minus mg, 637? So 1179-637=542 N?

No, a and b are not the same.
For a, what is the relationship between net force and acceleration?
For b, you have some signs wrong. Draw the FBD at top of circle. What forces apply in what directions? What must the net force be to move in a circle?

 

[timnswede]

Well for part b I took the positive y-axis to be down at the top, I should've mentioned that, otherwise I'm not sure what would be wrong.
Net force and acceleration are towards the center of the circle in part a I think

 

[haruspex]

Well for part b I took the positive y-axis to be down at the top.

OK, but then be careful how you interpret the answer. For part b, top of circle you got a negative value. So is the seat pushing up on the pilot or down?
For part b, bottom of circle, even taking positive as down your answer is still wrong. Think that through again. E.g. which way is the centripetal force now?

Net force and acceleration are towards the center of the circle in part a I think

That's not what I asked. If the net force on a mass m is F and the resultant acceleration is a, what equation do you have? Apply that.