Centripetal Force Airplace Problem

[Shackleford]

Homework Statement

A 2000 kg plane does a vertical loop with radius 600 m at a velocity of 120 m/s. At the very top of the loop, what is the force from the air required?

Plane's mass = 2000 kg
Radius = 600 m
Velocity = 120 m/s

Homework Equations

F = (mv^2)/R
Wt = mg
Net F-sub y = ma = 0

The Attempt at a Solution

-Wt -Fcentripetal + Fair = 0

-19600 N - 48000 N + Fair = 0

Fair = 67600 N

 

[Dick]

Seems right. Is that a question? Just to be complete in what direction does Fair push?

 

[Shackleford]

Seems right. Is that a question? Just to be complete in what direction does Fair push?

Fair would have to push in the positive direction, which in this case would be up.

 

[Dick]

Thanks for giving the wrong answer. It made me rethink my response and realize I was wrong as well. The total force on the plane to maintain it's centripetal acceleration is Fcentripetal. And it points inward towards the center of the loop. I.e. DOWN. Wt also points DOWN but is not enough. So Fair has to act DOWN to add to Wt to equal Fcentripetal. Can you correct your answer?

 

[Shackleford]

Thanks for giving the wrong answer. It made me rethink my response and realize I was wrong as well. The total force on the plane to maintain it's centripetal acceleration is Fcentripetal. And it points inward towards the center of the loop. I.e. DOWN. Wt also points DOWN but is not enough. So Fair has to act DOWN to add to Wt to equal Fcentripetal. Can you correct your answer?

Well, I got it wrong on the exam then. I thought Fgravity would contribute to the Fc but didn't use Newton's Law to reflect that. Dammit.

 

[Dick]

Fc isn't a real force. It's the value that the 'real' forces have to add up to to keep you in the circular trajectory.

 

[Shackleford]

Fc isn't a real force. It's the value that the 'real' forces have to add up to to keep you in the circular trajectory.

Yes, I know. I'm ticked off now. Ruined weekend.

 

[Dick]

That wasn't the whole exam, was it? If it makes you feel any better, remember I made the same mistake.

 

[Shackleford]

That wasn't the whole exam, was it? If it makes you feel any better, remember I made the same mistake.

No. There were four more questions. Well, I kept asking myself during the exam, shouldn't gravity contribute to the needed centripetal force? Ugh. It was a centripetal force, momentum, and conservation of energy exam. We even did this type of problem in class. Obviously, I didn't make sure I understood it completely. Making stupid mistakes like this in my first university level physics course initially makes we not want to keep going. So far, I've gotten an 85 and 90 on the first two exams.

 

[Dick]

Umm, you are too easily discouraged. You figured out what was wrong the instant I told you. I've had questions here that aren't that much more involved than yours. But I can tell them what they did wrong 5 times, and they still don't get it. The weird thing is that they are taking courses like 'string theory'.

 

[Shackleford]

Umm, you are too easily discouraged. You figured out what was wrong the instant I told you. I've had questions here that aren't that much more involved than yours. But I can tell them what they did wrong 5 times, and they still don't get it. The weird thing is that they are taking courses like 'string theory'.

Well, I'm discouraged because I knew how to do the problem correctly but didn't. I always get frustrated at myself. I made a few stupid mistakes on my first Cal 3 exam and ended up with an 87. Fortunately, I was more careful and got a 100 on the second Cal 3 exam.