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Circular motion  plane going around a loop 
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#1
Mar1810, 06:18 PM

P: 82

1. The problem statement, all variables and given/known data
A pilot flies an airplane in a vertical circular loop at a constant speed of v = 160 m/s. If the pilot's apparent weight at the top of the loop is onethird of his true weight on the ground, find the radius R of the plane's circular path. Answer: R= 1960m 2. Relevant equations F_net = ma a_normal = v^2 / R 3. The attempt at a solution Top of the loop  mg  N = mv^2 / R => N = mg  mv^2/R mg  mv^2/R = (1/3) * mg g  v^2/R = (1/3)g 25600 / R = (2/3)g => R = 3918.367347 m This is wrong. The answer should be 1960 m, which is exactly half of my answer strangely enough. I am not seeing what I did wrong here at all, can someone point out where I screwed up? Thank you 


#2
Mar1810, 06:38 PM

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What direction is the normal force of the plane on the pilot? (Realize that he's upside down.)



#3
Mar1810, 06:48 PM

P: 82

EDIT: I think I might understand now. I'm imagining the floor of the plane (which is "above") pressing downward on his feet. Is this why it is in the same direction as the weight? 


#4
Mar1810, 06:58 PM

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Circular motion  plane going around a loop
The plane pushes up on the pilot's butt, but since the plane is upside down, that's a downward force. The normal force will be whatever it needs to be to maintain the required acceleration. In this problem, you are told that the pilot's weight is insufficient to keep him moving in that vertical circle at the top of the loop (he's going too fast)so the seat has to exert additional force to help provide the centripetal acceleration.



#5
Mar1810, 07:12 PM

P: 82

And I know this is not part of the problem, but on the sides of the circle, what would the directions for normal force and weight be? 


#6
Mar1910, 05:16 AM

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