(adsbygoogle = window.adsbygoogle || []).push({}); 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 one-third 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

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# Circular motion - plane going around a loop

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