Calculating Radius of a Circular Loop in Motion with Varied Weight

[JonathanSnow]

Homework Statement

someone is flying a plane and he is being chased and at the bottom of the loop his guages say he is traveling at 180km/h he is sitting on a bathroom scale which says he weighs 4 times what he normally does, what is the radius of the loop in meters?

Homework Equations

Fc=Fn ?
R=v^2/g

The Attempt at a Solution

well 180km/h is 50m/s and since he is 4 times as heavy the acceleration due to gravity will be 4 times greater? so i used the formula and it comes out as 63.71 m which seems unbelievable so i figured id ask, probably somthing stupid I am doing wrong

thanks

 

[mgb_phys]

To pull 4g at only 180km/h you would have to have a pretty tight loop so that might be correct.

See http://en.wikipedia.org/wiki/Centripetal_force for a derivation of the V^2/R formula.

 

[JonathanSnow]

thanks i think its right :)

 

[Dr. Jekyll]

well 180km/h is 50m/s and since he is 4 times as heavy the acceleration due to gravity will be 4 times greater?

Aren't the forces on the body at the bottom of the loop $\vec{F_{cf}}+\vec{W}=4\vec{W}$? Then we get different acceleration.