Find the radius of the circle for this airplane

[isukatphysics69]

Homework Statement

Homework Equations

f=ma
v^2/r

The Attempt at a Solution

Σf_x = FNcos(θ) = (v^2/r)*m
Σf_y = FNsin(θ) - mg = 0
FN = mg/sin(θ)
(mg/sin(θ))*cos(θ) = (v^2/r)*m
gcos(θ)*r = v^2*sin(θ)
r = v^2sin(θ)/gcos(θ) v = 150m/s θ = 38
r = 1793m
i have already solved this one a while ago and am reviewing for test tommorow and getting a bullocks answer that is not correct what on Earth am i doing wrong here?

 

[FactChecker]

Try a sanity check of your final formula. For very tiny bank angle, you get r nearly 0 because of the sin(theta). You should get r very large. What does that tell you?

 

[isukatphysics69]

Try a sanity check of your final formula. For very tiny bank angle, you get r nearly 0 because of the sin(theta). You should get r very large. What does that tell you?

ok i just used cotangent and got the correct answer.. i am not seeing what i did wrong algabraicly let me look back thank you

 

[isukatphysics69]

 

[isukatphysics69]

i do not see what i did wrong algabraically

 

[Nathanael]

View attachment 224584

Theta from the OP is the angle the wings make with the horizontal. Have you drawn it consistently with that definition? When theta equals zero (that is, when the plane is horizontal) are you saying the normal force will be horizontal too? (That’s what your picture shows.)

 

[Dr Dr news]

The force that drives an airplane in a curved path is the component of lift directed toward the center of the path, L sin θ, where θ is the bank angle. So L sin θ = m v^2/r. If the airplane is flying in a horizontal path, that also means the vertical component of lift equals the weight, L cos θ = mg..And of course L = CL q S, where CL= lift coefficient, q=dynamic pressure, S=wing area.

 

[Dr Dr news]

If you solve the vertical equation for the lift and substitute it into the radial equation and solve for the radius, you will find the tangent function in the denominator not the numerator.

 

[Ignacio]

@isukatphysics69 Hi, can you explain where did you put the cotangent in your formula?

 

[Dr Dr news]

See #7 & #8.