- #1
mvs1c
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Homework Statement
A runner is running on the banked turn of a track. The radius of the turn is 30 meters. The speed of the runner is 10 m/s. The coefficient of static friction between the runner's shoes and the track is .71. What is the maximum banking angle that will still allow the runner to run through the turn?
µf : .71
speed of runner : 10 m/s
radius of the turn: 30 m
Choices of answers:
33.7 degrees
23.8
54.1
46.8
Homework Equations
F = m(V^2/R)
Fs-max = µs*Fn
Fn= normal force
The Attempt at a Solution
I haven't had much luck. My professor has covered a few example problems that were similar, but they had negligible friction or a different angle set up.
I did try taking µs*Fn*sinθ = m(-v^2/R) and dividing it by Fncosθ = mg
resulting in tan θ = -V^2*µs/(g*R), which is equivalent to tan θ = -100^2*.71/(30*9.81)
but that resulted in an angle of 13.56 degrees, which isn't even on the answer choices.
I would appreciate any help you can give =)