A curve of radius 45 m is banked for a design speed of 90 km/hr. If the coefficient of static friction is .3 what is the maximum speed that the car can go around the curve safely. What is the minimum speed?
The Attempt at a Solution
θ = tan^-1((25 m/s)^2/(45m * 9.8 m/s^2) = 54.8 degrees
Fn(sinθ) + Ff = (m)(v^2)/r
Fn(cosθ) = mg
mg(tanθ) + μ(Fn) = (m)(v^2)/r
mg(tanθ) + μ(mg/cosθ) = (m)(v^2)/r
g(tanθ) + μ(g/cosθ) = (v^2)/r
45m((9.8m/s^s(tan(54.8)) + .3(9.8m/s^s/cos(54.8)) = (v^2)
v = 29.23 m/s or 105.25 km/hr.
The key that I'm checking this with says that the above answer is not correct. I haven't tried to find the minimum speed yet because my maximum is incorrect. Could someone please let me know where I'm making a mistake or if I'm going about this the wrong way? Thanks.