Physics of Vehichle
posted by Mike Joseph .
A 1400 kg car rounds a curve of 57 m banked at an angle of 14 degrees
If the car is traveling at 98 km/h, will a friction force be required? If so, in what direction?
May someone please walk me through this problem step by step? Thank you

Let the xaxis point toward the center of curvature and the yaxis point upward. Use Newton’s second law
ΣFy = N• cos θ = mg, N
ΣFx = N• sin θ = m•v²/R,
Dividing the 2nd equation by the 1st equation, we obtain
tan θ = v² /R•g
v=sqrt(R•g•tan θ)=sqrt(57•9.8•tan14)=11.8 m/s,
V = 98 km/h =98000/3600 =27.2 m/s
V>v => the friction force is required (directed to the center of the curvature)