A highway curve has a radius of 123 m. At what angle should the road be banked so that a car traveling at 26.5 m/s has no tendency to skid sideways on the road? [Hint: No tendency to skid means the frictional force is zero.]

Question

I can't get this one right either please someone explain this and help me out. Thank you.

Answer 1

Let the x-axis point toward the center of curvature and the y-axis point upward. Use Newton’s
second law.
ΣFy = N• cos θ − − f •sin θ = 0
ΣFx = N• sin θ + f •cos θ = m•v²/R,
Solving the 1st equation for N, we obtain
N =( f •sin θ + m•g)/cos θ,
Substitute N to the 2nd equation and obtain friction force
f =m[(v²•cosθ/R) - g•sinθ].
f=0 =>
(v²•cosθ/R) - g•sinθ = 0,
v²•cosθ/R = g•sinθ,
v²•/R•g = sinθ/cosθ = tanθ.
θ =arctan(v²•/R•g) =
= arctan(26.5²•/123•9.8) =
=arctan(0.158) = 8.98 º

Answer 2

Thanks Elena, but I tried the answer and its wrong I don't know why. Could you please help me. Thanks.

Answer 3

Adam?...Elena thanks for the answer, but it says its wrong.

Answer 4

The first line is
ΣFy = N• cos θ − mg − f •sin θ = 0

The general solution is correct.
May be your answer is 9º

Answer 5

Ohh!
I calculated
arctan(0.58) =30,2º

Answer 6

Thank you Elena! :)