Question

A car is on a banked curve

Angle is 13 degrees with r = 150.

Static fric = 0.35

What is the max speed and minimum speed it can make this curve?

Answer 1

To determine the maximum speed, the centripetal acceleration is going to overcome gravity and friction.

Gravitational acceleration = Ag = g·sinΘ = 9.8m/s² * sin13º = 2.2 m/s²
Frictional acceleration = Af = µg·cosΘ = 0.35 * 9.8m/s² * cos13º = 3.34 m/s²
Centripetal acceleration = Ac = v²/r = v² / 150 m
Ac = Ag + Af
v² / 150 m = (2.2 + 3.34) m/s²

=> v² = 831

=> v = 28.83 m/s

And for minimum speed, the concern is gravity overcoming friction and centripetal:

Af = Ag + Ac
3.34 m/s² = 2.2 m/s² + v²/150 m
v = sqrt( (3.3 - 2.2)m/s² * 150m) = 12.8 m/s