Transportation engineers are designing a frictionless
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
Transportation engineers are designing a frictionless, banked highway curve of radius 85m so that vehicles traveling at the posted speed limit of 20ms−1 will remain in circular motion without relying on tire friction. Assume a representative vehicle traveling the curve has mass m.
(a) Draw a clearly labeled free-body diagram for the vehicle while it is on the banked section of the road.
(b) Starting from your diagram, apply Newton’s second law to obtain an expression that relates the banking angle θ to the given quantities v, r, and g.
(c) Calculate the numerical value of θ required for the design speed.
(d) During winter the same curve is measured to have an actual banking angle of only 12∘. Determine the minimum coefficient of static friction needed for a vehicle to negotiate the curve safely at the posted speed under these conditions.