A civil engineer designs a stretch of highway so that passenger cars can negotiate a…
PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion
Problem
A civil engineer designs a stretch of highway so that passenger cars can negotiate a horizontal curve of radius 150m without relying on tire–road friction when they move at the posted speed of 27m⋅s−1. Assume the curve is ideally banked and frictionless.
Answer the following qualitatively. Support each answer with clear physical reasoning that refers to the forces acting on the vehicle, but do not perform numerical calculations.
(a) Draw and label a free-body diagram for the car while it travels at the posted speed on the banked curve.
(b) Explain why no static friction force is required when the car travels exactly at the posted speed.
(c) The driver enters the curve at 20m⋅s−1, which is slower than the posted speed. Describe the direction of the static friction force that must act on the tires, and explain why that direction is necessary for circular motion.
(d) The driver instead enters at 35m⋅s−1, which is faster than the posted speed. Describe the direction of the static friction force in this case, and justify your answer using the components of the forces on the car.